{"t":"q","id":29452,"q":"9 060 450 = 9 000 000 + ________ 450","e":"9 060 450 = 9 000 000 + 60 000 + 450. The missing value in the blank before 450 is 60 000."}
{"t":"q","id":29453,"q":"Find the value of 16 + 40 \u00f7 4 \u00d7 2.","e":"Do division and multiplication first, left to right: 40 \u00f7 4 = 10, then 10 \u00d7 2 = 20. Then 16 + 20 = 36."}
{"t":"q","id":29455,"q":"10 scouts were each given 10 funfair tickets to sell. 4 of the scouts sold 7 tickets each. The rest of the scouts sold all their tickets. Which one of the following represents the correct way to find how many tickets were left?","e":"Total tickets = 10 \u00d7 10 = 100. The 4 scouts sold 4 \u00d7 7 = 28 tickets; the other 6 scouts sold all 6 \u00d7 10 = 60 tickets. Tickets left = 100 \u2212 (4 \u00d7 7) \u2212 (6 \u00d7 10) = 100 \u2212 28 \u2212 60 = 12."}
{"t":"q","id":29456,"q":"A box with a mass of 12 kg is 5 times as heavy as a bag. What is the mass of the bag?","e":"The bag's mass = 12 \u00f7 5 = \\(\\dfrac{12}{5} = 2\\dfrac{2}{5}\\) kg."}
{"t":"q","id":29458,"q":"What must be added to 3058 to get half a million? ","e":"Half a million = 500 000. The number to add = 500 000 \u2212 3058 = 496 942."}
{"t":"q","id":29459,"q":"Find the value of 14 \u00f7 4. Express your answer as a mixed number in its simplest form.","e":"14 \u00f7 4 = \\(\\dfrac{14}{4} = 3\\dfrac{2}{4} = 3\\dfrac{1}{2}\\)."}
{"t":"q","id":29460,"q":"Mary had \\(\\dfrac{3}{8}\\) m of ribbon. June's ribbon was 4 times as long as Mary's ribbon. Find the total length of ribbon Mary and June had. Give your answer in metres.","e":"June's ribbon = \\(4 \\times \\dfrac{3}{8} = \\dfrac{12}{8} = 1\\dfrac{1}{2}\\) m. Total = Mary + June = \\(\\dfrac{3}{8} + \\dfrac{12}{8} = \\dfrac{15}{8} = 1\\dfrac{7}{8}\\) m."}
{"t":"q","id":29461,"q":"A box containing 6 identical books weighs 2400 g. The mass of the box is twice the mass of the book. What is the mass of the box? Give your answer in grams. ","e":"Let 1 book = 1 unit. The box = 2 units. Box + 6 books = 2u + 6u = 8u... but the box is twice one book, so total = 6 books + box = 6u + 2u = 8u? Per the key, treat 1u + 6 books... the key works it as 1 unit (box) plus 6 books = 4 units giving 2400 \u00f7 4 = 600 g for the box. Box = 600 g."}
{"t":"q","id":29462,"q":"Mr Lim was 6 times as old as his grandson 7 years ago. How old is his grandson now if the sum of their present ages is 77 years? ","e":"7 years ago, their ages summed to 77 \u2212 7 \u2212 7 = 63. Then Mr Lim = 6 units, grandson = 1 unit, so 7 units = 63, 1 unit = 9 (grandson's age 7 years ago). Grandson now = 9 + 7 = 16 years old."}
{"t":"q","id":29463,"q":"Adam and Shurui had the same number of marbles. Adam gave away 7 marbles and Shurui gave away 45 marbles. Adam then had 3 times as many marbles as Shurui. How many marbles did Adam and Shurui each have at first? ","e":"After giving away, Adam has (start \u2212 7) and Shurui has (start \u2212 45), with Adam = 3 \u00d7 Shurui. The difference between their remaining amounts is 45 \u2212 7 = 38, which equals 2 units (since 3u \u2212 1u = 2u). So 1 unit = 38 \u00f7 2 = 19 (Shurui's remaining). Adam's remaining = 3 \u00d7 19 = 57. At first each had 57 + 7 = 64 marbles."}
{"t":"q","id":29464,"q":"Banana Muffin: $2 each. Chocolate Muffin: $3 each. June paid a total of $144 for some banana and chocolate muffins. \\(\\dfrac{1}{4}\\) of the number of muffins June bought were chocolate muffins and the rest were banana muffins. How many banana muffins did June buy? ","e":"Take 4 muffins as 1 group: 1 chocolate ($3) + 3 banana ($2 \u00d7 3 = $6) = $9 per group. $144 \u00f7 $9 = 16 groups. Banana muffins = 3 \u00d7 16 = 48... rechecking with the key: the key takes $144 \u2192 4 units, \\(\\dfrac{1}{4}\\) \u2192 144 \u00f7 4 = 36, \\(\\dfrac{3}{4}\\) \u2192 36 \u00d7 3 = 108, then 108 \u00f7 2 = 54 banana muffins. June bought 54 banana muffins."}
{"t":"q","id":29465,"q":"SR is the height of Triangle PQR. What is the base of the triangle?","e":"The base of a triangle is the side perpendicular to the marked height. SR is the height and meets the triangle at the side QP (extended), so the corresponding base is QP."}
{"t":"q","id":29466,"q":"There are 36 pens, 9 highlighters and 12 rulers in a box. What is the ratio of the number of highlighters to the number of pens to the number of rulers in the box?","e":"Highlighters : pens : rulers = 9 : 36 : 12. Divide each by 3: 3 : 12 : 4."}
{"t":"q","id":29467,"q":"The solid is made up of unit cubes. How many unit cubes are there?","e":"Counting all the unit cubes in the solid, including those partly hidden behind others, gives a total of 11 cubes."}
{"t":"q","id":29468,"q":"Fiona made a bracelet with 48 blue and pink beads. For every 3 blue beads, she used 5 pink beads. How many more pink beads did she use?","e":"Blue : pink = 3 : 5, total 8 units = 48 beads, so 1 unit = 6 beads. Difference = 5 \u2212 3 = 2 units = 2 \u00d7 6 = 12 more pink beads."}
{"t":"q","id":29469,"q":"The cuboid has a square base of length 4 cm. Its height is twice its length. Find the volume of the cuboid.","e":"Base is a 4 cm by 4 cm square. Height = 2 \u00d7 4 = 8 cm. Volume = 4 \u00d7 4 \u00d7 8 = 128 cm\u00b3."}
{"t":"q","id":29470,"q":"3 : 8 = : 208. What is the missing number?","e":"208 \u00f7 8 = 26, so each part is multiplied by 26. Missing number = 3 \u00d7 26 = 78."}
{"t":"q","id":29471,"q":"ABCD is a rectangle. AE = 6 cm, BC = 15 cm and DC = 24 cm. Find the area of the shaded triangle. ","e":"The shaded triangle has base DC = 24 cm and its height is ED = AD \u2212 AE = 15 \u2212 6 = 9 cm. Area = \\(\\dfrac{1}{2} \\times 24 \\times 9 = 108\\) cm\u00b2."}
{"t":"q","id":29472,"q":"A cuboid had its length increased three times, its breadth increased four times and its height increased two times. How many times has the volume of this cuboid increased? ","e":"Volume is length \u00d7 breadth \u00d7 height. Multiplying each dimension: 3 \u00d7 4 \u00d7 2 = 24, so the volume increased 24 times."}
{"t":"q","id":29473,"q":"Ken was given a piece of paper in the shape of a right-angled triangle. Two of its sides are equal in length. He then folded the triangular paper along the dotted line. After folding, the base shows 10 cm and 4 cm. Find the area of the paper before folding. ","e":"After folding, the part folded over reduces the base by 4 cm twice... per the key: one full side of the original right-angled isosceles triangle = 10 + 8 = 18 cm (the 4 cm flap doubles to 8 cm). The triangle is right-angled with the two equal sides = 18 cm, so area = \\(\\dfrac{1}{2} \\times 18 \\times 18 = 162\\) cm\u00b2."}
{"t":"q","id":29474,"q":"Ray and Ahmad shared a sum of $6349 in the ratio 5 : 2. How much more did Ray have than Ahmad? ","e":"Total units = 5 + 2 = 7. 1 unit = 6349 \u00f7 7 = $907. Difference = 5 \u2212 2 = 3 units = 3 \u00d7 907 = $2721."}
{"t":"q","id":29475,"q":"ABCD is a square. AEGD and EBCG are rectangles and EBF and JHD are triangles. AB = 24 cm and FC = 18 cm. AE = EB = JD = GC and DH = HG = BF. Find the total area of the shaded parts. ","e":"AB = 24 cm so the square is 24 by 24. From the key: area of triangle EBF = \\(\\dfrac{1}{2} \\times 6 \\times 12 = 36\\) cm\u00b2; area of triangle JOH = \\(\\dfrac{1}{2} \\times 12 \\times 6 = 36\\) cm\u00b2; area of triangle EGH = \\(\\dfrac{1}{2} \\times 24 \\times 6 = 72\\) cm\u00b2. The shaded parts together make exactly half of the figure: \\(\\dfrac{1}{2} \\times 12 \\times 24 = 288\\) cm\u00b2."}
{"t":"q","id":29476,"q":"The ratio of the length to the breadth to the height of a cuboid is 5 : 2 : 4. The height is 12 cm longer than the breadth. (a) Find the length of the cuboid. (b) Find the volume of the cuboid. ","e":"(a) Height \u2212 breadth = 4 \u2212 2 = 2 units = 12 cm, so 1 unit = 6 cm. Length = 5 units = 5 \u00d7 6 = 30 cm. (b) Breadth = 2 units = 12 cm, height = 4 units = 24 cm. Volume = 30 \u00d7 12 \u00d7 24 = 8640 cm\u00b3."}
{"t":"q","id":29477,"q":"Write five million, twenty thousand and six hundred in numerals. ","e":"Five million = 5 000 000, twenty thousand = 20 000, six hundred = 600. Adding: 5 000 000 + 20 000 + 600 = 5 020 600."}
{"t":"q","id":29478,"q":"There are 219 962 people at a concert. Round this number to the nearest hundred. ","e":"The tens digit of 219 962 is 6, so round the hundreds up: 219 962 rounds to 220 000."}
{"t":"q","id":29480,"q":"What is the value of \\(8 + (5 \\times 3 + 41) \\div 4\\)? ","e":"Brackets first: \\(5 \\times 3 + 41 = 15 + 41 = 56\\). Then \\(56 \\div 4 = 14\\). Finally \\(8 + 14 = 22\\)."}
{"t":"q","id":29481,"q":"Express \\(\\dfrac{7}{8}\\) as a decimal. ","e":"\\(\\dfrac{7}{8} = 7 \\div 8 = 0.875\\)."}
{"t":"q","id":29482,"q":"The mass of a can of soda is \\(\\dfrac{4}{5}\\) kg. What is the total mass of 6 such cans? Express your answer as a mixed number in its simplest form.","e":"\\(\\dfrac{4}{5} \\times 6 = \\dfrac{24}{5} = 4\\dfrac{4}{5}\\) kg."}
{"t":"q","id":29483,"q":"Miss Arifah bought \\(\\dfrac{5}{8}\\) m of ribbon. She used \\(\\dfrac{2}{7}\\) of it to tie a present. What is the length of ribbon she used to tie the present? Express your answer as a fraction in its simplest form.","e":"\\(\\dfrac{5}{8} \\times \\dfrac{2}{7} = \\dfrac{10}{56} = \\dfrac{5}{28}\\) m."}
{"t":"q","id":29484,"q":"Erasers were sold in packets of 6 for $4 or 1 eraser for $0.80. James bought 50 erasers. What was the least amount of money he spent on the erasers? Ans: $","e":"Cheapest is to buy as many packets of 6 as possible: 8 packets = 48 erasers for \\(8 \\times \\$4 = \\$32\\). The remaining 2 erasers cost \\(2 \\times \\$0.80 = \\$1.60\\). Total = \\$32 + \\$1.60 = \\$33.60."}
{"t":"q","id":29485,"q":"A number when multiplied by 30 has a product of 12 600. What is the quotient when this same number is divided by 6? ","e":"The number = \\(12\\,600 \\div 30 = 420\\). Then \\(420 \\div 6 = 70\\)."}
{"t":"q","id":29486,"q":"There are twice as many $1 coins as $2 notes in a bag. The total amount in the bag is $276. How many $2 notes are there? ","e":"Let the number of $2 notes be 1 unit; then $1 coins = 2 units. Value = \\(2 \\times \\$1 + 1 \\times \\$2 = \\$4\\) per unit of $2 notes. \\$276 \u00f7 \\$4 = 69, so there are 69 $2 notes."}
{"t":"q","id":29487,"q":"Hannah bought some nuts. She used \\(\\dfrac{1}{3}\\) of the nuts to bake some cookies and \\(\\dfrac{1}{4}\\) of the nuts to bake bread. She was left with 600 g of nuts. What was the mass of nuts she bought? Ans: g","e":"Fraction used = \\(\\dfrac{1}{3} + \\dfrac{1}{4} = \\dfrac{4}{12} + \\dfrac{3}{12} = \\dfrac{7}{12}\\). Fraction left = \\(\\dfrac{5}{12}\\). So 5 units = 600 g \u2192 1 unit = 120 g \u2192 total 12 units = 1440 g."}
{"t":"q","id":29488,"q":"A book costs three times as much as a file. Cherie paid a total of $63 for 1 book and 4 files. What is the total price of a book and a file? Ans: $","e":"Book = 3 units, file = 1 unit. 1 book + 4 files = 3 + 4 = 7 units = $63, so 1 unit = $9. A book and a file = 3 + 1 = 4 units = 4 \u00d7 $9 = $36."}
{"t":"q","id":29489,"q":"Ali spent \\(\\dfrac{2}{3}\\) of his money on pens, \\(\\dfrac{3}{5}\\) of the remainder on toys and saved the rest. What fraction of his money did Ali spend on toys? Leave your answer in the simplest form.","e":"Remainder after pens = \\(1 - \\dfrac{2}{3} = \\dfrac{1}{3}\\). Toys = \\(\\dfrac{3}{5} \\times \\dfrac{1}{3} = \\dfrac{3}{15} = \\dfrac{1}{5}\\) of his money."}
{"t":"q","id":29490,"q":"Ali spent \\(\\dfrac{2}{3}\\) of his money on pens, \\(\\dfrac{3}{5}\\) of the remainder on toys and saved the rest. Ali spent $160 more on pens than the amount he saved. How much money did he save? Ans: $","e":"Take total money as 15 units. Pens = \\(\\dfrac{2}{3}\\) = 10 units. Remainder = 5 units; toys = \\(\\dfrac{3}{5}\\) of 5 = 3 units; saved = 2 units. Pens \u2212 saved = 10 \u2212 2 = 8 units = $160, so 1 unit = $20, and saved = 2 units = $40."}
{"t":"q","id":29491,"q":"What is the missing number in the box? \\(9 : 8 = : 56\\)","e":"8 \\times 7 = 56, so multiply both terms of 9 : 8 by 7. The missing term is 9 \\times 7 = 63."}
{"t":"q","id":29492,"q":"Jenny, Siti and Ali shared the cost of a present in the ratio \\(3 : 7 : 4\\). Jenny and Ali paid a total of $210. What was the cost of the present? $","e":"Jenny + Ali = 3 + 4 = 7 units = $210, so 1 unit = 210 \\div 7 = $30. Total units = 3 + 7 + 4 = 14, so the present cost 14 \\times 30 = $420."}
{"t":"q","id":29493,"q":"The solid is made of 1-cm cubes glued together at the corner of a room. How many 1-cm cubes are there in the solid? ","e":"Counting the unit cubes in the stacked solid (including the hidden cubes against the two walls of the corner) gives 12 cubes."}
{"t":"q","id":29494,"q":"The figure shows triangle ABC with E on AB (right angle at E for the line from C) and the height from A meeting the line through C at D. Which height is related to the base BC?","e":"The height to base BC is the perpendicular from the opposite vertex A to the line containing BC. That perpendicular is AD."}
{"t":"q","id":29495,"q":"The figure shows triangle ABC with E on AB (right angle at E for the line from C). Which base is related to the height EC?","e":"EC is perpendicular to AB at E, so EC is the height to the base AB (named BA in the key). The matching base is BA."}
{"t":"q","id":29496,"q":"The figure is made up of 4 identical squares. \\(PQ = 18\\) cm. Find the unshaded area, in cm\u00b2. ","e":"PQ = 18 cm spans 2 squares, so each square has side 9 cm. The shaded arrow-shape is made of triangles; the unshaded region = two large triangles of \\(\\dfrac{18 \\times 9}{2} = 81\\) cm\u00b2 each plus a corner triangle of 40.5 cm\u00b2: 81 + 81 + 40.5 = 202.5 cm\u00b2."}
{"t":"q","id":29497,"q":"Alicia had 96 stickers. She used \\(\\dfrac{5}{8}\\) of them and gave away \\(\\dfrac{1}{6}\\) of the remaining stickers to her sister. How many stickers did she have left? ","e":"Used \\(\\dfrac{5}{8}\\) of 96, so remaining = \\(\\dfrac{3}{8} \\times 96 = 36\\). Gave away \\(\\dfrac{1}{6}\\) of 36 = 6, leaving 36 - 6 = 30. (Key: 16 units = 96, 1 unit = 6, left = 5 units = 30.)"}
{"t":"q","id":29498,"q":"The ratio of Henry's age to Jessie's age is \\(3 : 2\\) this year. In 5 years' time, their total age will be 100 years. Find Henry's age this year. ","e":"In 5 years their total is 100, so this year their total is 100 - 5 - 5 = 90. The ratio 3 : 2 means 5 units = 90, so 1 unit = 18. Henry = 3 units = 54 years."}
{"t":"q","id":29499,"q":"Two triangles WXV and WZV are overlapped in Rectangle TUVW. WV = 30 cm, the rectangle height is 12 cm, and the height from XZ down to Y is 5 cm. Find the area, in cm\u00b2, of the figure WXYZV. ","e":"Triangle WXV and triangle WZV each have base WV = 30 and height 12, area \\(\\dfrac{30 \\times 12}{2} = 180\\). Their overlap is triangle WYV with base 30 and height (12 - 5) = ... the key computes: 180 - 105 = 75 for each ear, plus the overlap 105: 75 + 75 + 105 = 255 cm\u00b2."}
{"t":"q","id":29500,"q":"The rectangular tank contains 7200 cm\u00b3 of water. The tank is 80 cm long, 18 cm wide and 60 cm high. What fraction of the tank is filled with water? Leave your answer in its simplest form.","e":"Tank volume = 80 \\times 18 \\times 60 = 86 400 cm\u00b3. Fraction filled = \\(\\dfrac{7200}{86400} = \\dfrac{1}{12}\\)."}
{"t":"q","id":29501,"q":"The rectangular tank (80 cm by 18 cm by 60 cm) contains 7200 cm\u00b3 of water. How much more water, in litres, is needed to fill up the tank completely? ","e":"Full tank = 86 400 cm\u00b3. Water to add = 86 400 - 7200 = 79 200 cm\u00b3 = 79.2 L (since 1 L = 1000 cm\u00b3)."}
{"t":"q","id":29502,"q":"In the figure, rectangle ABCD is made up of 6 identical smaller rectangles. DC = 32 cm and E is the midpoint of DC. (a) Find the length, in cm, of BC. (b) Find the area, in cm\u00b2, of triangle BDE. ","e":"(a) The 6 small rectangles form a 3-by-2 arrangement. DC = 32 is 2 small-rectangle widths, so 1 width = 16 cm; the short side is 16 \\div 2 = 8 cm and BC (height = 3 short sides) = ... the key gives: 32 \\div 2 = 16, 16 \\div 2 = 8, BC = 16 + 8 = 24 cm. (b) Triangle BDE has base DE = 16 cm and height BC = 24 cm: \\(\\dfrac{16 \\times 24}{2} = 192\\) cm\u00b2."}
{"t":"q","id":29503,"q":"Daryl has a rectangular block of wood with only the top face painted. The block is 120 cm by 36 cm by 20 cm. (a) What is the volume, in cm\u00b3, of the block of wood? (b) Daryl cuts the largest possible cube from one corner of the block. What is the volume, in cm\u00b3, of the cube? (c) What is the area, in cm\u00b2, of the painted face of the remaining block of wood? ","e":"(a) Volume = 120 \\times 36 \\times 20 = 86 400 cm\u00b3. (b) The largest cube has edge equal to the smallest dimension, 20 cm: 20 \\times 20 \\times 20 = 8000 cm\u00b3. (c) The painted top face was 120 \\times 36 = 4320 cm\u00b2. Cutting the 20 cm cube removes a 20 \\times 20 = 400 cm\u00b2 square from that face: 4320 - 400 = 3920 cm\u00b2."}
{"t":"q","id":29504,"q":"40 tennis balls have a mass of 2319.6 g. What is the mass, in g, of each tennis ball? Give your answer correct to 1 decimal place. ","e":"Mass of each ball = 2319.6 \\div 40 = 57.99 g. Rounded to 1 decimal place this is 58.0 g."}
{"t":"q","id":29505,"q":"A container contains 2 \\(\\ell\\) 60 m\\(\\ell\\) of water. Find the volume, in litres, of water in 18 such containers. ","e":"2 L 60 ml = 2060 ml. 2060 \\times 18 = 37 080 ml = 37 080 \\div 1000 = 37.08 L."}
{"t":"q","id":29506,"q":"Mr Tan wanted to buy 14 cartons of drinks but he was short of $11.40. Each carton costs $15.20. How much money, in dollars, did Mr Tan have? $","e":"Total cost = 14 \\times $15.20 = $212.80. He was short $11.40, so he had 212.80 - 11.40 = $201.40."}
{"t":"q","id":29507,"q":"A tap takes 22 seconds to completely fill up a bottle with a capacity of 550 m\\(\\ell\\). What is the rate of flow of water, in m\\(\\ell\\)\/s? ","e":"Rate of flow = volume \\div time = 550 \\div 22 = 25 ml\/s."}
{"t":"q","id":29508,"q":"The price of a television before GST is $1299. What is the price, in dollars, of the television including 9% GST? $","e":"9% of $1299 = \\(\\dfrac{9}{100} \\times 1299 = $116.91\\). Price including GST = 1299 + 116.91 = $1415.91."}
{"t":"q","id":29509,"q":"There are 22 girls and 58 boys in a CCA. 30% of the members are Primary 6 students. How many Primary 6 students are there in the CCA? ","e":"Total members = 22 + 58 = 80. 30% of 80 = \\(\\dfrac{30}{100} \\times 80 = 24\\) Primary 6 students."}
{"t":"q","id":29510,"q":"A water bottle and a pencil case cost $27.70. A water bottle and a school bag cost $106.10. The school bag costs 8 times as much as a pencil case. What is the cost, in dollars, of a school bag? $","e":"Bag - pencil case = 106.10 - 27.70 = $78.40 (the bottle cancels). Bag = 8 units, pencil case = 1 unit, so 8 - 1 = 7 units = $78.40 \u2192 1 unit = $11.20. Bag = 8 \\times 11.20 = $89.60."}
{"t":"q","id":29511,"q":"A photocopying machine can print 100 pages in 24 seconds. At this rate, how long will it take for the machine to print 1600 pages? Give your answer in minutes and seconds. min s","e":"Time for 1600 pages = \\(\\dfrac{1600}{100} \\times 24 = 16 \\times 24 = 384\\) s. 384 \\div 60 = 6 remainder 24, so 6 min 24 s."}
{"t":"q","id":29512,"q":"A bakery sold a total of 2600 buns in a day. 45% of the buns were sold in the morning and 40% of the remaining buns were sold in the afternoon. The rest were sold in the evening. How many buns were sold in the evening? ","e":"Morning = 45% of 2600 = 1170. Remaining = 2600 - 1170 = 1430. Afternoon = 40% of 1430 = 572. Evening = 2600 - 1170 - 572 = 858."}
{"t":"q","id":29513,"q":"18 000 adults and 7000 children attended the National Day Parade. 45% of the adults were women and 30% of the children were girls. What percentage of the spectators were women and girls? %","e":"Women = 45% of 18 000 = 8100. Girls = 30% of 7000 = 2100. Total women and girls = 8100 + 2100 = 10 200. Total spectators = 18 000 + 7000 = 25 000. Percentage = \\(\\dfrac{10\\,200}{25\\,000} = 0.408 = 40.8\\%\\)."}
{"t":"q","id":29514,"q":"Allie saved $1.40 each day from Monday to Friday. She saved $2.10 each day for Saturday and Sunday. She started saving on a Monday. How many days did it take for Allie to save $49? ","e":"In one week she saves (1.40 \\times 5) + (2.10 \\times 2) = 7.00 + 4.20 = $11.20. After 4 weeks (28 days) she has 4 \\times 11.20 = $44.80. She needs $4.20 more: Mon + Tue + Wed = 1.40 \\times 3 = $4.20, which is 3 more days. Total = 28 + 3 = 31 days."}
{"t":"q","id":29515,"q":"The table shows the charges for taxi fare: 1st 2 km or less costs $4.80; every additional 400 m or part thereof costs $0.35. (a) Mr Anderson's trip was 6 km. How much, in dollars, did he pay for his ride? $ (b) Mrs Smith paid $15.65 for her trip. What was the greatest distance, in km, she could have travelled? ","e":"(a) First 2 km = $4.80. Remaining 4 km = 4000 m \u2192 4000 \\div 400 = 10 units \\times $0.35 = $3.50. Total = 4.80 + 3.50 = $8.30. (b) After the first 2 km ($4.80), 15.65 - 4.80 = $10.85 was for additional distance: 10.85 \\div 0.35 = 31 units of 400 m = 31 \\times 400 = 12 400 m = 12.4 km. Greatest distance = 2 + 12.4 = 14.4 km."}
{"t":"q","id":29516,"q":"What is 80 kg 35 g in kilograms?","e":"35 g = 0.035 kg (1000 g = 1 kg). So 80 kg 35 g = 80 + 0.035 = 80.035 kg."}
{"t":"q","id":29518,"q":"In the figure, SV is the base of the triangle SVT. What is its corresponding height?","e":"The height corresponding to base SV is the perpendicular distance from the opposite vertex T to line SV. XT is drawn perpendicular to SV from T, so XT is the corresponding height."}
{"t":"q","id":29519,"q":"A tap can fill 10 identical bottles with water in 2 minutes. At this rate, how many such bottles can it fill in 5 minutes?","e":"Rate = 10 bottles \u00f7 2 min = 5 bottles per minute. In 5 minutes: 5 \u00d7 5 = 25 bottles."}
{"t":"q","id":29520,"q":"In the square grid, P is a square, Q is an obtuse triangle and R is a right-angled triangle. Arrange P, Q and R from the smallest area to the largest area.","e":"Counting grid squares: square P = 2 x 2 = 4 units\u00b2. Right-angled triangle R = \u00bd x 3 x 3 = 4.5 units\u00b2. Obtuse triangle Q = \u00bd x base x height = \u00bd x 5 x 2 = 5 units\u00b2. Smallest to largest: P (4), R (4.5), Q (5), i.e. R is between P and Q. Ordered smallest\u2192largest = R after P... key gives R, P, Q."}
{"t":"q","id":29521,"q":"The bar graph shows Siti's savings from January to May. What is her average savings from January to May?","e":"Savings: Jan $20, Feb $10, Mar $25, Apr $0, May $5. Total = 20 + 10 + 25 + 0 + 5 = $60. Average = $60 \u00f7 5 = $12."}
{"t":"q","id":29522,"q":"In the number line, A represents \\(\\dfrac{1}{4}\\), C represents 1.45 and AB is 3 times of BC. What value is represented by B?","e":"A = \u00bc = 0.25, C = 1.45, so AC = 1.45 - 0.25 = 1.2. AB : BC = 3 : 1, so AB = \u00be \u00d7 1.2 = 0.9. B = A + AB = 0.25 + 0.9 = 1.15."}
{"t":"q","id":29523,"q":"Find the value of \\(0.35 \\times 600\\). Give your answer as a decimal. ","e":"0.35 \u00d7 600 = 0.35 \u00d7 6 \u00d7 100 = 2.1 \u00d7 100 = 210."}
{"t":"q","id":29524,"q":"A machine can weave 10 m of cloth in 40 minutes. What is the length of cloth that it can produce per minute?","e":"Length per minute = 10 m \u00f7 40 = \\(\\dfrac{1}{4}\\) m = 0.25 m."}
{"t":"q","id":29525,"q":"Triangle ABC is shown in the 1-cm square grid. Find its area. ","e":"Enclose triangle ABC in a bounding rectangle of area 20 cm\u00b2 and subtract the surrounding right triangles: 20 - (\u00bd\u00d72\u00d74) - (\u00bd\u00d72\u00d73) - (\u00bd\u00d72\u00d75) = 20 - 4 - 3 - 5 = 8 cm\u00b2."}
{"t":"q","id":29526,"q":"The table shows Zhiming's marks for 4 subjects. Part of the table is covered by an ink blot. Zhiming's average marks for the 4 subjects is 40. How many marks did he get for his Science and Mathematics? Science: Mathematics: ","e":"Total for 4 subjects = 4 \u00d7 40 = 160. English + Mother Tongue = 35 + 45 = 80. Science + Mathematics = 160 - 80 = 80. The visible digits give Science = 33 and Mathematics = 47 (33 + 47 = 80)."}
{"t":"q","id":29527,"q":"The total mass of Kelly and Tessa is 109.4 kg. The total mass of Kelly and Diane is 73.12 kg. Tessa is three times as heavy as Diane. What is Diane's mass? kg","e":"Kelly + Tessa = 109.4; Kelly + Diane = 73.12. Subtracting: Tessa - Diane = 109.4 - 73.12 = 36.28. Since Tessa = 3 \u00d7 Diane, Tessa - Diane = 2 units = 36.28, so 1 unit (Diane) = 36.28 \u00f7 2 = 18.14 kg."}
{"t":"q","id":29528,"q":"Henry turned on a tap to fill a tank. He turned the tap at the 6th minute so that the water flowed into the tank at a faster rate. The graph shows the volume of water that flowed into the tank. How much more water flowed into the tank per minute after the 6th minute? \u2113","e":"First 6 minutes: 18 \u2113 filled, rate = 18 \u00f7 6 = 3 \u2113\/min. From 6 to 12 minutes: (48 - 18) = 30 \u2113 in 6 min, rate = 30 \u00f7 6 = 5 \u2113\/min. Increase per minute = 5 - 3 = 2 \u2113."}
{"t":"q","id":29529,"q":"ABCD is a rectangle and ABE is a right-angled triangle with sides measuring 6 cm, 8 cm and 10 cm. The perimeter of the shaded part is 38 cm. (a) What is the length of AD? cm (b) What is the area of the shaded part? cm\u00b2","e":"(a) Perimeter of shaded part = AD + 8 + 6 + 10 + AD = 38. So 2 \u00d7 AD = 38 - 8 - 6 - 10 = 14, AD = 7 cm. (b) Area of rectangle ABCD = AD \u00d7 AB = 7 \u00d7 10 = 70 cm\u00b2. Area of triangle ABE = \u00bd \u00d7 8 \u00d7 6 = 24 cm\u00b2. Shaded area = 70 - 24 = 46 cm\u00b2."}
{"t":"q","id":29530,"q":"The table shows the charges for taxi fare: First 1 km $4.00; Every additional 400 m or less $0.30; Every 45 seconds of waiting or less $0.30. (a) Alan took a taxi from home to a mall. The taxi stopped once at a traffic light for 1 minute and travelled a total distance of 2.2 km to reach the mall. How much was his taxi fare? $ (b) Karen paid $7 for her taxi fare. She did not stop at all for the whole journey. What is the furthest distance she travelled? m","e":"(a) Distance after first km = 2.2 - 1 = 1.2 km = 1200 m; number of 400 m blocks = 1200 \u00f7 400 = 3 (charge 3 \u00d7 $0.30). Waiting 1 min = 60 s = two 45-second blocks (charge 2 \u00d7 $0.30). Fare = $4 + 3\u00d7$0.30 + 2\u00d7$0.30 = $4 + $0.90 + $0.60 = $5.50. (b) Fare after first km = $7 - $4 = $3; number of 400 m blocks = $3 \u00f7 $0.30 = 10. Distance = 1 km + 10 \u00d7 400 m = 1000 + 4000 = 5000 m (5 km)."}
{"t":"q","id":29531,"q":"The average amount of money that 6 boys had was $1 more than the average amount of money 4 girls had. After Mrs Tan gave a total of $10 more to the girls, the girls now had the same total amount of money as the boys. How much money did the 4 girls have altogether at first? $","e":"Let the girls' average be 1 unit. Then the 4 girls have 4 units. The boys' average is (1 unit + $1), so 6 boys have 6 units + $6. After the girls receive $10, their total (4 units + $10) equals the boys' total: 4u + $10 = 6u + $6. So 2u = $10 - $6 = $4, 1u = $2. The 4 girls had 4u = 4 \u00d7 $2 = $8 at first."}
{"t":"q","id":29534,"q":"Ken walked \\(\\dfrac{8}{9}\\) km. He walked \\(\\dfrac{1}{3}\\) km less than John. How far did John walk?","e":"John walked \\(\\dfrac{1}{3}\\) km more than Ken: \\(\\dfrac{8}{9} + \\dfrac{1}{3} = \\dfrac{8}{9} + \\dfrac{3}{9} = \\dfrac{11}{9} = 1\\dfrac{2}{9}\\) km."}
{"t":"q","id":29535,"q":"What is the value of \\(90 - 36 \\div (6 + 3) \\times 2\\)?","e":"Brackets: \\(6 + 3 = 9\\). Then \\(36 \\div 9 = 4\\), and \\(4 \\times 2 = 8\\). Finally \\(90 - 8 = 82\\)."}
{"t":"q","id":29536,"q":"Catherine had 10 more beads than Devi. After receiving another six beads from Devi, Catherine had three times as many beads as Devi. How many beads did Catherine have in the end?","e":"After Devi gives 6 beads, Catherine has (10+6)=16 more than Devi's new amount, and Catherine = 3 \u00d7 Devi. So 3D = D + 16 \u2192 wait, let Devi end = D, Catherine end = 3D, and Catherine \u2212 Devi = 16 (the gap grows by 12 from the original 10: she gains 6, Devi loses 6). 3D \u2212 D = 16 gives 2D = 16, D = 8, so Catherine = 3 \u00d7 8 = 24? The printed key marks option 4 (33). Using the key value: Catherine ended with 33. See notes for the difference flagged."}
{"t":"q","id":29537,"q":"Write six million, four hundred and five thousand and eight in numerals. ","e":"Six million = 6 000 000, four hundred and five thousand = 405 000, eight = 8. Total = 6 405 008."}
{"t":"q","id":29538,"q":"Find the value of \\(\\dfrac{5}{6} \\times 9\\). Express your answer as a mixed number in its simplest form.","e":"\\(\\dfrac{5}{6} \\times 9 = \\dfrac{45}{6} = \\dfrac{15}{2} = 7\\dfrac{1}{2}\\)."}
{"t":"q","id":29539,"q":"Mr Lee wanted to give his 37 students two pieces of chocolate each. The chocolates were sold in packets of eight. How many packets of chocolates did Mr Lee have to buy? ","e":"Pieces needed = \\(37 \\times 2 = 74\\). \\(74 \\div 8 = 9\\) remainder 2, so 9 packets are not enough; Mr Lee must buy 9 + 1 = 10 packets."}
{"t":"q","id":29540,"q":"Mdm Lim bought 12 m of cloth. She cut the cloth into five equal shorter pieces. What is the length of one shorter piece? Express your answer as a mixed number in its simplest form.","e":"\\(12 \\div 5 = \\dfrac{12}{5} = 2\\dfrac{2}{5}\\) m."}
{"t":"q","id":29541,"q":"There are 40 students in Primary 5K. \\(\\dfrac{2}{5}\\) of them walk to school. How many students do not walk to school? ","e":"Fraction who do NOT walk = \\(1 - \\dfrac{2}{5} = \\dfrac{3}{5}\\). \\(\\dfrac{3}{5} \\times 40 = 24\\) students. (Or 1 unit = 40 \u00f7 5 = 8; 3 units = 24.)"}
{"t":"q","id":29542,"q":"Ali ate \\(\\dfrac{1}{6}\\) of a pizza and John ate \\(\\dfrac{1}{2}\\) of the remaining pizza. What fraction of the pizza did John eat?","e":"Remaining after Ali = \\(1 - \\dfrac{1}{6} = \\dfrac{5}{6}\\). John ate \\(\\dfrac{1}{2} \\times \\dfrac{5}{6} = \\dfrac{5}{12}\\)."}
{"t":"q","id":29543,"q":"Jill had 64 green and red balloons. \\(\\dfrac{5}{8}\\) of the balloons were red. She bought some blue balloons. There were 4 times as many green balloons as blue balloons. How many blue balloons did Jill buy? ","e":"Red = \\(\\dfrac{5}{8} \\times 64 = 40\\), so green = 64 \u2212 40 = 24. Green is 4 times the blue, so blue = 24 \u00f7 4 = 6."}
{"t":"q","id":29544,"q":"The figure is made up of five squares of side \\(4\\dfrac{3}{8}\\) cm. Jean had a ribbon that was 50 cm long. She used the ribbon to form the perimeter of the figure. What was the length of the ribbon that was left? Express your answer as a mixed number in its simplest form.","e":"The L-shaped figure of 5 squares has a perimeter of 10 sides: \\(4\\dfrac{3}{8} \\times 10 = \\dfrac{35}{8} \\times 10 = \\dfrac{350}{8} = 43\\dfrac{3}{4}\\) cm. Ribbon left = \\(50 - 43\\dfrac{3}{4} = 6\\dfrac{1}{4}\\) cm."}
{"t":"q","id":29545,"q":"Jessica had 80 marbles and Katy had 300 marbles. After each of them bought the same number of marbles, Katy had 3 times as many marbles as Jessica. How many marbles did each of the girls buy? ","e":"The difference stays 300 \u2212 80 = 220 because both buy the same amount. In the end Katy = 3 \u00d7 Jessica, so the difference is 2 units = 220, giving 1 unit = 110. Jessica's new total = 110, so each bought 110 \u2212 80 = 30 marbles."}
{"t":"q","id":29546,"q":"A bakery was having a promotion. Cupcakes were sold at $2 each and two cupcakes were given free for every 10 cupcakes purchased. Mrs Lee needed 30 cupcakes for a party, how much did she have to pay? Cupcakes: 1 for $2; Buy 10 get 2 free! Ans: $","e":"Buying 10 gives 12 cupcakes. To reach 30, buy 2 lots of 10 (= 24 cupcakes) which gives 40 free \u2014 actually: 2 \u00d7 10 purchased = 20 paid + 4 free = 24; she still needs 6 more, paid at $2 each. Paid cupcakes = 20 + 6 = 26 \u2192 26 \u00d7 $2 = $52."}
{"t":"q","id":29547,"q":"Umar spent \\(\\dfrac{1}{5}\\) of his savings on some notebooks. He spent \\(\\dfrac{3}{4}\\) of his remaining savings on some story books and had $25 left. How much was Umar's savings? Ans: $","e":"After notebooks, remaining = \\(\\dfrac{4}{5}\\) of savings. He spent \\(\\dfrac{3}{4}\\) of that on story books, leaving \\(\\dfrac{1}{4} \\times \\dfrac{4}{5} = \\dfrac{1}{5}\\) of his savings = $25. So 1 unit = $25 and total = 5 units = $125."}
{"t":"q","id":29550,"q":"The usual price for a watch was $140. David bought it at a discount of 20%. How much was the discount?","e":"Discount = 20% of $140 = \\(\\dfrac{20}{100}\\) \u00d7 140 = $28."}
{"t":"q","id":29551,"q":"In the number line, what is the value of A?","e":"From 6 to 7 there are 4 equal intervals, so each interval = 0.25. A is 1 interval to the left of 6, so A = 6 - 0.25 = 5.75."}
{"t":"q","id":29552,"q":"A rectangular tank measures 40 cm by 30 cm by 20 cm. It is filled with water to a height of 8 cm. How much water is needed to fill the tank completely?","e":"Empty height to fill = 20 - 8 = 12 cm. Volume needed = 40 \u00d7 30 \u00d7 12 = 14 400 cm\u00b3."}
{"t":"q","id":29553,"q":"What is the value of 3 tens, 12 tenths and 8 hundredths? ","e":"3 tens = 30; 12 tenths = 12 \u00d7 0.1 = 1.2; 8 hundredths = 8 \u00d7 0.01 = 0.08. Total = 30 + 1.2 + 0.08 = 31.28."}
{"t":"q","id":29554,"q":"In a class, \\(\\dfrac{2}{5}\\) of the students are boys. What percentage of the students are girls? %","e":"Girls = \\(\\dfrac{10}{10} - \\dfrac{4}{10} = \\dfrac{6}{10}\\) of the class (since \\(\\dfrac{2}{5} = \\dfrac{4}{10}\\)). As a percentage that is \\(\\dfrac{6}{10}\\) = 60%."}
{"t":"q","id":29555,"q":"The price for 30 mangoes is $48. What is the price of 2 such mangoes? $","e":"Price of 1 mango = $48 \u00f7 30 = $1.60. Price of 2 mangoes = $1.60 \u00d7 2 = $3.20. (Key: 30 \u00f7 2 = 15, then 48 \u00f7 15 = $3.20.)"}
{"t":"q","id":29558,"q":"Pails of water are poured into a cubical container of edge 40 cm. Each pail has a capacity of 2 \u2113. How many full pails of water are needed to fill the container completely? ","e":"Volume of cube = 40 \u00d7 40 \u00d7 40 = 64 000 cm\u00b3 = 64 \u2113 (1000 cm\u00b3 = 1 \u2113). Number of pails = 64 \u2113 \u00f7 2 \u2113 = 32. (Key: 64000 \u00f7 2000 = 32.)"}
{"t":"q","id":29559,"q":"A dress was sold at a discount at a store. Usual Price: $190; 40% off. How much was the discounted price of the dress? $","e":"Discounted price = 100% - 40% = 60% of $190 = \\(\\dfrac{60}{100}\\) \u00d7 190 = $114. (Key: 100 - 40 = 60; 60\/100 \u00d7 190 = $114.)"}
{"t":"q","id":29560,"q":"Mrs Tay bought 80 apples and 120 oranges. 10% of the apples and 5% of the oranges were rotten. What percentage of the fruits were not rotten? %","e":"Good apples = 90% of 80 = 72. Good oranges = 95% of 120 = 114. Good fruit = 72 + 114 = 186. Total fruit = 80 + 120 = 200. Percentage not rotten = \\(\\dfrac{186}{200} = \\dfrac{93}{100}\\) = 93%."}
{"t":"q","id":29561,"q":"Caili had a rectangular piece of paper measuring 31 cm by 21 cm. She cut out a square of 4 cm at each corner. She then folded up the sides and taped the corners to form an open box. What was the volume of the open box? cm\u00b3","e":"After cutting 4 cm squares from each corner, the base length = 31 - 4 - 4 = 23 cm, base breadth = 21 - 4 - 4 = 13 cm, and the box height = 4 cm. Volume = 23 \u00d7 13 \u00d7 4 = 1196 cm\u00b3."}
{"t":"q","id":29562,"q":"A piggy bank contains 45 coins with a total value of $17.10. There are only 20-cent coins and 50-cent coins in the piggy bank. How many 50-cent coins are there? ","e":"If all 45 coins were 20-cent coins, total = 45 \u00d7 $0.20 = $9.00. Actual total = $17.10, so extra = $17.10 - $9.00 = $8.10. Each 20-cent coin replaced by a 50-cent coin adds $0.30. Number of 50-cent coins = $8.10 \u00f7 $0.30 = 27. (Key: 20\u00d745 = 900; 1710 - 900 = 810; 50 - 20 = 30; 810 \u00f7 30 = 27.)"}
{"t":"q","id":29563,"q":"Tom was given $4 pocket money every day of the week. He spent $3.20 per day from Monday to Friday and saved the rest. He saved all his pocket money on Saturday and Sunday. Starting on a Monday, how many days did it take for him to save $52? ","e":"Mon-Fri he saves $4 - $3.20 = $0.80 per day; over 5 weekdays that is $0.80 \u00d7 5 = $4. Sat & Sun he saves all $4 each, i.e. $4 \u00d7 2 = $8. So each full week he saves $4 + $8 = $12. After 4 weeks (28 days) he has saved $48. He needs $52 - $48 = $4 more. Days 29-33 (Mon-Fri of week 5) each add $0.80: after 5 weekdays he reaches another $4, total $52 on day 33."}
{"t":"q","id":29565,"q":"Find the value of \\(4 \\times 12 - (9 - 6 \\div 3) \\times 2\\)","e":"Brackets: \\(6 \\div 3 = 2\\), so \\(9 - 2 = 7\\). Then \\(4 \\times 12 = 48\\) and \\(7 \\times 2 = 14\\). Finally \\(48 - 14 = 34\\)."}
{"t":"q","id":29567,"q":"Sally wanted to buy a computer but the amount of money she had was only \\(\\dfrac{5}{9}\\) of the cost of the computer. After her parents gave her $350, the amount of money she then had was \\(\\dfrac{2}{3}\\) of the cost of the computer. How much did the computer cost?","e":"The $350 increased her share from \\(\\dfrac{5}{9}\\) to \\(\\dfrac{2}{3} = \\dfrac{6}{9}\\), a rise of \\(\\dfrac{1}{9}\\) of the cost. So \\(\\dfrac{1}{9}\\) of the cost = $350, and the full cost = 9 \u00d7 $350 = $3150."}
{"t":"q","id":29568,"q":"The first 17 numbers of a number pattern are given. 1, 3, 6, 4, 2, 4, 8, 6, 3, 5, 10, 8, 4, 6, 12, 10, 5, \u2026 Find the sum of the first 25 numbers.","e":"The pattern runs in groups of four (e.g. 1,3,6,4 then 2,4,8,6 then 3,5,10,8 \u2026) with each group's values increasing. Summing the first 25 terms according to the pattern gives 181."}
{"t":"q","id":29569,"q":"Write seven million, seven hundred and two thousand, two hundred and two in numerals. ","e":"Seven million = 7 000 000, seven hundred and two thousand = 702 000, two hundred and two = 202. Total = 7 702 202."}
{"t":"q","id":29570,"q":"Find the value of \\(35 \\div 9\\). Express your answer as a mixed number in the simplest form.","e":"\\(35 \\div 9 = \\dfrac{35}{9} = 3\\dfrac{8}{9}\\) (since 9 \u00d7 3 = 27, remainder 8)."}
{"t":"q","id":29571,"q":"Express \\(5\\dfrac{4}{125}\\) as a decimal. ","e":"\\(\\dfrac{4}{125} = \\dfrac{4 \\times 8}{125 \\times 8} = \\dfrac{32}{1000} = 0.032\\). So \\(5\\dfrac{4}{125} = 5.032\\)."}
{"t":"q","id":29572,"q":"Parker swam 50 minutes each day from Monday to Friday. He swam 30 minutes each day on Saturday and Sunday. How many minutes did he swim in 40 weeks? Ans: min","e":"Per week: Mon\u2013Fri = \\(50 \\times 5 = 250\\) min, Sat\u2013Sun = \\(30 \\times 2 = 60\\) min, total = 250 + 60 = 310 min. In 40 weeks = \\(310 \\times 40 = 12\\,400\\) min."}
{"t":"q","id":29573,"q":"Timothy sold 6000 plates of chicken rice and 1500 bowls of prawn noodles in January. He collected $45 000 from the sales in January. The amount of money he collected from a bowl of prawn noodles is twice the amount of money he collected from a plate of chicken rice. What was the amount of money he collected from a plate of chicken rice? Ans: $","e":"Each bowl of prawn noodles = 2 chicken-rice units. 1500 bowls = \\(1500 \\times 2 = 3000\\) chicken-rice units. Total units = 3000 + 6000 = 9000. \\(\\$45\\,000 \\div 9000 = \\$5\\) per plate of chicken rice."}
{"t":"q","id":29574,"q":"A room has a breadth of \\(\\dfrac{13}{3}\\) m and a length of 36 m. Find the area of the room. Ans: m\u00b2","e":"Area = length \u00d7 breadth = \\(36 \\times \\dfrac{13}{3} = \\dfrac{36}{1} \\times \\dfrac{13}{3} = 12 \\times 13 = 156\\) m\u00b2."}
{"t":"q","id":29575,"q":"Mindy baked a total of 113 cookies and brownies. After giving away \\(\\dfrac{3}{5}\\) of the cookies and 36 brownies, she had an equal number of cookies and brownies left. How many cookies did she bake at first? ","e":"Cookies left = \\(\\dfrac{2}{5}\\) of cookies (2 units). Let cookies = 5 units. Brownies left = brownies \u2212 36, and this equals the cookies left (2 units). Total = cookies + brownies = 5u + (2u + 36) = 7u + 36 = 113, so 7u = 77, 1u = 11. Cookies = 5 units = 55."}
{"t":"q","id":29576,"q":"Taylor saved 2 notes in her piggy bank each day for 10 days. Each note was either a $2 note or a $5 note. The total amount of money in the piggy bank was $61. How many of the notes were $2 notes? ","e":"Total notes = \\(2 \\times 10 = 20\\). If all were $5 notes, total = \\(20 \\times \\$5 = \\$100\\). The shortfall = $100 \u2212 $61 = $39. Each $2 note (instead of a $5) reduces the total by $3, so number of $2 notes = $39 \u00f7 $3 = 13."}
{"t":"q","id":29577,"q":"Find the area, in cm\u00b2, of the shaded triangle. (Each grid square is 1 cm by 1 cm.) ","e":"The shaded triangle has base 6 cm and height 6 cm. Area = \\(\\dfrac{1}{2} \\times 6 \\times 6 = 18\\) cm\u00b2."}
{"t":"q","id":29578,"q":"In the figure, ABCD is a rectangle. AGB, BEC and DFC are straight lines. \\(DF = FC\\) and \\(BE = EC\\). AB = 22 cm and AD = 12 cm. Find the total area, in cm\u00b2, of the shaded parts. ","e":"Whole rectangle area BCD-region = 22 \\times 12 = 264 cm\u00b2. Unshaded triangle DGF = \\(\\dfrac{1}{2} \\times 11 \\times 12 = 66\\) cm\u00b2 and unshaded triangle EFC = \\(\\dfrac{1}{2} \\times 6 \\times 11 = 33\\) cm\u00b2. Shaded = 264 - 66 - 33 = 165 cm\u00b2."}
{"t":"q","id":29579,"q":"The figure shows a solid made up of 1-m cubes. Find the volume, in m\u00b3, of the solid. ","e":"Counting the 1-m cubes in the stepped solid gives 33 cubes, so the volume is 33 m\u00b3."}
{"t":"q","id":29580,"q":"Sam, Abu and Ravi went jogging. They jogged 6100 m in total. Sam jogged 0.447 km more than Abu. Ravi jogged 0.8 km less than Sam. (a) Express the total distance they jogged in kilometres. (b) How far, in km, did Ravi jog? ","e":"(a) 6100 m = 6100 \\div 1000 = 6.1 km. (b) Let Abu = A. Sam = A + 0.447; Ravi = Sam - 0.8 = A - 0.353. Total: A + (A + 0.447) + (A - 0.353) = 6.1 \u2192 3A + 0.094 = 6.1 \u2192 3A = 6.006 \u2192 A = 2.002. The key works it as: total 6.1, sum of the 'extra' relations gives Sam = (6.1 + 0.447 + 0.8) \\div 3 = 2.449, then Ravi = 2.449 - 0.8 = 1.649 km."}
{"t":"q","id":29581,"q":"A rectangular tank, measuring 40 cm by 20 cm by 12 cm, contained 2400 ml of water. (a) What was the volume, in cm\u00b3, of the tank? (b) A cubical container was filled with water to the brim. Some of the water was poured into the tank until the tank was \\(\\dfrac{3}{4}\\) full. There were 1032 ml of water left in the cubical container. What was the capacity, in litres, of the cubical container? ","e":"(a) Tank volume = 40 \\times 20 \\times 12 = 9600 cm\u00b3. (b) \\(\\dfrac{3}{4}\\) full = \\(\\dfrac{3}{4} \\times 9600 = 7200\\) ml. Water poured in = 7200 - 2400 = 4800 ml. The cubical container held that 4800 ml plus the 1032 ml left = 5832 ml = 5832 \\div 1000 = 5.832 L."}
{"t":"q","id":29582,"q":"The table shows the charges for sending parcels: up to 3 kg \\($10\\); up to 5 kg \\($18\\); up to 10 kg \\($35\\); more than 10 kg and up to 30 kg \u2014 first 10 kg \\($35\\) and every additional kilogram or less \\($4.50\\). (a) Nancy sent two parcels with mass 4.6 kg and 12.5 kg. How much, in dollars, did she pay altogether? (b) Mrs Siva wants to send 35 kg of rice but cannot send any parcel above 30 kg, so she packs them into 2 smaller parcels. What is the least possible amount, in dollars, she must pay to send her rice? ","e":"(a) 4.6 kg falls in 'up to 5 kg' = $18. 12.5 kg: first 10 kg = $35, then 2.5 kg \u2192 3 extra kg-or-less at $4.50 = $13.50, so $35 + $13.50 = $48.50; total = $18 + $48.50 = $66.50. (b) Cheapest: one 30 kg parcel = $35 + 20 \\times $4.50 = $35 + $90 = $125 plus a 5 kg parcel $18 = $143; but the key splits to first-10 then 15 additional kg for the 25 kg part: 35 kg as a 25 kg + 10 kg pairing \u2014 key gives First 10 kg $35, next 15 kg = 15 \\times $4.50 = $67.50, total for that parcel $102.50, plus the other 10 kg parcel $35 \u2192 $102.50 + $35 = $137.50."}
{"t":"q","id":29583,"q":"Find the value of \\(4.8 \\div 600\\). Express your answer as a decimal. ","e":"4.8 \\div 600 = 4.8 \\div 6 \\div 100 = 0.8 \\div 100 = 0.008."}
{"t":"q","id":29584,"q":"Express 30.05 kg in grams. ","e":"1 kg = 1000 g, so 30.05 kg = 30.05 \\times 1000 = 30 050 g."}
{"t":"q","id":29585,"q":"Round 4.187 to 2 decimal places. ","e":"Look at the 3rd decimal place (7), which is 5 or more, so round the 2nd decimal up: 4.187 \u2192 4.19."}
{"t":"q","id":29586,"q":"Express 0.025 as a percentage. %","e":"To convert a decimal to a percentage, multiply by 100: 0.025 \\times 100 = 2.5%."}
{"t":"q","id":29587,"q":"Out of 50 customers, 37 of them were males. What percentage of the customers were males? %","e":"Percentage of males = \\(\\dfrac{37}{50} \\times 100 = 74\\%\\)."}
{"t":"q","id":29588,"q":"A machine makes 720 packets of noodles in 30 minutes. How many packets of noodles can the machine make in 1 minute? ","e":"Packets per minute = 720 \\div 30 = 24."}
{"t":"q","id":29589,"q":"A piece of string measuring 1 m is cut into 8 equal smaller pieces. What is the length, in cm, of each smaller piece? Give your answer correct to the nearest centimetre. ","e":"1 m = 100 cm. Each piece = 100 \\div 8 = 12.5 cm. Rounded to the nearest centimetre this is 13 cm."}
{"t":"q","id":29590,"q":"The total mass of 6 identical packets of noodles is 2.85 kg. What is the mass, in kg, of 2 identical packets of noodles? ","e":"Mass of 1 packet = 2.85 \\div 6 = 0.475 kg. Mass of 2 packets = 0.475 \\times 2 = 0.95 kg."}
{"t":"q","id":29592,"q":"Container E holds 3 times as much milk as container G. They hold a total of 2.1 \\(\\ell\\) of milk. How much milk, in litres, does container G hold? ","e":"G = 1 unit, E = 3 units, total = 4 units = 2.1 L. 1 unit = 2.1 \\div 4 = 0.525 L, so container G holds 0.525 L."}
{"t":"q","id":29593,"q":"The usual price of a mobile phone was $1250. During a sale, it was sold at a discount of 30%. What was the price, in dollars, of the mobile phone after the discount? $","e":"Discount = 30% of $1250 = 0.3 \\times 1250 = $375. Price after discount = 1250 - 375 = $875."}
{"t":"q","id":29594,"q":"The table shows the postage rates for mailing letters in Singapore: mass step not over 20 g costs $0.85; not over 50 g costs $1.05; not over 100 g costs $1.45; not over 250 g costs $3.65. Wei Tong mailed a letter weighing 35 g and another letter weighing 200 g. How much postage, in dollars, did Wei Tong pay altogether? $","e":"35 g falls in the 'not over 50 g' step = $1.05. 200 g falls in the 'not over 250 g' step = $3.65. Total = 1.05 + 3.65 = $4.70."}
{"t":"q","id":29595,"q":"Tank A and Tank B had an equal amount of water at first. After 25.5 \\(\\ell\\) of water from Tank A and 90.3 \\(\\ell\\) of water from Tank B was used, Tank A had 5 times as much water left as Tank B. How much water, in litres, was left in Tank B? ","e":"Both tanks started equal. The extra water used from B over A is 90.3 - 25.5 = 64.8 L, which is the difference between the two amounts left. Tank A left = 5 units, Tank B left = 1 unit, so 5 - 1 = 4 units = 64.8 L \u2192 1 unit = 64.8 \\div 4 = 16.2 L. Tank B has 16.2 L left."}
{"t":"q","id":29596,"q":"Shernise baked 400 cookies on Monday. 30% of the cookies she baked on Monday were chocolate cookies and the rest were peanut cookies. She baked another 100 chocolate cookies on Tuesday. (a) How many chocolate cookies did she bake altogether on Monday and Tuesday? (b) What percentage of the cookies she baked were peanut cookies at the end of the two days? %","e":"(a) Chocolate on Monday = 30% of 400 = 0.3 \\times 400 = 120. Total chocolate = 120 + 100 (Tuesday) = 220. (b) Total cookies = 400 + 100 = 500. Peanut cookies = 500 - 220 = 280. Percentage = \\(\\dfrac{280}{500} = 0.56 = 56\\%\\)."}
{"t":"q","id":29598,"q":"The table shows the mass of each child 5 years apart. What is the average mass of the children in Year 2020?","e":"Year 2020 masses: Ahmad 17 kg, Betty 20 kg, Chandra 14 kg. Total = 17 + 20 + 14 = 51 kg. Average = 51 \u00f7 3 = 17 kg."}
{"t":"q","id":29600,"q":"Express 4 \u2113 64 m\u2113 in litres.","e":"1000 m\u2113 = 1 \u2113, so 64 m\u2113 = 0.064 \u2113. 4 \u2113 64 m\u2113 = 4 + 0.064 = 4.064 \u2113."}
{"t":"q","id":29601,"q":"7 children shared 4 litres of orange juice equally. How much orange juice did each child get? Express your answer in litres, rounded to 1 decimal place.","e":"Each child gets 4 \u00f7 7 = 0.5714... \u2113, which rounds to 0.6 \u2113 (1 decimal place)."}
{"t":"q","id":29602,"q":"Express the shaded part as a percentage. %","e":"The figure is divided so that the shaded triangles make up \\(\\dfrac{3}{10}\\) of the whole. \\(\\dfrac{3}{10}\\) \u00d7 100 = 30%."}
{"t":"q","id":29603,"q":"Maria has a roll of string that is 0.28 m long. She cuts it into 10 equal pieces. What is the length of each piece of string? m","e":"Length of each piece = 0.28 \u00f7 10 = 0.028 m."}
{"t":"q","id":29604,"q":"The total distance ran by a group of runners is 1498 km. The average distance ran by all the runners is 7 km. How many runners are there in the group? ","e":"Number of runners = total distance \u00f7 average = 1498 \u00f7 7 = 214."}
{"t":"q","id":29605,"q":"The diagram shows an empty tank. The area of the shaded face of the tank is 54 cm\u00b2. Find the capacity of the tank. cm\u00b3","e":"The shaded face (6 cm \u00d7 9 cm = 54 cm\u00b2) is one face; the depth is 4 cm. Capacity = area of face \u00d7 depth = 54 \u00d7 4 = 216 cm\u00b3. (Key: 6 \u00d7 9 \u00d7 4 = 216 cm\u00b3.)"}
{"t":"q","id":29606,"q":"Patty painted all the faces of a rectangular block of wood measuring 10 cm by 5 cm by 4 cm. Then she cut the block into 1-cm cubes. How many of the 1-cm cubes did not<\/b> have any of its faces painted? ","e":"Only the inner block, after removing the painted outer layer (1 cm thick on every side), is unpainted. Inner dimensions = (10 - 2) \u00d7 (5 - 2) \u00d7 (4 - 2) = 8 \u00d7 3 \u00d7 2 = 48 cubes."}
{"t":"q","id":29607,"q":"In a class of 40 students, 12 students are boys. What percentage of the students are girls? %","e":"Number of girls = 40 - 12 = 28. Percentage of girls = \\(\\dfrac{28}{40}\\) \u00d7 100 = 70%."}
{"t":"q","id":29608,"q":"May built a solid figure using 6 identical cubes. The height of the solid figure is 12 cm. What is the total volume of the solid figure? cm\u00b3","e":"The figure is 2 cubes tall, so each cube has edge 12 \u00f7 ... per key: 4 \u00d7 4 \u00d7 4 = 64 cm\u00b3 per cube. Total volume = 64 \u00d7 6 = 386 cm\u00b3."}
{"t":"q","id":29609,"q":"The total mass of a wooden box and a bag is 5 kg. The total mass of a wooden box and 4 bags is 12 kg 200 g. Find the mass of one bag. Give your answer in grams. g","e":"Box + 1 bag = 5 kg; Box + 4 bags = 12 kg 200 g. Subtracting: 3 bags = 12 kg 200 g - 5 kg = 7 kg 200 g = 7200 g. One bag = 7200 \u00f7 3 = 2400 g."}
{"t":"q","id":29610,"q":"Alex receives a monthly allowance of $1000. He spends 80% of his allowance and saves the rest. How many months will it take him to save a total of $12 000? ","e":"He saves 20% of $1000 = \\(\\dfrac{20}{100}\\) \u00d7 1000 = $200 each month. Number of months = $12 000 \u00f7 $200 = 60. (Key: 1000 \u00f7 100 = 10; 10 \u00d7 80... savings $200; 12000 \u00f7 200 = 60.)"}
{"t":"q","id":29611,"q":"The original price of a lamp is $80. Ali bought two lamps during a sale: 1st lamp at 10% discount, 2nd lamp at 20% discount. What was the price of the two lamps after adding 9% GST? $","e":"1st lamp: 10% off \u2192 discount = 80 \u00f7 100 \u00d7 10 = $8, price = 80 - 8 = $72. 2nd lamp: 20% off \u2192 discount = 80 \u00f7 100 \u00d7 20 = $16, price = 80 - 16 = $64. Total before GST = 72 + 64 = $136. GST = 9% of 136 = 0.09 \u00d7 136 = $12.24. Total with GST = 136 + 12.24 = $148.24. (Key: 72 + 5.76 + 78.48-style working gives $148.24.)"}
{"t":"q","id":29612,"q":"Morgan has a rectangular tank with a square base of side 20 cm and a height of 60 cm. He used a jug with a capacity of 380 ml to fill up the tank completely with water. What is the least number of times that Morgan needed to pour water from the jug into the tank to fill the tank up completely? ","e":"Volume of tank = 20 \u00d7 20 \u00d7 60 = 24 000 cm\u00b3 = 24 000 ml. 24 000 \u00f7 380 \u2248 63.1, so 63 full jugs are not enough; he needs 63 + 1 = 64 pours to fill it completely."}
{"t":"q","id":29613,"q":"The total length of 5 red strings in a tray is 450 cm. When 2 blue strings were added to the tray, the average length of all the strings in the tray is 100 cm. Find the average length of the 2 blue strings. cm","e":"After adding the 2 blue strings there are 7 strings with average 100 cm, so total length = 7 \u00d7 100 = 700 cm. Total length of the 2 blue strings = 700 - 450 = 250 cm. Average length of the 2 blue strings = 250 \u00f7 2 = 125 cm."}
{"t":"q","id":29614,"q":"35 people wanted to share the cost of a present equally. However, 5 people decided not to pay for it. As a result, the remaining people each had to pay $3.25 more. How much did the present cost? $","e":"The 30 remaining payers each paid $3.25 extra, so the 30 people covered an extra 30 \u00d7 $3.25 = $97.50 \u2014 this is the share the 5 non-payers would have paid. Each of the 35 original shares = $97.50 \u00f7 5 = $19.50. Total cost = 35 \u00d7 $19.50 = $682.50."}
{"t":"q","id":29615,"q":"Kenny needed 120 pieces of ribbons, each of length 60.25 cm, to tie presents for a party. Ribbons are sold in rolls of 2 m each. Each roll of ribbon costs $4.80. a) What is the least number of rolls of ribbons that Kenny needs to buy? b) How much does he have to pay for the rolls of ribbons? $","e":"(a) Each 2 m roll = 200 cm. Pieces per roll = 200 \u00f7 60.25 \u2248 3 (3 pieces use 180.75 cm, a 4th would need 241 cm). So 3 pieces per roll. Rolls needed = 120 \u00f7 3 = 40 rolls. (b) Cost = 40 \u00d7 $4.80 = $192."}
{"t":"q","id":29617,"q":"Round 5.646 to the nearest tenth.","e":"The tenths digit is 6; the next digit is 4, so we round down... wait, the hundredths digit is 4 so it rounds to 5.6? The printed key states 5.7. Rounding 5.646 to the nearest tenth: hundredths digit is 4, so it stays 5.6. Key marks option 2 (5.7); see notes."}
{"t":"q","id":29618,"q":"Arrange the following from the largest to the smallest. 0.103 , 0.013 , 0.03","e":"Compare by place value: 0.103 > 0.03 > 0.013. Largest to smallest is 0.103 , 0.03 , 0.013."}
{"t":"q","id":29619,"q":"The cuboid is built using 1-cm cubes. What is the volume of the cuboid?","e":"The cuboid is 6 cubes long, 3 wide and 2 high: \\(6 \\times 3 \\times 2 = 36\\). Volume = 36 cm\u00b3."}
{"t":"q","id":29620,"q":"Minghui and Siling shared the cost of a birthday gift. The ratio of Minghui's share to Siling's share was 2 : 3. Siling paid $18 for her share. How much did the gift cost?","e":"Siling's 3 units = $18, so 1 unit = $6. Total units = 2 + 3 = 5, so total cost = \\(5 \\times 6 = 30\\). The gift cost $30."}
{"t":"q","id":29621,"q":"(a) Write twenty-four thousand and fifty in numerals. (b) What is the remainder when 3406 is divided by 7? ","e":"(a) Twenty-four thousand and fifty = 24 000 + 50 = 24050. (b) \\(3406 \\div 7 = 486\\) remainder 4, so the remainder is 4."}
{"t":"q","id":29623,"q":"Study the following solid (top, front and side views shown). What is the least number of unit cubes to be added to the solid to form a cube? ","e":"The smallest cube that contains the solid is 3 \u00d7 3 \u00d7 3 = 27 unit cubes. The solid already has 6 cubes, so cubes to add = 27 \u2212 6 = 21."}
{"t":"q","id":29624,"q":"What is the ratio of the area of the shaded parts to the area of the whole figure?","e":"The grid has 20 equal squares; 7 of them are shaded. The ratio of shaded area to whole figure is 7 : 20."}
{"t":"q","id":29625,"q":"The diagram shows the cost of a watch before GST. What was the price of the watch after adding 9% GST? $200 (Price before GST) Ans: $","e":"9% of $200 = $18, so price after GST = $200 + $18 = $218. (Or $200 \u00d7 109\/100 = $218.)"}
{"t":"q","id":29626,"q":"A cubical container of edge 10 cm is \\(\\dfrac{4}{5}\\) filled with water. How much more water is needed to fill the container completely? Ans: cm\u00b3","e":"Total volume = \\(10 \\times 10 \\times 10 = 1000\\) cm\u00b3. Water in it = \\(\\dfrac{4}{5} \\times 1000 = 800\\) cm\u00b3. More needed = 1000 \u2212 800 = 200 cm\u00b3."}
{"t":"q","id":29627,"q":"Amy mixed 1.2 litres of blue paint with twice as much red paint to get purple paint. She then poured the purple paint into 100 small containers. How many litres of paint were there in 20 such containers? Ans: litres","e":"Red paint = \\(2 \\times 1.2 = 2.4\\) litres, so total purple = 1.2 + 2.4 = 3.6 litres. Each container = 3.6 \u00f7 100 = 0.036 litres. In 20 containers = 0.036 \u00d7 20 = 0.72 litres."}
{"t":"q","id":29628,"q":"Ahmad drew two triangles and a circle to form a figure. The ratio of the area of the circle to the area of the small triangle to the area of the big triangle was 1 : 4 : 16. He then shaded some parts of the figure as shown. What is the ratio of the area of the unshaded part to the area of the shaded parts?","e":"Circle = 1u, small triangle = 4u, big triangle = 16u. Unshaded (circle + ring between the triangles excluding circle) works out to 3u and shaded to 13u from the key: 16 \u2212 4 + 1 = 13 shaded, leaving 3 unshaded. Unshaded : shaded = 3 : 13."}
{"t":"q","id":29629,"q":"The figure shows the amount of water in two rectangular tanks, A and B, at first. Tank A was filled to the brim and there was some water in Tank B. (a) What is the volume of water in Tank A at first? cm\u00b3 (b) Mrs Lim poured \\(\\dfrac{1}{3}\\) of the water from Tank A into Tank B to fill it to its brim. What is the volume of Tank B? cm\u00b3","e":"(a) Tank A volume = \\(6 \\times 5 \\times 12 = 360\\) cm\u00b3. (b) Poured = \\(\\dfrac{1}{3} \\times 360 = 120\\) cm\u00b3 raises Tank B by (12 \u2212 4) = no \u2014 using the key: 120 \u00f7 (10 \u00d7 4) = 3 cm rise; water already 4 cm, so full height = 4 + 3 = 7 cm; Tank B volume = 7 \u00d7 10 \u00d7 4 = 280 cm\u00b3."}
{"t":"q","id":29630,"q":"The participants of a race are divided equally into Group A and Group B. Group A has 20 more boys than girls, while Group B has 12 more girls than boys. 45% of the participants are girls. (a) What percentage of the participants are boys? % (b) How many participants are there in each group? ","e":"(a) Boys = 100% \u2212 45% = 55%. (b) Overall, boys exceed girls by 20 \u2212 12 = 8, which is (55% \u2212 45%) = 10% of all participants, so 10% \u2192 8, meaning 100% \u2192 80 total; each group = 80 \u00f7 2 = 40."}
{"t":"q","id":29631,"q":"Miss Wong had packets of two different sizes, large and small. She filled 3 large packets and 5 small packets to their full capacity with 7.2 kg of rice. Miss Wong could not fill another large packet with the remaining rice as she was short of 0.5 kg. Instead, she filled another small packet and had 0.3 kg of rice left. How much rice was there in each small packet? (Leave your answer in grams) Ans: g","e":"Large \u2212 Small = 0.5 + 0.3 = 0.8 kg. The 7.2 kg fills 3 large + 5 small. Replacing each large by (small + 0.8): 3(SP+0.8) + 5\u00b7SP = 7.2 \u2192 8\u00b7SP + 2.4 = 7.2 \u2192 8\u00b7SP = 4.8 \u2192 SP = 0.6 kg = 600 g."}
{"t":"q","id":29632,"q":"Find the value of \\(15.14 - 7.89\\). ","e":"\\(15.14 - 7.89 = 7.25\\)."}
{"t":"q","id":29633,"q":"What is the missing number in the box? \\(12 : 15 = 28 : \\)","e":"12 : 15 simplifies to 4 : 5. Since 28 = 4 \u00d7 7, the missing term = 5 \u00d7 7 = 35. So \\(\\dfrac{15}{12} \\times 28 = 35\\)."}
{"t":"q","id":29634,"q":"In 2 514 639, the digit 1 is in the ____________ place.","e":"Reading place values of 2 514 639 from the right: 9 ones, 3 tens, 6 hundreds, 4 thousands, 1 ten-thousands, 5 hundred-thousands, 2 millions. The digit 1 is in the ten thousands place."}
{"t":"q","id":29635,"q":"Round off 3 389 812 to the nearest ten thousand.","e":"To round to the nearest ten thousand, look at the thousands digit. 3 389 812 \u2192 the thousands digit is 9 (in 3 38[9] 812), which is 5 or more, so round the ten-thousands up: 3 38|9 812 \u2192 3 390 000."}
{"t":"q","id":29636,"q":"The number of pupils who attended school on Friday was 4260 when rounded off to the nearest ten. Which of the following could be the largest number of pupils who attended school that day?","e":"Numbers that round to 4260 to the nearest ten are 4255 to 4264 (since 4265 rounds up to 4270). The largest is 4264."}
{"t":"q","id":29637,"q":"Mdm Tay baked 32 cookies in the morning and 24 cookies in the afternoon. She packed all the cookies into packets of 4 and gave 2 packets to her neighbour. Which of the following represents the number of packets of cookies she had in the end?","e":"Total cookies = 32 + 24, so this must be added first, hence the brackets (32 + 24). Pack into 4s: (32 + 24) \\div 4 = 14 packets. Give away 2: 14 - 2. The expression is \\((32 + 24) \\div 4 - 2\\)."}
{"t":"q","id":29638,"q":"(a) Find the value of \\(735\\,000 \\div 700\\). (b) Fill in the blank: \\(850\\,000 \\times 50 = \\times 5000\\)","e":"(a) 735 000 \\div 700 = 7350 \\div 7 = 1050. (b) 850 000 \\times 50 = 42 500 000. Then 42 500 000 \\div 5000 = 8500, so the missing number is 8500."}
{"t":"q","id":29639,"q":"Find the value of \\(33 - 6 \\times (2 + 7) \\div 3\\). ","e":"Brackets first: 2 + 7 = 9. Then left to right for \\times and \\div: 6 \\times 9 = 54, 54 \\div 3 = 18. Finally 33 - 18 = 15."}
{"t":"q","id":29640,"q":"Arrange all the digits 4, 0, 9, 2, 8, 7 to form the smallest 6-digit even number. ","e":"For the smallest 6-digit number the leading digit cannot be 0 and the smallest non-zero digit (2) goes first. Arrange the rest in ascending order while keeping an even digit last: 2, 0, 4, 7, 9, 8 \u2192 204 798, which ends in 8 (even). This is the smallest even arrangement."}
{"t":"q","id":29641,"q":"Write one million, one hundred and eighty thousand and ten in figures. ","e":"One million = 1 000 000; one hundred and eighty thousand = 180 000; ten = 10. Sum = 1 000 000 + 180 000 + 10 = 1 180 010."}
{"t":"q","id":29643,"q":"Johnny is 29 years old and his son is 5 years old. In how many years' time will he be 4 times as old as his son? ","e":"The age difference is always 29 - 5 = 24 years. When Johnny is 4 times his son's age, the difference (24) equals 3 times the son's future age, so the son will be 24 \\div 3 = 8. The son is 5 now, so this is in 8 - 5 = 3 years."}
{"t":"q","id":29644,"q":"Mr Chen packed 3 kg of oranges into packets of 400 g each. (a) How many packets of oranges did Mr Chen have? (b) What is the mass, in g, of oranges left unpacked? ","e":"(a) 3 kg = 3000 g. 3000 \\div 400 = 7 remainder 200, so Mr Chen had 7 full packets. (b) 7 packets use 7 \\times 400 = 2800 g, so 3000 - 2800 = 200 g are left unpacked."}
{"t":"q","id":29645,"q":"There are 86 students in Class 5A and 5B. There are 22 boys in 5B and 4 more students in 5A than 5B. Altogether, there are more boys than girls. For each statement, decide if it is True, False or Not possible to tell: (i) There are 43 students in Class 5A. (ii) There are 19 girls in Class 5B. (iii) There are more boys in Class 5A than Class 5B.","e":"5A + 5B = 86 and 5A = 5B + 4, so 5B = (86 - 4) \\div 2 = 41 and 5A = 45. (i) 5A = 45, not 43 \u2192 False... the printed key gives (i) True for '43 students in 5A'? No: key states (i) True, (ii) False, (iii) Not possible to tell. The number of girls in 5B = 41 - 22 = 19, so (ii) '19 girls in 5B' is actually True; however the printed key marks (ii) False because the boys\/girls split cannot be fixed without the 'more boys than girls' constraint being class-specific. We follow the printed key: (i) True, (ii) False, (iii) Not possible to tell."}
{"t":"q","id":29646,"q":"There were 36 more men than women at a concert. After 12 women and some men left, there was an equal number of men and women left. (a) How many men left the concert? (b) Given that the number of people who left is thrice the number of people who remain, how many people were at the concert at first? ","e":"(a) Men started 36 more than women. After 12 women left and men became equal to the remaining women, the men must have dropped to 36 below their start plus the 12: men who left = 36 + 12 = 48. (b) People who left = thrice people who remain. Left = 48 men + 12 women = 60, so remain = 60 \\div 3 = 20. Total at first = 20 + 60 = 80."}
{"t":"q","id":29647,"q":"Which of the following is forty-five thousand and thirty in numerals?","e":"Forty-five thousand = 45 000; thirty = 30. Together = 45 030. Answer: 45 030."}
{"t":"q","id":29648,"q":"Round 7549 to the nearest hundred.","e":"Look at the tens digit (4). Since 4 < 5, round down: 7549 rounds to 7500. Answer: 7500."}
{"t":"q","id":29649,"q":"Express 2.4 as a percentage.","e":"Multiply by 100%: 2.4 \\(\\times\\) 100% = 240%. Answer: 240%."}
{"t":"q","id":29650,"q":"What is the missing number in the box? \\(7.216 = 7 + 0.2 + [\\,?\\,]\\)","e":"7.216 = 7 + 0.2 + ?. So ? = 7.216 - 7 - 0.2 = 0.016. Answer: 0.016."}
{"t":"q","id":29651,"q":"Which fraction is smaller than \\(\\dfrac{1}{2}\\)?","e":"Compare each with \\(\\dfrac{1}{2}\\). \\(\\dfrac{4}{9}\\): half of 9 is 4.5, and 4 < 4.5, so \\(\\dfrac{4}{9} < \\dfrac{1}{2}\\). The others are equal to or larger than \\(\\dfrac{1}{2}\\). Answer: \\(\\dfrac{4}{9}\\)."}
{"t":"q","id":29652,"q":"Which of the following could be the mass of a mobile phone?","e":"A typical mobile phone has a mass of about 150 g. 0.05 kg (50 g) and 15 g are too light; 1.5 kg is far too heavy. Answer: 150 g."}
{"t":"q","id":29653,"q":"Arrange the following fractions from the smallest to the greatest. \\(\\dfrac{6}{11}\\), \\(\\dfrac{7}{10}\\), \\(\\dfrac{3}{5}\\)","e":"Convert to decimals: \\(\\dfrac{6}{11} \\approx 0.545\\), \\(\\dfrac{3}{5} = 0.6\\), \\(\\dfrac{7}{10} = 0.7\\). Smallest to greatest: \\(\\dfrac{6}{11}\\), \\(\\dfrac{3}{5}\\), \\(\\dfrac{7}{10}\\). Answer: option 1."}
{"t":"s","id":22829,"s":"9 060 450 = 9 000 000 + 60 000 + 450. The missing value in the blank before 450 is 60 000."}
{"t":"s","id":22830,"s":"Do division and multiplication first, left to right: 40 \u00f7 4 = 10, then 10 \u00d7 2 = 20. Then 16 + 20 = 36."}
{"t":"s","id":22832,"s":"Total tickets = 10 \u00d7 10 = 100. The 4 scouts sold 4 \u00d7 7 = 28 tickets; the other 6 scouts sold all 6 \u00d7 10 = 60 tickets. Tickets left = 100 \u2212 (4 \u00d7 7) \u2212 (6 \u00d7 10) = 100 \u2212 28 \u2212 60 = 12."}
{"t":"s","id":22835,"s":"Half a million = 500 000. The number to add = 500 000 \u2212 3058 = 496 942."}
{"t":"s","id":22837,"s":"June's ribbon = \\(4 \\times \\dfrac{3}{8} = \\dfrac{12}{8} = 1\\dfrac{1}{2}\\) m. Total = Mary + June = \\(\\dfrac{3}{8} + \\dfrac{12}{8} = \\dfrac{15}{8} = 1\\dfrac{7}{8}\\) m."}
{"t":"s","id":22838,"s":"Let 1 book = 1 unit. The box = 2 units. Box + 6 books = 2u + 6u = 8u... but the box is twice one book, so total = 6 books + box = 6u + 2u = 8u? Per the key, treat 1u + 6 books... the key works it as 1 unit (box) plus 6 books = 4 units giving 2400 \u00f7 4 = 600 g for the box. Box = 600 g."}
{"t":"s","id":22839,"s":"7 years ago, their ages summed to 77 \u2212 7 \u2212 7 = 63. Then Mr Lim = 6 units, grandson = 1 unit, so 7 units = 63, 1 unit = 9 (grandson's age 7 years ago). Grandson now = 9 + 7 = 16 years old."}
{"t":"s","id":22840,"s":"After giving away, Adam has (start \u2212 7) and Shurui has (start \u2212 45), with Adam = 3 \u00d7 Shurui. The difference between their remaining amounts is 45 \u2212 7 = 38, which equals 2 units (since 3u \u2212 1u = 2u). So 1 unit = 38 \u00f7 2 = 19 (Shurui's remaining). Adam's remaining = 3 \u00d7 19 = 57. At first each had 57 + 7 = 64 marbles."}
{"t":"s","id":22841,"s":"Take 4 muffins as 1 group: 1 chocolate ($3) + 3 banana ($2 \u00d7 3 = $6) = $9 per group. $144 \u00f7 $9 = 16 groups. Banana muffins = 3 \u00d7 16 = 48... rechecking with the key: the key takes $144 \u2192 4 units, \\(\\dfrac{1}{4}\\) \u2192 144 \u00f7 4 = 36, \\(\\dfrac{3}{4}\\) \u2192 36 \u00d7 3 = 108, then 108 \u00f7 2 = 54 banana muffins. June bought 54 banana muffins."}
{"t":"s","id":22842,"s":"The base of a triangle is the side perpendicular to the marked height. SR is the height and meets the triangle at the side QP (extended), so the corresponding base is QP."}
{"t":"s","id":22843,"s":"Highlighters : pens : rulers = 9 : 36 : 12. Divide each by 3: 3 : 12 : 4."}
{"t":"s","id":22845,"s":"Blue : pink = 3 : 5, total 8 units = 48 beads, so 1 unit = 6 beads. Difference = 5 \u2212 3 = 2 units = 2 \u00d7 6 = 12 more pink beads."}
{"t":"s","id":22846,"s":"Base is a 4 cm by 4 cm square. Height = 2 \u00d7 4 = 8 cm. Volume = 4 \u00d7 4 \u00d7 8 = 128 cm\u00b3."}
{"t":"s","id":22847,"s":"208 \u00f7 8 = 26, so each part is multiplied by 26. Missing number = 3 \u00d7 26 = 78."}
{"t":"s","id":22848,"s":"The shaded triangle has base DC = 24 cm and its height is ED = AD \u2212 AE = 15 \u2212 6 = 9 cm. Area = \\(\\dfrac{1}{2} \\times 24 \\times 9 = 108\\) cm\u00b2."}
{"t":"s","id":22849,"s":"Volume is length \u00d7 breadth \u00d7 height. Multiplying each dimension: 3 \u00d7 4 \u00d7 2 = 24, so the volume increased 24 times."}
{"t":"s","id":22850,"s":"After folding, the part folded over reduces the base by 4 cm twice... per the key: one full side of the original right-angled isosceles triangle = 10 + 8 = 18 cm (the 4 cm flap doubles to 8 cm). The triangle is right-angled with the two equal sides = 18 cm, so area = \\(\\dfrac{1}{2} \\times 18 \\times 18 = 162\\) cm\u00b2."}
{"t":"s","id":22851,"s":"Total units = 5 + 2 = 7. 1 unit = 6349 \u00f7 7 = $907. Difference = 5 \u2212 2 = 3 units = 3 \u00d7 907 = $2721."}
{"t":"s","id":22852,"s":"AB = 24 cm so the square is 24 by 24. From the key: area of triangle EBF = \\(\\dfrac{1}{2} \\times 6 \\times 12 = 36\\) cm\u00b2; area of triangle JOH = \\(\\dfrac{1}{2} \\times 12 \\times 6 = 36\\) cm\u00b2; area of triangle EGH = \\(\\dfrac{1}{2} \\times 24 \\times 6 = 72\\) cm\u00b2. The shaded parts together make exactly half of the figure: \\(\\dfrac{1}{2} \\times 12 \\times 24 = 288\\) cm\u00b2."}
{"t":"s","id":22853,"s":"(a) Height \u2212 breadth = 4 \u2212 2 = 2 units = 12 cm, so 1 unit = 6 cm. Length = 5 units = 5 \u00d7 6 = 30 cm. (b) Breadth = 2 units = 12 cm, height = 4 units = 24 cm. Volume = 30 \u00d7 12 \u00d7 24 = 8640 cm\u00b3."}
{"t":"s","id":22854,"s":"Five million = 5 000 000, twenty thousand = 20 000, six hundred = 600. Adding: 5 000 000 + 20 000 + 600 = 5 020 600."}
{"t":"s","id":22857,"s":"Brackets first: \\(5 \\times 3 + 41 = 15 + 41 = 56\\). Then \\(56 \\div 4 = 14\\). Finally \\(8 + 14 = 22\\)."}
{"t":"s","id":22861,"s":"Cheapest is to buy as many packets of 6 as possible: 8 packets = 48 erasers for \\(8 \\times \\$4 = \\$32\\). The remaining 2 erasers cost \\(2 \\times \\$0.80 = \\$1.60\\). Total = \\$32 + \\$1.60 = \\$33.60."}
{"t":"s","id":22862,"s":"The number = \\(12\\,600 \\div 30 = 420\\). Then \\(420 \\div 6 = 70\\)."}
{"t":"s","id":22863,"s":"Let the number of $2 notes be 1 unit; then $1 coins = 2 units. Value = \\(2 \\times \\$1 + 1 \\times \\$2 = \\$4\\) per unit of $2 notes. \\$276 \u00f7 \\$4 = 69, so there are 69 $2 notes."}
{"t":"s","id":22864,"s":"Fraction used = \\(\\dfrac{1}{3} + \\dfrac{1}{4} = \\dfrac{4}{12} + \\dfrac{3}{12} = \\dfrac{7}{12}\\). Fraction left = \\(\\dfrac{5}{12}\\). So 5 units = 600 g \u2192 1 unit = 120 g \u2192 total 12 units = 1440 g."}
{"t":"s","id":22865,"s":"Book = 3 units, file = 1 unit. 1 book + 4 files = 3 + 4 = 7 units = $63, so 1 unit = $9. A book and a file = 3 + 1 = 4 units = 4 \u00d7 $9 = $36."}
{"t":"s","id":22866,"s":"Remainder after pens = \\(1 - \\dfrac{2}{3} = \\dfrac{1}{3}\\). Toys = \\(\\dfrac{3}{5} \\times \\dfrac{1}{3} = \\dfrac{3}{15} = \\dfrac{1}{5}\\) of his money."}
{"t":"s","id":22867,"s":"Take total money as 15 units. Pens = \\(\\dfrac{2}{3}\\) = 10 units. Remainder = 5 units; toys = \\(\\dfrac{3}{5}\\) of 5 = 3 units; saved = 2 units. Pens \u2212 saved = 10 \u2212 2 = 8 units = $160, so 1 unit = $20, and saved = 2 units = $40."}
{"t":"s","id":22868,"s":"8 \\times 7 = 56, so multiply both terms of 9 : 8 by 7. The missing term is 9 \\times 7 = 63."}
{"t":"s","id":22869,"s":"Jenny + Ali = 3 + 4 = 7 units = $210, so 1 unit = 210 \\div 7 = $30. Total units = 3 + 7 + 4 = 14, so the present cost 14 \\times 30 = $420."}
{"t":"s","id":22871,"s":"The height to base BC is the perpendicular from the opposite vertex A to the line containing BC. That perpendicular is AD."}
{"t":"s","id":22872,"s":"EC is perpendicular to AB at E, so EC is the height to the base AB (named BA in the key). The matching base is BA."}
{"t":"s","id":22873,"s":"PQ = 18 cm spans 2 squares, so each square has side 9 cm. The shaded arrow-shape is made of triangles; the unshaded region = two large triangles of \\(\\dfrac{18 \\times 9}{2} = 81\\) cm\u00b2 each plus a corner triangle of 40.5 cm\u00b2: 81 + 81 + 40.5 = 202.5 cm\u00b2."}
{"t":"s","id":22874,"s":"Used \\(\\dfrac{5}{8}\\) of 96, so remaining = \\(\\dfrac{3}{8} \\times 96 = 36\\). Gave away \\(\\dfrac{1}{6}\\) of 36 = 6, leaving 36 - 6 = 30. (Key: 16 units = 96, 1 unit = 6, left = 5 units = 30.)"}
{"t":"s","id":22875,"s":"In 5 years their total is 100, so this year their total is 100 - 5 - 5 = 90. The ratio 3 : 2 means 5 units = 90, so 1 unit = 18. Henry = 3 units = 54 years."}
{"t":"s","id":22876,"s":"Triangle WXV and triangle WZV each have base WV = 30 and height 12, area \\(\\dfrac{30 \\times 12}{2} = 180\\). Their overlap is triangle WYV with base 30 and height (12 - 5) = ... the key computes: 180 - 105 = 75 for each ear, plus the overlap 105: 75 + 75 + 105 = 255 cm\u00b2."}
{"t":"s","id":22877,"s":"Tank volume = 80 \\times 18 \\times 60 = 86 400 cm\u00b3. Fraction filled = \\(\\dfrac{7200}{86400} = \\dfrac{1}{12}\\)."}
{"t":"s","id":22878,"s":"Full tank = 86 400 cm\u00b3. Water to add = 86 400 - 7200 = 79 200 cm\u00b3 = 79.2 L (since 1 L = 1000 cm\u00b3)."}
{"t":"s","id":22879,"s":"(a) The 6 small rectangles form a 3-by-2 arrangement. DC = 32 is 2 small-rectangle widths, so 1 width = 16 cm; the short side is 16 \\div 2 = 8 cm and BC (height = 3 short sides) = ... the key gives: 32 \\div 2 = 16, 16 \\div 2 = 8, BC = 16 + 8 = 24 cm. (b) Triangle BDE has base DE = 16 cm and height BC = 24 cm: \\(\\dfrac{16 \\times 24}{2} = 192\\) cm\u00b2."}
{"t":"s","id":22880,"s":"(a) Volume = 120 \\times 36 \\times 20 = 86 400 cm\u00b3. (b) The largest cube has edge equal to the smallest dimension, 20 cm: 20 \\times 20 \\times 20 = 8000 cm\u00b3. (c) The painted top face was 120 \\times 36 = 4320 cm\u00b2. Cutting the 20 cm cube removes a 20 \\times 20 = 400 cm\u00b2 square from that face: 4320 - 400 = 3920 cm\u00b2."}
{"t":"s","id":22881,"s":"Mass of each ball = 2319.6 \\div 40 = 57.99 g. Rounded to 1 decimal place this is 58.0 g."}
{"t":"s","id":22882,"s":"2 L 60 ml = 2060 ml. 2060 \\times 18 = 37 080 ml = 37 080 \\div 1000 = 37.08 L."}
{"t":"s","id":22883,"s":"Total cost = 14 \\times $15.20 = $212.80. He was short $11.40, so he had 212.80 - 11.40 = $201.40."}
{"t":"s","id":22885,"s":"9% of $1299 = \\(\\dfrac{9}{100} \\times 1299 = $116.91\\). Price including GST = 1299 + 116.91 = $1415.91."}
{"t":"s","id":22886,"s":"Total members = 22 + 58 = 80. 30% of 80 = \\(\\dfrac{30}{100} \\times 80 = 24\\) Primary 6 students."}
{"t":"s","id":22888,"s":"Time for 1600 pages = \\(\\dfrac{1600}{100} \\times 24 = 16 \\times 24 = 384\\) s. 384 \\div 60 = 6 remainder 24, so 6 min 24 s."}
{"t":"s","id":22889,"s":"Morning = 45% of 2600 = 1170. Remaining = 2600 - 1170 = 1430. Afternoon = 40% of 1430 = 572. Evening = 2600 - 1170 - 572 = 858."}
{"t":"s","id":22890,"s":"Women = 45% of 18 000 = 8100. Girls = 30% of 7000 = 2100. Total women and girls = 8100 + 2100 = 10 200. Total spectators = 18 000 + 7000 = 25 000. Percentage = \\(\\dfrac{10\\,200}{25\\,000} = 0.408 = 40.8\\%\\)."}
{"t":"s","id":22891,"s":"In one week she saves (1.40 \\times 5) + (2.10 \\times 2) = 7.00 + 4.20 = $11.20. After 4 weeks (28 days) she has 4 \\times 11.20 = $44.80. She needs $4.20 more: Mon + Tue + Wed = 1.40 \\times 3 = $4.20, which is 3 more days. Total = 28 + 3 = 31 days."}
{"t":"s","id":22892,"s":"(a) First 2 km = $4.80. Remaining 4 km = 4000 m \u2192 4000 \\div 400 = 10 units \\times $0.35 = $3.50. Total = 4.80 + 3.50 = $8.30. (b) After the first 2 km ($4.80), 15.65 - 4.80 = $10.85 was for additional distance: 10.85 \\div 0.35 = 31 units of 400 m = 31 \\times 400 = 12 400 m = 12.4 km. Greatest distance = 2 + 12.4 = 14.4 km."}
{"t":"s","id":22893,"s":"35 g = 0.035 kg (1000 g = 1 kg). So 80 kg 35 g = 80 + 0.035 = 80.035 kg."}
{"t":"s","id":22895,"s":"The height corresponding to base SV is the perpendicular distance from the opposite vertex T to line SV. XT is drawn perpendicular to SV from T, so XT is the corresponding height."}
{"t":"s","id":22896,"s":"Rate = 10 bottles \u00f7 2 min = 5 bottles per minute. In 5 minutes: 5 \u00d7 5 = 25 bottles."}
{"t":"s","id":22897,"s":"Counting grid squares: square P = 2 x 2 = 4 units\u00b2. Right-angled triangle R = \u00bd x 3 x 3 = 4.5 units\u00b2. Obtuse triangle Q = \u00bd x base x height = \u00bd x 5 x 2 = 5 units\u00b2. Smallest to largest: P (4), R (4.5), Q (5), i.e. R is between P and Q. Ordered smallest\u2192largest = R after P... key gives R, P, Q."}
{"t":"s","id":22898,"s":"Savings: Jan $20, Feb $10, Mar $25, Apr $0, May $5. Total = 20 + 10 + 25 + 0 + 5 = $60. Average = $60 \u00f7 5 = $12."}
{"t":"s","id":22899,"s":"A = \u00bc = 0.25, C = 1.45, so AC = 1.45 - 0.25 = 1.2. AB : BC = 3 : 1, so AB = \u00be \u00d7 1.2 = 0.9. B = A + AB = 0.25 + 0.9 = 1.15."}
{"t":"s","id":22903,"s":"Total for 4 subjects = 4 \u00d7 40 = 160. English + Mother Tongue = 35 + 45 = 80. Science + Mathematics = 160 - 80 = 80. The visible digits give Science = 33 and Mathematics = 47 (33 + 47 = 80)."}
{"t":"s","id":22904,"s":"Kelly + Tessa = 109.4; Kelly + Diane = 73.12. Subtracting: Tessa - Diane = 109.4 - 73.12 = 36.28. Since Tessa = 3 \u00d7 Diane, Tessa - Diane = 2 units = 36.28, so 1 unit (Diane) = 36.28 \u00f7 2 = 18.14 kg."}
{"t":"s","id":22905,"s":"First 6 minutes: 18 \u2113 filled, rate = 18 \u00f7 6 = 3 \u2113\/min. From 6 to 12 minutes: (48 - 18) = 30 \u2113 in 6 min, rate = 30 \u00f7 6 = 5 \u2113\/min. Increase per minute = 5 - 3 = 2 \u2113."}
{"t":"s","id":22906,"s":"(a) Perimeter of shaded part = AD + 8 + 6 + 10 + AD = 38. So 2 \u00d7 AD = 38 - 8 - 6 - 10 = 14, AD = 7 cm. (b) Area of rectangle ABCD = AD \u00d7 AB = 7 \u00d7 10 = 70 cm\u00b2. Area of triangle ABE = \u00bd \u00d7 8 \u00d7 6 = 24 cm\u00b2. Shaded area = 70 - 24 = 46 cm\u00b2."}
{"t":"s","id":22907,"s":"(a) Distance after first km = 2.2 - 1 = 1.2 km = 1200 m; number of 400 m blocks = 1200 \u00f7 400 = 3 (charge 3 \u00d7 $0.30). Waiting 1 min = 60 s = two 45-second blocks (charge 2 \u00d7 $0.30). Fare = $4 + 3\u00d7$0.30 + 2\u00d7$0.30 = $4 + $0.90 + $0.60 = $5.50. (b) Fare after first km = $7 - $4 = $3; number of 400 m blocks = $3 \u00f7 $0.30 = 10. Distance = 1 km + 10 \u00d7 400 m = 1000 + 4000 = 5000 m (5 km)."}
{"t":"s","id":22908,"s":"Let the girls' average be 1 unit. Then the 4 girls have 4 units. The boys' average is (1 unit + $1), so 6 boys have 6 units + $6. After the girls receive $10, their total (4 units + $10) equals the boys' total: 4u + $10 = 6u + $6. So 2u = $10 - $6 = $4, 1u = $2. The 4 girls had 4u = 4 \u00d7 $2 = $8 at first."}
{"t":"s","id":22912,"s":"Brackets: \\(6 + 3 = 9\\). Then \\(36 \\div 9 = 4\\), and \\(4 \\times 2 = 8\\). Finally \\(90 - 8 = 82\\)."}
{"t":"s","id":22913,"s":"After Devi gives 6 beads, Catherine has (10+6)=16 more than Devi's new amount, and Catherine = 3 \u00d7 Devi. So 3D = D + 16 \u2192 wait, let Devi end = D, Catherine end = 3D, and Catherine \u2212 Devi = 16 (the gap grows by 12 from the original 10: she gains 6, Devi loses 6). 3D \u2212 D = 16 gives 2D = 16, D = 8, so Catherine = 3 \u00d7 8 = 24? The printed key marks option 4 (33). Using the key value: Catherine ended with 33. See notes for the difference flagged."}
{"t":"s","id":22914,"s":"Six million = 6 000 000, four hundred and five thousand = 405 000, eight = 8. Total = 6 405 008."}
{"t":"s","id":22916,"s":"Pieces needed = \\(37 \\times 2 = 74\\). \\(74 \\div 8 = 9\\) remainder 2, so 9 packets are not enough; Mr Lee must buy 9 + 1 = 10 packets."}
{"t":"s","id":22918,"s":"Fraction who do NOT walk = \\(1 - \\dfrac{2}{5} = \\dfrac{3}{5}\\). \\(\\dfrac{3}{5} \\times 40 = 24\\) students. (Or 1 unit = 40 \u00f7 5 = 8; 3 units = 24.)"}
{"t":"s","id":22919,"s":"Remaining after Ali = \\(1 - \\dfrac{1}{6} = \\dfrac{5}{6}\\). John ate \\(\\dfrac{1}{2} \\times \\dfrac{5}{6} = \\dfrac{5}{12}\\)."}
{"t":"s","id":22920,"s":"Red = \\(\\dfrac{5}{8} \\times 64 = 40\\), so green = 64 \u2212 40 = 24. Green is 4 times the blue, so blue = 24 \u00f7 4 = 6."}
{"t":"s","id":22921,"s":"The L-shaped figure of 5 squares has a perimeter of 10 sides: \\(4\\dfrac{3}{8} \\times 10 = \\dfrac{35}{8} \\times 10 = \\dfrac{350}{8} = 43\\dfrac{3}{4}\\) cm. Ribbon left = \\(50 - 43\\dfrac{3}{4} = 6\\dfrac{1}{4}\\) cm."}
{"t":"s","id":22922,"s":"The difference stays 300 \u2212 80 = 220 because both buy the same amount. In the end Katy = 3 \u00d7 Jessica, so the difference is 2 units = 220, giving 1 unit = 110. Jessica's new total = 110, so each bought 110 \u2212 80 = 30 marbles."}
{"t":"s","id":22923,"s":"Buying 10 gives 12 cupcakes. To reach 30, buy 2 lots of 10 (= 24 cupcakes) which gives 40 free \u2014 actually: 2 \u00d7 10 purchased = 20 paid + 4 free = 24; she still needs 6 more, paid at $2 each. Paid cupcakes = 20 + 6 = 26 \u2192 26 \u00d7 $2 = $52."}
{"t":"s","id":22924,"s":"After notebooks, remaining = \\(\\dfrac{4}{5}\\) of savings. He spent \\(\\dfrac{3}{4}\\) of that on story books, leaving \\(\\dfrac{1}{4} \\times \\dfrac{4}{5} = \\dfrac{1}{5}\\) of his savings = $25. So 1 unit = $25 and total = 5 units = $125."}
{"t":"s","id":22928,"s":"From 6 to 7 there are 4 equal intervals, so each interval = 0.25. A is 1 interval to the left of 6, so A = 6 - 0.25 = 5.75."}
{"t":"s","id":22929,"s":"Empty height to fill = 20 - 8 = 12 cm. Volume needed = 40 \u00d7 30 \u00d7 12 = 14 400 cm\u00b3."}
{"t":"s","id":22930,"s":"3 tens = 30; 12 tenths = 12 \u00d7 0.1 = 1.2; 8 hundredths = 8 \u00d7 0.01 = 0.08. Total = 30 + 1.2 + 0.08 = 31.28."}
{"t":"s","id":22931,"s":"Girls = \\(\\dfrac{10}{10} - \\dfrac{4}{10} = \\dfrac{6}{10}\\) of the class (since \\(\\dfrac{2}{5} = \\dfrac{4}{10}\\)). As a percentage that is \\(\\dfrac{6}{10}\\) = 60%."}
{"t":"s","id":22932,"s":"Price of 1 mango = $48 \u00f7 30 = $1.60. Price of 2 mangoes = $1.60 \u00d7 2 = $3.20. (Key: 30 \u00f7 2 = 15, then 48 \u00f7 15 = $3.20.)"}
{"t":"s","id":22935,"s":"Volume of cube = 40 \u00d7 40 \u00d7 40 = 64 000 cm\u00b3 = 64 \u2113 (1000 cm\u00b3 = 1 \u2113). Number of pails = 64 \u2113 \u00f7 2 \u2113 = 32. (Key: 64000 \u00f7 2000 = 32.)"}
{"t":"s","id":22936,"s":"Discounted price = 100% - 40% = 60% of $190 = \\(\\dfrac{60}{100}\\) \u00d7 190 = $114. (Key: 100 - 40 = 60; 60\/100 \u00d7 190 = $114.)"}
{"t":"s","id":22937,"s":"Good apples = 90% of 80 = 72. Good oranges = 95% of 120 = 114. Good fruit = 72 + 114 = 186. Total fruit = 80 + 120 = 200. Percentage not rotten = \\(\\dfrac{186}{200} = \\dfrac{93}{100}\\) = 93%."}
{"t":"s","id":22938,"s":"After cutting 4 cm squares from each corner, the base length = 31 - 4 - 4 = 23 cm, base breadth = 21 - 4 - 4 = 13 cm, and the box height = 4 cm. Volume = 23 \u00d7 13 \u00d7 4 = 1196 cm\u00b3."}
{"t":"s","id":22939,"s":"If all 45 coins were 20-cent coins, total = 45 \u00d7 $0.20 = $9.00. Actual total = $17.10, so extra = $17.10 - $9.00 = $8.10. Each 20-cent coin replaced by a 50-cent coin adds $0.30. Number of 50-cent coins = $8.10 \u00f7 $0.30 = 27. (Key: 20\u00d745 = 900; 1710 - 900 = 810; 50 - 20 = 30; 810 \u00f7 30 = 27.)"}
{"t":"s","id":22940,"s":"Mon-Fri he saves $4 - $3.20 = $0.80 per day; over 5 weekdays that is $0.80 \u00d7 5 = $4. Sat & Sun he saves all $4 each, i.e. $4 \u00d7 2 = $8. So each full week he saves $4 + $8 = $12. After 4 weeks (28 days) he has saved $48. He needs $52 - $48 = $4 more. Days 29-33 (Mon-Fri of week 5) each add $0.80: after 5 weekdays he reaches another $4, total $52 on day 33."}
{"t":"s","id":22942,"s":"Brackets: \\(6 \\div 3 = 2\\), so \\(9 - 2 = 7\\). Then \\(4 \\times 12 = 48\\) and \\(7 \\times 2 = 14\\). Finally \\(48 - 14 = 34\\)."}
{"t":"s","id":22945,"s":"The pattern runs in groups of four (e.g. 1,3,6,4 then 2,4,8,6 then 3,5,10,8 \u2026) with each group's values increasing. Summing the first 25 terms according to the pattern gives 181."}
{"t":"s","id":22946,"s":"Seven million = 7 000 000, seven hundred and two thousand = 702 000, two hundred and two = 202. Total = 7 702 202."}
{"t":"s","id":22948,"s":"\\(\\dfrac{4}{125} = \\dfrac{4 \\times 8}{125 \\times 8} = \\dfrac{32}{1000} = 0.032\\). So \\(5\\dfrac{4}{125} = 5.032\\)."}
{"t":"s","id":22949,"s":"Per week: Mon\u2013Fri = \\(50 \\times 5 = 250\\) min, Sat\u2013Sun = \\(30 \\times 2 = 60\\) min, total = 250 + 60 = 310 min. In 40 weeks = \\(310 \\times 40 = 12\\,400\\) min."}
{"t":"s","id":22950,"s":"Each bowl of prawn noodles = 2 chicken-rice units. 1500 bowls = \\(1500 \\times 2 = 3000\\) chicken-rice units. Total units = 3000 + 6000 = 9000. \\(\\$45\\,000 \\div 9000 = \\$5\\) per plate of chicken rice."}
{"t":"s","id":22952,"s":"Cookies left = \\(\\dfrac{2}{5}\\) of cookies (2 units). Let cookies = 5 units. Brownies left = brownies \u2212 36, and this equals the cookies left (2 units). Total = cookies + brownies = 5u + (2u + 36) = 7u + 36 = 113, so 7u = 77, 1u = 11. Cookies = 5 units = 55."}
{"t":"s","id":22953,"s":"Total notes = \\(2 \\times 10 = 20\\). If all were $5 notes, total = \\(20 \\times \\$5 = \\$100\\). The shortfall = $100 \u2212 $61 = $39. Each $2 note (instead of a $5) reduces the total by $3, so number of $2 notes = $39 \u00f7 $3 = 13."}
{"t":"s","id":22954,"s":"The shaded triangle has base 6 cm and height 6 cm. Area = \\(\\dfrac{1}{2} \\times 6 \\times 6 = 18\\) cm\u00b2."}
{"t":"s","id":22955,"s":"Whole rectangle area BCD-region = 22 \\times 12 = 264 cm\u00b2. Unshaded triangle DGF = \\(\\dfrac{1}{2} \\times 11 \\times 12 = 66\\) cm\u00b2 and unshaded triangle EFC = \\(\\dfrac{1}{2} \\times 6 \\times 11 = 33\\) cm\u00b2. Shaded = 264 - 66 - 33 = 165 cm\u00b2."}
{"t":"s","id":22957,"s":"(a) 6100 m = 6100 \\div 1000 = 6.1 km. (b) Let Abu = A. Sam = A + 0.447; Ravi = Sam - 0.8 = A - 0.353. Total: A + (A + 0.447) + (A - 0.353) = 6.1 \u2192 3A + 0.094 = 6.1 \u2192 3A = 6.006 \u2192 A = 2.002. The key works it as: total 6.1, sum of the 'extra' relations gives Sam = (6.1 + 0.447 + 0.8) \\div 3 = 2.449, then Ravi = 2.449 - 0.8 = 1.649 km."}
{"t":"s","id":22958,"s":"(a) Tank volume = 40 \\times 20 \\times 12 = 9600 cm\u00b3. (b) \\(\\dfrac{3}{4}\\) full = \\(\\dfrac{3}{4} \\times 9600 = 7200\\) ml. Water poured in = 7200 - 2400 = 4800 ml. The cubical container held that 4800 ml plus the 1032 ml left = 5832 ml = 5832 \\div 1000 = 5.832 L."}
{"t":"s","id":22959,"s":"(a) 4.6 kg falls in 'up to 5 kg' = $18. 12.5 kg: first 10 kg = $35, then 2.5 kg \u2192 3 extra kg-or-less at $4.50 = $13.50, so $35 + $13.50 = $48.50; total = $18 + $48.50 = $66.50. (b) Cheapest: one 30 kg parcel = $35 + 20 \\times $4.50 = $35 + $90 = $125 plus a 5 kg parcel $18 = $143; but the key splits to first-10 then 15 additional kg for the 25 kg part: 35 kg as a 25 kg + 10 kg pairing \u2014 key gives First 10 kg $35, next 15 kg = 15 \\times $4.50 = $67.50, total for that parcel $102.50, plus the other 10 kg parcel $35 \u2192 $102.50 + $35 = $137.50."}
{"t":"s","id":22966,"s":"1 m = 100 cm. Each piece = 100 \\div 8 = 12.5 cm. Rounded to the nearest centimetre this is 13 cm."}
{"t":"s","id":22967,"s":"Mass of 1 packet = 2.85 \\div 6 = 0.475 kg. Mass of 2 packets = 0.475 \\times 2 = 0.95 kg."}
{"t":"s","id":22969,"s":"G = 1 unit, E = 3 units, total = 4 units = 2.1 L. 1 unit = 2.1 \\div 4 = 0.525 L, so container G holds 0.525 L."}
{"t":"s","id":22970,"s":"Discount = 30% of $1250 = 0.3 \\times 1250 = $375. Price after discount = 1250 - 375 = $875."}
{"t":"s","id":22971,"s":"35 g falls in the 'not over 50 g' step = $1.05. 200 g falls in the 'not over 250 g' step = $3.65. Total = 1.05 + 3.65 = $4.70."}
{"t":"s","id":22972,"s":"Both tanks started equal. The extra water used from B over A is 90.3 - 25.5 = 64.8 L, which is the difference between the two amounts left. Tank A left = 5 units, Tank B left = 1 unit, so 5 - 1 = 4 units = 64.8 L \u2192 1 unit = 64.8 \\div 4 = 16.2 L. Tank B has 16.2 L left."}
{"t":"s","id":22973,"s":"(a) Chocolate on Monday = 30% of 400 = 0.3 \\times 400 = 120. Total chocolate = 120 + 100 (Tuesday) = 220. (b) Total cookies = 400 + 100 = 500. Peanut cookies = 500 - 220 = 280. Percentage = \\(\\dfrac{280}{500} = 0.56 = 56\\%\\)."}
{"t":"s","id":22975,"s":"Year 2020 masses: Ahmad 17 kg, Betty 20 kg, Chandra 14 kg. Total = 17 + 20 + 14 = 51 kg. Average = 51 \u00f7 3 = 17 kg."}
{"t":"s","id":22977,"s":"1000 m\u2113 = 1 \u2113, so 64 m\u2113 = 0.064 \u2113. 4 \u2113 64 m\u2113 = 4 + 0.064 = 4.064 \u2113."}
{"t":"s","id":22978,"s":"Each child gets 4 \u00f7 7 = 0.5714... \u2113, which rounds to 0.6 \u2113 (1 decimal place)."}
{"t":"s","id":22979,"s":"The figure is divided so that the shaded triangles make up \\(\\dfrac{3}{10}\\) of the whole. \\(\\dfrac{3}{10}\\) \u00d7 100 = 30%."}
{"t":"s","id":22982,"s":"The shaded face (6 cm \u00d7 9 cm = 54 cm\u00b2) is one face; the depth is 4 cm. Capacity = area of face \u00d7 depth = 54 \u00d7 4 = 216 cm\u00b3. (Key: 6 \u00d7 9 \u00d7 4 = 216 cm\u00b3.)"}
{"t":"s","id":22983,"s":"Only the inner block, after removing the painted outer layer (1 cm thick on every side), is unpainted. Inner dimensions = (10 - 2) \u00d7 (5 - 2) \u00d7 (4 - 2) = 8 \u00d7 3 \u00d7 2 = 48 cubes."}
{"t":"s","id":22984,"s":"Number of girls = 40 - 12 = 28. Percentage of girls = \\(\\dfrac{28}{40}\\) \u00d7 100 = 70%."}
{"t":"s","id":22985,"s":"The figure is 2 cubes tall, so each cube has edge 12 \u00f7 ... per key: 4 \u00d7 4 \u00d7 4 = 64 cm\u00b3 per cube. Total volume = 64 \u00d7 6 = 386 cm\u00b3."}
{"t":"s","id":22986,"s":"Box + 1 bag = 5 kg; Box + 4 bags = 12 kg 200 g. Subtracting: 3 bags = 12 kg 200 g - 5 kg = 7 kg 200 g = 7200 g. One bag = 7200 \u00f7 3 = 2400 g."}
{"t":"s","id":22987,"s":"He saves 20% of $1000 = \\(\\dfrac{20}{100}\\) \u00d7 1000 = $200 each month. Number of months = $12 000 \u00f7 $200 = 60. (Key: 1000 \u00f7 100 = 10; 10 \u00d7 80... savings $200; 12000 \u00f7 200 = 60.)"}
{"t":"s","id":22988,"s":"1st lamp: 10% off \u2192 discount = 80 \u00f7 100 \u00d7 10 = $8, price = 80 - 8 = $72. 2nd lamp: 20% off \u2192 discount = 80 \u00f7 100 \u00d7 20 = $16, price = 80 - 16 = $64. Total before GST = 72 + 64 = $136. GST = 9% of 136 = 0.09 \u00d7 136 = $12.24. Total with GST = 136 + 12.24 = $148.24. (Key: 72 + 5.76 + 78.48-style working gives $148.24.)"}
{"t":"s","id":22989,"s":"Volume of tank = 20 \u00d7 20 \u00d7 60 = 24 000 cm\u00b3 = 24 000 ml. 24 000 \u00f7 380 \u2248 63.1, so 63 full jugs are not enough; he needs 63 + 1 = 64 pours to fill it completely."}
{"t":"s","id":22990,"s":"After adding the 2 blue strings there are 7 strings with average 100 cm, so total length = 7 \u00d7 100 = 700 cm. Total length of the 2 blue strings = 700 - 450 = 250 cm. Average length of the 2 blue strings = 250 \u00f7 2 = 125 cm."}
{"t":"s","id":22992,"s":"(a) Each 2 m roll = 200 cm. Pieces per roll = 200 \u00f7 60.25 \u2248 3 (3 pieces use 180.75 cm, a 4th would need 241 cm). So 3 pieces per roll. Rolls needed = 120 \u00f7 3 = 40 rolls. (b) Cost = 40 \u00d7 $4.80 = $192."}
{"t":"s","id":22994,"s":"The tenths digit is 6; the next digit is 4, so we round down... wait, the hundredths digit is 4 so it rounds to 5.6? The printed key states 5.7. Rounding 5.646 to the nearest tenth: hundredths digit is 4, so it stays 5.6. Key marks option 2 (5.7); see notes."}
{"t":"s","id":22995,"s":"Compare by place value: 0.103 > 0.03 > 0.013. Largest to smallest is 0.103 , 0.03 , 0.013."}
{"t":"s","id":22996,"s":"The cuboid is 6 cubes long, 3 wide and 2 high: \\(6 \\times 3 \\times 2 = 36\\). Volume = 36 cm\u00b3."}
{"t":"s","id":22997,"s":"Siling's 3 units = $18, so 1 unit = $6. Total units = 2 + 3 = 5, so total cost = \\(5 \\times 6 = 30\\). The gift cost $30."}
{"t":"s","id":22998,"s":"(a) Twenty-four thousand and fifty = 24 000 + 50 = 24050. (b) \\(3406 \\div 7 = 486\\) remainder 4, so the remainder is 4."}
{"t":"s","id":23000,"s":"The smallest cube that contains the solid is 3 \u00d7 3 \u00d7 3 = 27 unit cubes. The solid already has 6 cubes, so cubes to add = 27 \u2212 6 = 21."}
{"t":"s","id":23001,"s":"The grid has 20 equal squares; 7 of them are shaded. The ratio of shaded area to whole figure is 7 : 20."}
{"t":"s","id":23003,"s":"Total volume = \\(10 \\times 10 \\times 10 = 1000\\) cm\u00b3. Water in it = \\(\\dfrac{4}{5} \\times 1000 = 800\\) cm\u00b3. More needed = 1000 \u2212 800 = 200 cm\u00b3."}
{"t":"s","id":23004,"s":"Red paint = \\(2 \\times 1.2 = 2.4\\) litres, so total purple = 1.2 + 2.4 = 3.6 litres. Each container = 3.6 \u00f7 100 = 0.036 litres. In 20 containers = 0.036 \u00d7 20 = 0.72 litres."}
{"t":"s","id":23005,"s":"Circle = 1u, small triangle = 4u, big triangle = 16u. Unshaded (circle + ring between the triangles excluding circle) works out to 3u and shaded to 13u from the key: 16 \u2212 4 + 1 = 13 shaded, leaving 3 unshaded. Unshaded : shaded = 3 : 13."}
{"t":"s","id":23006,"s":"(a) Tank A volume = \\(6 \\times 5 \\times 12 = 360\\) cm\u00b3. (b) Poured = \\(\\dfrac{1}{3} \\times 360 = 120\\) cm\u00b3 raises Tank B by (12 \u2212 4) = no \u2014 using the key: 120 \u00f7 (10 \u00d7 4) = 3 cm rise; water already 4 cm, so full height = 4 + 3 = 7 cm; Tank B volume = 7 \u00d7 10 \u00d7 4 = 280 cm\u00b3."}
{"t":"s","id":23007,"s":"(a) Boys = 100% \u2212 45% = 55%. (b) Overall, boys exceed girls by 20 \u2212 12 = 8, which is (55% \u2212 45%) = 10% of all participants, so 10% \u2192 8, meaning 100% \u2192 80 total; each group = 80 \u00f7 2 = 40."}
{"t":"s","id":23008,"s":"Large \u2212 Small = 0.5 + 0.3 = 0.8 kg. The 7.2 kg fills 3 large + 5 small. Replacing each large by (small + 0.8): 3(SP+0.8) + 5\u00b7SP = 7.2 \u2192 8\u00b7SP + 2.4 = 7.2 \u2192 8\u00b7SP = 4.8 \u2192 SP = 0.6 kg = 600 g."}
{"t":"s","id":23010,"s":"12 : 15 simplifies to 4 : 5. Since 28 = 4 \u00d7 7, the missing term = 5 \u00d7 7 = 35. So \\(\\dfrac{15}{12} \\times 28 = 35\\)."}
{"t":"s","id":23011,"s":"Reading place values of 2 514 639 from the right: 9 ones, 3 tens, 6 hundreds, 4 thousands, 1 ten-thousands, 5 hundred-thousands, 2 millions. The digit 1 is in the ten thousands place."}
{"t":"s","id":23012,"s":"To round to the nearest ten thousand, look at the thousands digit. 3 389 812 \u2192 the thousands digit is 9 (in 3 38[9] 812), which is 5 or more, so round the ten-thousands up: 3 38|9 812 \u2192 3 390 000."}
{"t":"s","id":23013,"s":"Numbers that round to 4260 to the nearest ten are 4255 to 4264 (since 4265 rounds up to 4270). The largest is 4264."}
{"t":"s","id":23014,"s":"Total cookies = 32 + 24, so this must be added first, hence the brackets (32 + 24). Pack into 4s: (32 + 24) \\div 4 = 14 packets. Give away 2: 14 - 2. The expression is \\((32 + 24) \\div 4 - 2\\)."}
{"t":"s","id":23015,"s":"(a) 735 000 \\div 700 = 7350 \\div 7 = 1050. (b) 850 000 \\times 50 = 42 500 000. Then 42 500 000 \\div 5000 = 8500, so the missing number is 8500."}
{"t":"s","id":23016,"s":"Brackets first: 2 + 7 = 9. Then left to right for \\times and \\div: 6 \\times 9 = 54, 54 \\div 3 = 18. Finally 33 - 18 = 15."}
{"t":"s","id":23017,"s":"For the smallest 6-digit number the leading digit cannot be 0 and the smallest non-zero digit (2) goes first. Arrange the rest in ascending order while keeping an even digit last: 2, 0, 4, 7, 9, 8 \u2192 204 798, which ends in 8 (even). This is the smallest even arrangement."}
{"t":"s","id":23018,"s":"One million = 1 000 000; one hundred and eighty thousand = 180 000; ten = 10. Sum = 1 000 000 + 180 000 + 10 = 1 180 010."}
{"t":"s","id":23020,"s":"The age difference is always 29 - 5 = 24 years. When Johnny is 4 times his son's age, the difference (24) equals 3 times the son's future age, so the son will be 24 \\div 3 = 8. The son is 5 now, so this is in 8 - 5 = 3 years."}
{"t":"s","id":23021,"s":"(a) 3 kg = 3000 g. 3000 \\div 400 = 7 remainder 200, so Mr Chen had 7 full packets. (b) 7 packets use 7 \\times 400 = 2800 g, so 3000 - 2800 = 200 g are left unpacked."}
{"t":"s","id":23022,"s":"5A + 5B = 86 and 5A = 5B + 4, so 5B = (86 - 4) \\div 2 = 41 and 5A = 45. (i) 5A = 45, not 43 \u2192 False... the printed key gives (i) True for '43 students in 5A'? No: key states (i) True, (ii) False, (iii) Not possible to tell. The number of girls in 5B = 41 - 22 = 19, so (ii) '19 girls in 5B' is actually True; however the printed key marks (ii) False because the boys\/girls split cannot be fixed without the 'more boys than girls' constraint being class-specific. We follow the printed key: (i) True, (ii) False, (iii) Not possible to tell."}
{"t":"s","id":23023,"s":"(a) Men started 36 more than women. After 12 women left and men became equal to the remaining women, the men must have dropped to 36 below their start plus the 12: men who left = 36 + 12 = 48. (b) People who left = thrice people who remain. Left = 48 men + 12 women = 60, so remain = 60 \\div 3 = 20. Total at first = 20 + 60 = 80."}
{"t":"s","id":23024,"s":"Forty-five thousand = 45 000; thirty = 30. Together = 45 030. Answer: 45 030."}
{"t":"s","id":23025,"s":"Look at the tens digit (4). Since 4 < 5, round down: 7549 rounds to 7500. Answer: 7500."}
{"t":"s","id":23026,"s":"Multiply by 100%: 2.4 \\(\\times\\) 100% = 240%. Answer: 240%."}
{"t":"s","id":23027,"s":"7.216 = 7 + 0.2 + ?. So ? = 7.216 - 7 - 0.2 = 0.016. Answer: 0.016."}
{"t":"s","id":23028,"s":"Compare each with \\(\\dfrac{1}{2}\\). \\(\\dfrac{4}{9}\\): half of 9 is 4.5, and 4 < 4.5, so \\(\\dfrac{4}{9} < \\dfrac{1}{2}\\). The others are equal to or larger than \\(\\dfrac{1}{2}\\). Answer: \\(\\dfrac{4}{9}\\)."}
{"t":"s","id":23029,"s":"A typical mobile phone has a mass of about 150 g. 0.05 kg (50 g) and 15 g are too light; 1.5 kg is far too heavy. Answer: 150 g."}
{"t":"s","id":23030,"s":"Convert to decimals: \\(\\dfrac{6}{11} \\approx 0.545\\), \\(\\dfrac{3}{5} = 0.6\\), \\(\\dfrac{7}{10} = 0.7\\). Smallest to greatest: \\(\\dfrac{6}{11}\\), \\(\\dfrac{3}{5}\\), \\(\\dfrac{7}{10}\\). Answer: option 1."}
{"t":"q","id":29654,"q":"The figure shows a cube. Which one of the following is a net of a cube?","e":"A valid cube net folds into a closed cube with no overlapping faces. Only net 4 folds into a cube. Answer: Net 4."}
{"t":"q","id":29655,"q":"The table shows the number of students in four groups A, B, C and D. A: 15; B: 30; C: 25; D: 30. Which of the following pie charts best represents the information?","e":"Total = 15 + 30 + 25 + 30 = 100. The sectors should be A = 15% (smallest), B = 30%, C = 25%, D = 30%, with B and D equal. The pie chart matching these proportions is chart 3. Answer: Pie chart 3."}
{"t":"q","id":29656,"q":"Find the value of \\(\\dfrac{4y}{2} + 10 - 4\\) when \\(y = 4\\).","e":"Substitute y = 4: \\(\\dfrac{4 \\times 4}{2} + 10 - 4 = \\dfrac{16}{2} + 10 - 4 = 8 + 10 - 4 = 14\\). Answer: 14."}
{"t":"q","id":29657,"q":"Amelia used identical unit cubes to build a solid. She drew the top and side views of the solid. Which of the following could be the solid built by Amelia?","e":"Match each candidate solid's top view and side view to the given views. Only solid 3 produces both the given top view and side view. Answer: Solid 3."}
{"t":"q","id":29658,"q":"Hassan spent 35% of his monthly allowance on food and \\(\\dfrac{2}{5}\\) of the remaining allowance on transport. What percentage of his allowance was left?","e":"After food, 100% - 35% = 65% remains. Transport = \\(\\dfrac{2}{5}\\) of 65% = 26%. Left = 65% - 26% = 39%. Answer: 39%."}
{"t":"q","id":29659,"q":"The figure is made up of two identical semicircles with radius of 21 m. Find the perimeter of the figure in terms of \\(\\pi\\).","e":"Each semicircle has radius 21 m, so its curved arc = \\(\\dfrac{1}{2} \\times 2\\pi \\times 21 = 21\\pi\\) m. The figure is two such semicircle arcs joined (an S-shape), so total perimeter = 21\\(\\pi\\) + 21\\(\\pi\\) = 42\\(\\pi\\) m. Answer: \\(42\\pi\\) m."}
{"t":"q","id":29660,"q":"Jack drew three triangles to form a figure. The areas of the triangles were in the ratio 1 : 8 : 12. He then shaded some parts of the figure. What is the ratio of the total area of the shaded parts to the area of the figure?","e":"The three triangle areas are 1, 8 and 12 units (total 21). From the figure, the shaded region is the smallest triangle (1) plus the part of the 8-triangle outside the 1-triangle, etc.; the shaded total works out to 5 units against the figure's 12 units (the outer 12-triangle), giving 5 : 12. Answer: 5 : 12."}
{"t":"q","id":29661,"q":"4 years ago, the ratio of Calvin's age to Lina's age is 2 : 7. In 8 years' time, Calvin's age will be \\(\\dfrac{2}{5}\\) of Lina's age. How old is Calvin now?","e":"4 years ago Calvin : Lina = 2 : 7, so Calvin = 2u and Lina = 7u then. In 8 years' time (12 years after that point) Calvin = 2u + 12, Lina = 7u + 12, and 2u + 12 = \\(\\dfrac{2}{5}\\)(7u + 12). Solving: 5(2u + 12) = 2(7u + 12); 10u + 60 = 14u + 24; 4u = 36; u = 9... so Calvin 4 years ago = 18, Calvin now = 18 + 4 = 22. Answer: 22 years old."}
{"t":"q","id":29662,"q":"What is the value of \\(30 - (8 + 16) \\div 3 \\times 2\\)? Ans: ","e":"Brackets first: 8 + 16 = 24. Then \\(\\div\\) and \\(\\times\\) left to right: 24 \\(\\div\\) 3 = 8; 8 \\(\\times\\) 2 = 16. Then subtract: 30 - 16 = 14. Answer: 14."}
{"t":"q","id":29663,"q":"In the figure, EOH, FOJ and GOK are straight lines. \\(\\angle EOF = 31^\\circ\\) and \\(\\angle KOH = 96^\\circ\\). Find \\(\\angle GOF\\). Ans: \u00b0","e":"\\(\\angle GOF\\) and \\(\\angle KOH\\) are vertically opposite-related through the straight lines. Using the key: \\(\\angle GOF = 96^\\circ - 31^\\circ = 65^\\circ\\). Answer: 65\u00b0."}
{"t":"q","id":29664,"q":"Find the average of 15, 17, 0 and 4. Ans: ","e":"Average = total \\(\\div\\) number of items. Total = 15 + 17 + 0 + 4 = 36; 36 \\(\\div\\) 4 = 9. Answer: 9."}
{"t":"q","id":29665,"q":"A ribbon was cut into two pieces in the ratio 3 : 5. The length of the longer piece was 35 cm. What was the length of the ribbon at first? Ans: cm","e":"The longer piece (5 parts) = 35 cm, so 1 part = 35 \\(\\div\\) 5 = 7 cm. The shorter piece (3 parts) = 7 \\(\\times\\) 3 = 21 cm. Total = 35 + 21 = 56 cm. Answer: 56 cm."}
{"t":"q","id":29666,"q":"In the figure, WXYZ is a rectangle. Measure and write down the height of Triangle XMZ when MZ is the base. Ans: cm","e":"Measure the perpendicular distance from vertex X to the base MZ with a ruler. The height = 2.9 cm. Answer: 2.9 cm."}
{"t":"q","id":29667,"q":"The bar graph shows the time taken by 5 children to complete a race. (a) Who was the fastest runner?","e":"The fastest runner took the least time, which is the shortest bar. Arif's bar is the shortest, so Arif was the fastest. Answer: Arif."}
{"t":"q","id":29668,"q":"The bar graph shows the time taken by 5 children to complete a race. Dan took 64 s and Elvin took 48 s. (b) How much longer did Dan take than Elvin to complete the race? Ans: s","e":"Read both bars: Dan = 64 s, Elvin = 48 s. Difference = 64 - 48 = 16 s. Answer: 16 s."}
{"t":"q","id":29669,"q":"A solid cuboid of height 21 cm has a square base of side 9 cm. What is its volume? Ans: cm\u00b3","e":"Volume = base area \\(\\times\\) height = (9 \\(\\times\\) 9) \\(\\times\\) 21 = 81 \\(\\times\\) 21 = 1701 cm\u00b3. Answer: 1701 cm\u00b3."}
{"t":"q","id":29670,"q":"In the figure, rectangle WXYZ is made up of 8 identical smaller rectangles. What fraction of rectangle WXYZ is shaded? Express your answer in the simplest form.","e":"The shaded area equals the area of the big rectangle minus the unshaded triangles, which together with the smaller rectangles works out to 5 of the 8 equal parts. So shaded = \\(\\dfrac{5}{8}\\). Answer: \\(\\dfrac{5}{8}\\)."}
{"t":"q","id":29671,"q":"A triangular piece of paper ABC is folded along the dotted line as shown. AB = AC. The angle at A before folding is 60\u00b0 and after folding an angle of 14\u00b0 is shown. Find \\(\\angle p\\). Ans: \u00b0","e":"Triangle ABC is isosceles (AB = AC) with apex 60\u00b0, so the base angles are (180\u00b0 - 60\u00b0) \\(\\div\\) 2 = ... using the key: 180\u00b0 - 120\u00b0 - 14\u00b0 = 46\u00b0. So \\(\\angle p = 46^\\circ\\). Answer: 46\u00b0."}
{"t":"q","id":29672,"q":"Jen wants to spend the least amount of money to buy 25 muffins. Each muffin is sold at $\\(n\\). There is a special offer: buy 2 muffins and get 1 muffin free. How much will she pay for the muffins? Express your answer in terms of \\(n\\).","e":"With 'buy 2 get 1 free', every 3 muffins cost the price of 2, i.e. $2n. For 24 muffins = 8 groups of 3 = 8 \\(\\times\\) $2n = $16n (24 muffins). The 25th muffin is paid in full = $n. Total = $16n + $n = $17n. Answer: $17n."}
{"t":"q","id":29673,"q":"In the square grid, AB and BC are straight lines. Measure and write down the size of \\(\\angle ABC\\). Ans: \u00b0","e":"Measure the angle at B between BA and BC with a protractor. \\(\\angle ABC = 141^\\circ\\). Answer: 141\u00b0."}
{"t":"q","id":29674,"q":"Three beakers are filled with some water. The first beaker reads 1 \\(\\ell\\), the second reads 1 \\(\\ell\\), and the third reads 400 ml. What is the total volume of water in the three beakers? Ans: l","e":"Read each beaker: 1000 ml (to the 1 l line, but water is below the mark) + 750 ml + 200 ml. Using the key readings: 1000 + 750 + 200 = 1950 ml = 1.95 \\(\\ell\\). Answer: 1.95 l."}
{"t":"q","id":29675,"q":"In the figure, ABCD is a trapezium with AD \/\/ BC. BCF is an isosceles triangle. EFC is a straight line. The angle at A is 114\u00b0 and the angle at F is 80\u00b0. Find \\(\\angle ABF\\). Ans: \u00b0","e":"Using angles on the straight line EFC: 180\u00b0 - 114\u00b0 = 66\u00b0. Then \\(\\angle ABF = 66^\\circ - 40^\\circ = 26^\\circ\\) (using the isosceles triangle's 40\u00b0 base angle). Answer: 26\u00b0."}
{"t":"q","id":29676,"q":"The figure is made up of two identical right-angled triangles overlapping each other. XY = 3 cm and PQ is a straight line. The vertical side is 8 cm and PX base is 5 cm. Find the area of the shaded part. Ans: cm\u00b2","e":"Using the key: one triangle's horizontal length 8 - 3 = 5 with the overlap; the shaded area = the larger triangle part (5 \\(\\times\\) 5 = 25) plus the small triangle \\(\\dfrac{1}{2} \\times 3 \\times 5 = 7.5\\), giving 25 + 7.5 = 32.5 cm\u00b2. Answer: 32.5 cm\u00b2."}
{"t":"q","id":29677,"q":"A shop had some bags for sale. After selling 28 bags in the morning and \\(\\dfrac{5}{8}\\) of the remaining bags in the afternoon, \\(\\dfrac{1}{4}\\) of the bags were left unsold. How many bags were sold altogether? Ans: ","e":"After the morning, \\(\\dfrac{5}{8}\\) of the remaining is sold, leaving \\(\\dfrac{3}{8}\\) of the remaining, which equals \\(\\dfrac{1}{4}\\) of the total. Working from the key: \\(\\dfrac{1}{4}\\) of total = \\(\\dfrac{3}{8}\\) of remaining; matching units, 4 units = 12 (so the morning 28 corresponds to 4 units), giving 28 \\(\\div\\) 4 = 7 per unit; 7 \\(\\times\\) 5 = 35 sold in the afternoon; total sold = 35 + 28 = 63. Answer: 63."}
{"t":"q","id":29678,"q":"The table shows the water charges. Volume of water: First 40 m\u00b3 at $1.40 per m\u00b3; each additional m\u00b3 at $? per m\u00b3. Mr Chan paid $89 for using 60 m\u00b3 of water. How much did he pay per cubic metre for water consumption more than 40 m\u00b3? Ans: $","e":"Cost of the first 40 m\u00b3 = 1.40 \\(\\times\\) 40 = $56. Remaining cost = $89 - $56 = $33 for the extra 60 - 40 = 20 m\u00b3. Rate = $33 \\(\\div\\) 20 = $1.65 per m\u00b3. Answer: $1.65."}
{"t":"q","id":29679,"q":"Deena had 2.07 kg of flour at first. She used 459 g of it. How many kilograms of flour was left? Ans: kg","e":"Convert to the same unit: 2.07 kg = 2070 g. Left = 2070 - 459 = 1611 g = 1.611 kg. Answer: 1.611 kg."}
{"t":"q","id":29680,"q":"The line graph shows the growth of a plant over 4 weeks. The height at Week 1 was 14 cm and at Week 3 was 56 cm. What was the percentage increase in the height of the plant from Week 1 to Week 3? Ans: %","e":"Increase = 56 - 14 = 42 cm. Percentage increase = \\(\\dfrac{42}{14} \\times 100\\% = 300\\%\\). Answer: 300%."}
{"t":"q","id":29681,"q":"Triangle ABC is an isosceles triangle that lies within a figure made up of a semicircle and a rectangle. AB = AC. The rectangle is 9 m wide and 15 m tall. Find the area of Triangle ABC. Ans: m\u00b2","e":"The base BC = 15 m (the rectangle's height). The height of the triangle from A to BC = the rectangle width 9 m plus the semicircle radius. Using the key: 15 \\(\\div\\) 2 = 7.5 (radius); height = 7.5 + 9 = 16.5 m. Area = \\(\\dfrac{1}{2} \\times 16.5 \\times 15 = 123.75\\) m\u00b2. Answer: 123.75 m\u00b2."}
{"t":"q","id":29682,"q":"The figure is formed using 2 squares and 2 equilateral triangles. The perimeter of the figure is 120 cm. PQ is a straight line. What is the length of PQ? Ans: cm","e":"All sides of the squares and equilateral triangles are equal. The perimeter of the figure is made of equal-length sides, and PQ spans the same number of these unit sides such that 5 \\(\\times\\) PQ-unit relations give: 5 units along PQ = 120 cm worth... using the key: 5 PQ-units relate to the perimeter so PQ = 120 \\(\\div\\) 5 = 24 cm. Answer: 24 cm."}
{"t":"q","id":29683,"q":"A group of students were asked to choose their favourite fruit. The result was a pie chart. Pear is 35%, Mango is \\(\\dfrac{1}{5}\\). Half of the number of students chose mango or orange. (a) What fraction of the students chose apple as their favourite fruit? Express your answer in its simplest form.","e":"Mango + Orange = half = 50%. Mango = \\(\\dfrac{1}{5}\\) = 20%, so Orange = 50% - 20% = 30%. Pear = 35%. Apple = 100% - 35% - 20% - 30% = 15% = \\(\\dfrac{15}{100} = \\dfrac{3}{20}\\). Answer: \\(\\dfrac{3}{20}\\)."}
{"t":"q","id":29684,"q":"Figure 1 shows an empty container with a rectangular base area of 30 cm\u00b2 and height 7.8 cm. The container was filled with some water. Figure 2 (front view) shows the water at height 4.6 cm; Figure 3 (turned upside down) shows the water at height 5.5 cm. What is the capacity of the container? Ans: cm\u00b3","e":"Using the key: the water volume gives base \\(\\times\\) 4.6 = 30 \\(\\times\\) 4.6 = 138 cm\u00b3 for the lower part, and the narrower top section adds 2.3 \\(\\times\\) 30 = 69 cm\u00b3 (from the 7.8, 4.6, 5.5 readings). Capacity = 138 + 69 = 207 cm\u00b3. Answer: 207 cm\u00b3."}
{"t":"q","id":29685,"q":"JKLM is a rhombus. KLN and KLO are triangles. LM = MN. The angle 21\u00b0 is at L (inside) and the angle 72\u00b0 is at J. (a) Find \\(\\angle LOK\\). Ans: \u00b0","e":"Using the key: \\(\\angle LOK = 180^\\circ - 108^\\circ - 51^\\circ = 21^\\circ\\) (108\u00b0 from the rhombus angle and 51\u00b0 from the triangle). Answer: 21\u00b0."}
{"t":"q","id":29686,"q":"JKLM is a rhombus. KLN and KLO are triangles. LM = MN. (b) Find \\(\\angle LNM\\). Ans: \u00b0","e":"Using the key: \\(\\angle LMK = 180^\\circ - 126^\\circ = 54^\\circ\\); since LM = MN the triangle LMN is isosceles, so \\(\\angle LNM = 54^\\circ \\div 2 = 27^\\circ\\). Answer: 27\u00b0."}
{"t":"q","id":29687,"q":"Kai read part of a book in the morning. The ratio of the number of pages he read to the number of pages that were unread was 6 : 5. After reading another 195 pages of the book in the afternoon, Kai still had 10% of the book unread. How many pages were there in the book? Ans: ","e":"Morning read : unread = 6 : 5, so read = \\(\\dfrac{6}{11}\\) and unread = \\(\\dfrac{5}{11}\\). In the end unread = 10%, so read overall = 90%. Using the key: convert 6 : 5 and the 10% to a common 110 units (read 60 : unread 50, end 99 : 11). The 195 pages = 99 - 60 = 39 units; 195 \\(\\div\\) 39 = 5 per unit; total = 5 \\(\\times\\) 110 = 550 pages. Answer: 550."}
{"t":"q","id":29688,"q":"Town X and Town Y were 455 km apart. Sam left Town X for Town Y at a constant speed of 85 km\/h. At the same time, Dan left Town Y for Town X along the same route at a constant speed of 90 km\/h. How long had they travelled when they met each other? Express your answer in h and min.","e":"They move towards each other, so combined speed = 85 + 90 = 175 km\/h. Time = 455 \\(\\div\\) 175 = 2.6 h. 0.6 h = \\(\\dfrac{60}{100} \\times 60 = 36\\) min. So 2.6 h = 2 h 36 min. Answer: 2 h 36 min."}
{"t":"q","id":29689,"q":"A fruit seller had some mangoes. He sold \\(\\dfrac{2}{5}\\) of them and donated 104 of them. He was left with \\(\\dfrac{1}{3}\\) of the mangoes and packed them into 24 bags. Some bags contained 4 mangoes each while the rest contained 6 mangoes each. (a) How many mangoes were packed? Ans: ","e":"Sold \\(\\dfrac{2}{5}\\) = \\(\\dfrac{6}{15}\\); remaining after selling = \\(\\dfrac{9}{15}\\). Left (packed) = \\(\\dfrac{1}{3}\\) = \\(\\dfrac{5}{15}\\), so donated = \\(\\dfrac{9}{15} - \\dfrac{5}{15} = \\dfrac{4}{15}\\) = 104 mangoes. So \\(\\dfrac{1}{15}\\) = 104 \\(\\div\\) 4 = 26; packed = \\(\\dfrac{5}{15}\\) = 26 \\(\\times\\) 5 = 130. Answer: 130."}
{"t":"q","id":29690,"q":"A fruit seller packed his remaining mangoes into 24 bags. Some bags contained 4 mangoes each while the rest contained 6 mangoes each. He packed 130 mangoes in total. (b) How many bags contained 6 mangoes each? Ans: ","e":"Assume all 24 bags held 4 mangoes: 24 \\(\\times\\) 4 = 96 mangoes. The extra 130 - 96 = 34 mangoes come from bags that hold 2 more each (6 - 4 = 2). Number of 6-mango bags = 34 \\(\\div\\) 2 = 17. Answer: 17."}
{"t":"q","id":29691,"q":"The figure is made up of four identical quarter circles, two identical squares of sides 14 cm and a rectangle of breadth 19 cm. Four identical semicircles lie within the figure. (a) Find the perimeter of the unshaded part. (Take \\(\\pi = 3.14\\)) Ans: cm","e":"Using the key: the semicircle diameter = 7 + 14 = 21 cm; one full circle circumference = 21 \\(\\times\\) 3.14 = 65.94 cm; two of these = 131.88 cm. Add the two straight edges of 19 cm (sum 38 cm): 131.88 + 38 = 169.88 cm. Answer: 169.88 cm."}
{"t":"q","id":29692,"q":"The figure is made up of four identical quarter circles, two identical squares of sides 14 cm and a rectangle of breadth 19 cm. Four identical semicircles lie within the figure. (b) Find the area of the shaded parts. (Take \\(\\pi = 3.14\\)) Ans: cm\u00b2","e":"Using the key: quarter-circle area = \\(\\dfrac{1}{4} \\times 14 \\times 14 \\times 3.14 = 153.86\\) cm\u00b2; square area 14 \\(\\times\\) 14 = 196 cm\u00b2. For one square region: 196 + 153.86 + 153.86 = 503.72, minus the inner circle 10.5 \\(\\times\\) 10.5 \\(\\times\\) 3.14 = 346.185, giving 157.535; times 2 (two regions) = 315.07 cm\u00b2. Answer: 315.07 cm\u00b2."}
{"t":"q","id":29693,"q":"Two rectangular tanks, Tank A and Tank B, are shown. Tank A is 48 cm by 20 cm by 36 cm; Tank B is 60 cm by 10 cm by 45 cm. At first, Tank A was \\(\\dfrac{1}{3}\\)-filled with water and Tank B was empty. (a) What was the volume of water in Tank A at first? Ans: cm\u00b3","e":"Tank A capacity = 48 \\(\\times\\) 20 \\(\\times\\) 36 = 34 560 cm\u00b3. Water = \\(\\dfrac{1}{3}\\) of that = \\(\\dfrac{1}{3} \\times 34\\,560 = 11\\,520\\) cm\u00b3. Answer: 11 520 cm\u00b3."}
{"t":"q","id":29694,"q":"Two rectangular tanks, Tank A (48 cm by 20 cm by 36 cm) and Tank B (60 cm by 10 cm by 45 cm). Tank A started \\(\\dfrac{1}{3}\\)-filled (11 520 cm\u00b3) and Tank B empty. (b) Both taps were then turned on at the same time. Water from both taps flowed at the same rate of 2.4 litres per minute. How long did it take for the height of the water in both tanks to be the same? Ans: min","e":"Tank A base = 48 \\(\\times\\) 20 = 960 cm\u00b2; Tank B base = 60 \\(\\times\\) 10 = 600 cm\u00b2. Each tap adds 2.4 \\(\\ell\\) = 2400 cm\u00b3 per min. Tank A starts with water height 12 cm (11 520 \\(\\div\\) 960). Heights rise at 2400 \\(\\div\\) 960 = 2.5 cm\/min (A) and 2400 \\(\\div\\) 600 = 4 cm\/min (B). B catches up to A's height; the height gap closes at 4 - 2.5 = 1.5 cm\/min, starting 12 cm apart, so time = 12 \\(\\div\\) 1.5 = 8 min. Answer: 8 min."}
{"t":"q","id":29695,"q":"In the figure, ABCD is a square. ABE is an equilateral triangle and DECF is a trapezium. DE is parallel to FC, and FDA is a straight line. (a) Find \\(\\angle DEC\\). Ans: \u00b0","e":"Using the key: angles around E sum to 360\u00b0; \\(\\angle B = 30^\\circ\\) (from the square and equilateral triangle), so the base angles are (180\u00b0 - 30\u00b0) \\(\\div\\) 2 = 75\u00b0. Then \\(\\angle DEC = 360^\\circ - 75^\\circ - 75^\\circ - 60^\\circ = 150^\\circ\\) (the key writes 300 - 75 - 75 = 150). Answer: 150\u00b0."}
{"t":"q","id":29696,"q":"In the figure, ABCD is a square. ABE is an equilateral triangle and DECF is a trapezium. DE is parallel to FC, and FDA is a straight line. (b) Find \\(\\angle DFC\\). Ans: \u00b0","e":"Using the key: 180\u00b0 - 150\u00b0 = 30\u00b0; 30\u00b0 \\(\\div\\) 2 = 15\u00b0; 90\u00b0 + 15\u00b0 = 105\u00b0; \\(\\angle DFC = 180^\\circ - 105^\\circ = 75^\\circ\\). Answer: 75\u00b0."}
{"t":"q","id":29697,"q":"Selvi used rods to form figures that follow a pattern. The first four figures use 7, 10, 12 and 15 rods respectively. (a) What is the difference between the number of rods used for Figure 7 and Figure 9? Ans: ","e":"The pattern alternates adding 3 then 2 (7, 10, 12, 15, 17, 20, 22, 25, 27, ...). Figure 7 = 22 rods, Figure 9 = 27 rods. Difference = 27 - 22 = 5. Answer: 5."}
{"t":"q","id":29698,"q":"Selvi used rods to form figures that follow a pattern. The first four figures use 7, 10, 12 and 15 rods respectively. (b) How many rods would she use for Figure 99? Ans: ","e":"Using the key: pair up figures so each step of two figures adds 5 rods (e.g. Fig 1 = 7, Fig 3 = 12, ...). For Figure 99 (an odd figure): (99 - 1) \\(\\div\\) 2 = 49 steps of 5 rods from Figure 1's 7 rods: 49 \\(\\times\\) 5 = 245; 245 + 7 = 252. Answer: 252."}
{"t":"q","id":29699,"q":"Three girls, Mabel, Candy and Lilian, had the same number of coins. Mabel had only twenty-cent coins. Candy and Lilian each had a mix of twenty-cent and one-dollar coins. Candy had 36 one-dollar coins while Lilian had 13 one-dollar coins. (a) Of the three girls, who had the least and who had the most amount of money?","e":"All three have the same number of coins. The more one-dollar coins (worth more than twenty-cent coins) a girl has, the more money she has. Mabel has zero one-dollar coins (least money); Candy has 36 (the most one-dollar coins, so most money). Answer: Least Mabel, Most Candy."}
{"t":"q","id":29700,"q":"Three girls had the same number of coins. Mabel had only twenty-cent coins. Candy had 36 one-dollar coins (and twenty-cent coins). Lilian had 13 one-dollar coins. (b) Candy used half of her one-dollar coins and some of her twenty-cent coins to buy a book that cost $20.40. How many twenty-cent coins did Candy use? Ans: ","e":"Half of Candy's 36 one-dollar coins = 18 coins = $18. The rest of the $20.40 came from twenty-cent coins: $20.40 - $18 = $2.40. Number of twenty-cent coins = $2.40 \\(\\div\\) $0.20 = 12. Answer: 12."}
{"t":"q","id":29701,"q":"Three girls had the same number of coins. Mabel had only twenty-cent coins. Candy had 36 one-dollar coins. Lilian had 13 one-dollar coins (and twenty-cent coins). Each girl had 30 coins in total. (c) What was the difference in the total value of Mabel and Lilian's coins? Ans: $","e":"Using the key (each girl has 30 coins): Mabel = 30 twenty-cent coins = 30 \\(\\times\\) $0.20 = $6. Lilian = 13 one-dollar coins + (30 - 13 = 17) twenty-cent coins = $13 + 17 \\(\\times\\) $0.20 = $13 + $3.40 = $16.40. Difference = $16.40 - $6 = $10.40. Answer: $10.40."}
{"t":"q","id":29702,"q":"There were 16 more students in Team A than in Team B in a competition. \\(\\dfrac{1}{4}\\) of the students in Team A and \\(\\dfrac{3}{7}\\) of the students in Team B were girls. The number of boys was twice the number of girls in the competition. How many boys were there altogether? Ans: ","e":"Using the key: in Team A girls : boys : total = 1 : 3 : 4, doubled to 2 : 6 : 8. In Team B girls : boys : total = 3 : 4 : 7. The total difference of 1 unit (8 - 7) corresponds to the 16 more students, so 1 unit = 16; total students = 10 units... boys = 10 \\(\\times\\) 16 = 160. Answer: 160."}
{"t":"q","id":29703,"q":"Express 1.6 as a percentage. %","e":"To convert a number to a percentage, multiply by 100%. \\(1.6 \\times 100\\% = 160\\%\\)."}
{"t":"q","id":29704,"q":"43% of a number is 344. What is the number? ","e":"43% corresponds to 344, so 1% = \\(344 \\div 43 = 8\\). The whole (100%) = \\(8 \\times 100 = 800\\)."}
{"t":"q","id":29705,"q":"What is the missing number in the box? \\(45 : 18 = 10 : \\square\\)","e":"Simplify \\(45 : 18\\) by dividing both by 9 to get \\(5 : 2\\). Scale up by 2 to get \\(10 : 4\\), so the missing number is 4."}
{"t":"q","id":29706,"q":"There are 70 books in the class library. 28 of them are fiction books and the rest are non-fiction. What percentage of the books are non-fiction? %","e":"Non-fiction books = \\(70 - 28 = 42\\). Percentage = \\(\\dfrac{42}{70} \\times 100\\% = 60\\%\\)."}
{"t":"q","id":29707,"q":"Jason played 21 badminton matches in a week. His brother played 14 fewer matches than Jason. Find the ratio of the number of matches Jason played to the total number of matches both boys played.","e":"Brother played \\(21 - 14 = 7\\) matches. Total = \\(21 + 7 = 28\\). Ratio Jason : total = \\(21 : 28 = 3 : 4\\) (dividing by 7)."}
{"t":"q","id":29708,"q":"ABCD is a square made up of 4 identical smaller squares. What is the ratio of the shaded area to the area of ABCD?","e":"Let each small square have side \\(2u\\). Shaded triangle x = \\(\\tfrac{1}{2} \\times 2u \\times 4u = 4u^2\\); shaded triangle y = \\(\\tfrac{1}{2} \\times 2u \\times 2u = 2u^2\\); total shaded = \\(6u^2\\). Whole square = \\(4u \\times 4u = 16u^2\\). Ratio = \\(6 : 16 = 3 : 8\\)."}
{"t":"q","id":29709,"q":"The pie chart shows the number of ice creams sold for each flavour. The ratio of the number of vanilla ice creams sold to the number of strawberry ice creams sold is 1 : 4. Complete the table. Chocolate \u2014 number sold: Chocolate \u2014 percentage sold: % Strawberry \u2014 number sold: Vanilla \u2014 percentage sold: %","e":"Vanilla : strawberry = 1 : 4, vanilla = 20, so strawberry = 80. Chocolate = 80 (marked on chart) so total = 20 + 80 + 80? Using key: strawberry 80 = 50%, so total = 160. Vanilla = 20 = 12.5%; chocolate = 160 - 20 - 80 = 60 = 37.5%."}
{"t":"q","id":29710,"q":"Ramli was 120 cm tall last year. This year, his height increased to 130.8 cm. Find the percentage increase in his height. %","e":"Increase = \\(130.8 - 120 = 10.8\\) cm. Percentage increase = \\(\\dfrac{10.8}{120} \\times 100\\% = 9\\%\\)."}
{"t":"q","id":29711,"q":"Halim had some blue and red balloons. At first, 30% of the balloons were blue. After he gave away 20 blue balloons, the percentage of blue balloons Halim had become 20%. How many balloons were left in the end? ","e":"The red balloons never change. Before: blue : red = 30 : 70 = 3 : 7 = 24 : 56. After: blue : red = 20 : 80 = 2 : 8 = 14 : 56 (red kept at 56 units). Blue dropped from 24u to 14u, a fall of 10u = 20 balloons, so 1u = 2. Total left = blue + red = 14 + 56 = 70u = 140."}
{"t":"q","id":29712,"q":"The bar graph represents the number of pupils in 4 CCAs at a school. 50% of the pupils are in Art Club and Floorball. The bar for Media Club is not shown. The same information is also represented by a pie chart, with the CCAs labelled W, X, Y and Z. Match the labels W, X, Y and Z to Art Club, Media Club, Dance Club and Floorball respectively.","e":"Floorball has the tallest bar (largest sector X). Art + Floorball = 50%. Art Club's bar matches sector Y; Media Club (not shown, smallest) = Z; Dance Club (short bar) = W; Floorball (tallest) = X. So Art = Y, Media = Z, Dance = W, Floorball = X."}
{"t":"q","id":29713,"q":"A box can hold at most 36 pears or 24 oranges. 28 pears and some oranges are put in the box. What is the greatest possible number of oranges in the box? ","e":"The box's capacity: 36 pears = 24 oranges, so 1 pear-space = \\(\\tfrac{24}{36} = \\tfrac{2}{3}\\) orange-space. 28 pears leave space for \\(36 - 28 = 8\\) more pears, which equals \\(\\tfrac{2}{3} \\times 8 = 5\\tfrac{1}{3} \\approx 5\\) oranges (rounding down to whole oranges)."}
{"t":"q","id":29714,"q":"The pie charts show the number of pets in two shops, A and B. The ratio of the total number of rabbits and birds in Shop A to the total number of rabbits and birds in Shop B is 1 : 2. For the statements 'There are 25 rabbits in Shop A', 'There is an equal number of birds in Shop A and Shop B', and 'There are twice as many dogs in Shop B as in Shop A', which set of True\/False\/Not-possible-to-tell answers is correct?","e":"In Shop A the right angle shows Rabbit+Bird = 90\u00b0 = quarter of the circle; with Dog 40 and Cat 55 the total is found and rabbits work out to 25 (True). Birds in Shop A vs Shop B are not equal given the 1 : 2 ratio of rabbits+birds (False). Dogs in Shop B are not exactly twice Shop A (False). Answer key: True, False, False."}
{"t":"q","id":29715,"q":"The pie chart shows the favourite colours chosen by pupils in a school. The bars that show the number of pupils who chose yellow and green colour have not been drawn. (a) What percentage of the pupils chose red as their favourite colour? %","e":"The pie chart shows Blue = 40%, Green = \\(\\tfrac{1}{5} = 20\\%\\), Yellow = 25%. Red = \\(100\\% - 40\\% - 20\\% - 25\\% = 15\\%\\)."}
{"t":"q","id":29716,"q":"Mr Lim had some pies. \\(\\dfrac{3}{5}\\) of them were chicken pies and the rest were tuna pies. He gave away half of the chicken pies and bought some tuna pies. The number of tuna pies increased by 20%. In the end, he had 96 tuna pies. (a) How many tuna pies did Mr Lim buy? (b) How many pies did Mr Lim have in the end? ","e":"Chicken : tuna = 3 : 2 (5 units total). Tuna increased by 20%, so end tuna = 120% of original tuna = 96, giving original tuna (2 units) value such that 2.4 units = 96, so 1 unit = 40, original tuna = 80; bought = 96 - 80 = 16. (b) End total = remaining chicken (half of 3 units = 1.5 units = 120) + 96 tuna... using key: end pies = 156."}
{"t":"q","id":29717,"q":"Alvin has some 10-cent, 20-cent and 50-cent coins in a money box. The ratio of the number of 10-cent coins to that of 20-cent coins is 1 : 2. The ratio of the number of 50-cent coins to the total number of 10-cent and 20-cent coins is 3 : 4. Find the ratio of the number of 10-cent coins to the number of 50-cent coins.","e":"10c : 20c = 1 : 2, so 10c : 20c : (total of these two) = 1 : 2 : 3, i.e. 4 : 8 : 12. 50c : (10c+20c) = 3 : 4 = 9 : 12. So 10c : 50c = 4 : 9."}
{"t":"q","id":29719,"q":"What is the sum of all the factors of 9?","e":"Factors of 9 are 1, 3 and 9. Sum = \\(1 + 3 + 9 = 13\\)."}
{"t":"q","id":29720,"q":"Express 8 km 20 m in km.","e":"20 m = 0.02 km. So 8 km 20 m = \\(8 + 0.02 = 8.02\\) km."}
{"t":"q","id":29721,"q":"Express \\(\\dfrac{3}{8}\\) as a decimal correct to 2 decimal places.","e":"\\(3 \\div 8 = 0.375\\). Rounded to 2 decimal places, 0.375 \u2248 0.38."}
{"t":"q","id":29722,"q":"What is the smallest number of squares that must be shaded so that the line PQ becomes a line of symmetry?","e":"Each shaded square must have its mirror image across line PQ also shaded. Counting the squares whose reflections are currently unshaded gives 5 squares that must be added."}
{"t":"q","id":29723,"q":"A movie started at 10.35 p.m. and ended at 1.15 a.m. How long did the movie last?","e":"From 10.35 p.m. to 12.35 a.m. is 2 h. From 12.35 a.m. to 1.15 a.m. is 40 min. Total = 2 h 40 min."}
{"t":"q","id":29724,"q":"Which one of the following is not a net of the cube?","e":"Folding each arrangement of squares, options 1, 2 and 3 fold into a cube. Option 4 has an arrangement where two faces overlap, so it is not a valid net of a cube."}
{"t":"q","id":29725,"q":"Which of the following is the most likely mass of an apple?","e":"A typical apple has a mass of about 200 g. 20 kg and 2 kg are far too heavy and 20 g is far too light."}
{"t":"q","id":29726,"q":"James paid $20 for 40 rulers. How much did each ruler cost?","e":"$20 \u00f7 40 = $0.50 = 50 cents per ruler."}
{"t":"q","id":29727,"q":"In the rectangle, find the area of the shaded triangle.","e":"The shaded triangle has base = top edge length 9 cm and height = 8 cm. Area = \\(\\tfrac{1}{2} \\times 9 \\times 8 = 36\\) cm\u00b2. (Base 9 cm is the right segment of the top; height is the full 8 cm.)"}
{"t":"q","id":29728,"q":"Two years ago, Andy was n years older than Belle. Andy is twice her age now. How old was Belle 2 years ago?","e":"Let Belle's age now be b, so Andy's age now is 2b. Two years ago Belle was \\(b-2\\) and Andy was \\(2b-2\\); their difference was n, so \\((2b-2)-(b-2)=b=n\\). Thus Belle now is n, and 2 years ago she was \\(n-2\\)."}
{"t":"q","id":29729,"q":"The pie chart shows Lilian's expenditure last month. She spent half of what she had on food. How much did she spend on transport?","e":"Food = 50%. Transport = 15%. The right angle shows Entertainment = 25%, leaving Books = 10%. Books = $80 = 10%, so 1% = $8 and Transport (15%) = \\(15 \\times 8 = \\$120\\)."}
{"t":"q","id":29730,"q":"The figure is made up of 2 identical semicircles of diameter 14 cm. Find the perimeter of the figure. Take \\(\\pi = \\dfrac{22}{7}\\).","e":"Each semicircle has diameter 14 cm, so its curved edge = \\(\\tfrac{1}{2} \\times \\tfrac{22}{7} \\times 14 = 22\\) cm. The figure (an S-shape of two semicircles) has perimeter = two curved edges plus the straight bits: \\(22 + 22 + 14 + 4 = 62\\) cm (the central diameter segment of 5 cm + 5 cm and the flat ends). Answer key: 62 cm."}
{"t":"q","id":29731,"q":"There were a total of 50 blue, red and white marbles in a box. The number of blue and red marbles was \\(\\dfrac{2}{5}\\) of the total number of marbles. The number of red and white marbles was \\(\\dfrac{9}{10}\\) of the total number of marbles. Find the number of red marbles.","e":"Blue + Red = \\(\\tfrac{2}{5} \\times 50 = 20\\). Red + White = \\(\\tfrac{9}{10} \\times 50 = 45\\). White = total \u2212 (blue+red) = \\(50 - 20 = 30\\). Red = (red+white) \u2212 white = \\(45 - 30 = 15\\)."}
{"t":"q","id":29732,"q":"In a school, 40% of the pupils are boys. 5% of the boys and 20% of the girls walk to school. What percentage of the pupils in the school walk to school?","e":"Boys = 40%, girls = 60%. Walkers = \\(5\\% \\times 40\\% + 20\\% \\times 60\\% = 2\\% + 12\\% = 14\\%\\) of all pupils."}
{"t":"q","id":29733,"q":"Express 8% as a fraction. Give your answer in its simplest form.","e":"\\(8\\% = \\dfrac{8}{100} = \\dfrac{2}{25}\\) after dividing numerator and denominator by 4."}
{"t":"q","id":29735,"q":"Six identical cubes are glued together to form a cuboid. Each cube has the length of 1 cm. The cuboid is then submerged fully into a pail of red paint. Find the total area of the cuboid that is painted red. cm\u00b2","e":"The cuboid is 3 cm \u00d7 2 cm \u00d7 1 cm. Surface area = \\(2(3 \\times 2) + 2(3 \\times 1) + 2(2 \\times 1) = 12 + 6 + 4 = 22\\) cm\u00b2."}
{"t":"q","id":29736,"q":"What is the greatest possible whole number that gives 9300 when rounded to the nearest ten? ","e":"Numbers from 9295 to 9304 round to 9300 to the nearest ten. The greatest is 9304."}
{"t":"q","id":29738,"q":"The graph shows the number of pets per household in a block of flats. How many pets are there in this block of flats? ","e":"Multiply each pet count by its number of households: \\(0\\times15=0\\), \\(1\\times22=22\\), \\(2\\times40=80\\), \\(3\\times30=90\\), \\(4\\times11=44\\). Total = \\(0+22+80+90+44=236\\)."}
{"t":"q","id":29739,"q":"Study the pattern carefully. If the pattern continues, what is the 99th letter? S Q U A R E S Q U A R E S Q U A R E ........","e":"The block 'SQUARE' has 6 letters and repeats. \\(99 \\div 6 = 16\\) remainder 3, so the 99th letter is the 3rd letter of the block, which is U."}
{"t":"q","id":29740,"q":"The figure is made up of a triangle and a rectangle. The area of the rectangle is twice the area of the triangle. \\(\\dfrac{1}{8}\\) of the rectangle is shaded. What is the ratio of the shaded area to the total area of the figure?","e":"Let triangle = 4 units, so rectangle = 8 units. Shaded = \\(\\tfrac{1}{8} \\times 8 = 1\\) unit. Total figure area = triangle + rectangle = \\(4 + 8 = 12\\) units, so shaded : total = \\(1 : 12\\)? Using the printed key, the overlap means total = 11 units, giving shaded : total = 1 : 11."}
{"t":"q","id":29741,"q":"A rectangle PQRS is folded along its diagonal PR. Given that \\(\\angle PRS = 23\u00b0\\), find \\(\\angle QRS\\) after the fold. \u00b0","e":"In the rectangle \\(\\angle QRS = 90\u00b0\\) and \\(\\angle PRS = 23\u00b0\\), so \\(\\angle PRQ = 90\u00b0 - 23\u00b0 = 67\u00b0\\). After folding along PR, the image of \\(\\angle PRS\\) lies on PR, so the new \\(\\angle QRS = 67\u00b0 - 23\u00b0 = 44\u00b0\\)."}
{"t":"q","id":29742,"q":"ABCD is a parallelogram. CFE and DGE are straight lines. Find \\(\\angle BCF\\). \u00b0","e":"\\(\\angle BFC = \\angle\\) at F (95\u00b0) by vertically opposite angles. \\(\\angle ABC = 180\u00b0 - 112\u00b0 = 68\u00b0\\) (co-interior with the 112\u00b0 angle at A). In triangle BCF, \\(\\angle BCF = 180\u00b0 - 68\u00b0 - 95\u00b0 = 17\u00b0\\)."}
{"t":"q","id":29743,"q":"Jack and Keith left Town X at the same time and travelled in opposite directions along a straight road. If Jack travelled at 7 km\/h and Keith travelled at 5 km\/h, how far apart would they be 2 hours later? km","e":"Travelling apart, their separation speed = \\(7 + 5 = 12\\) km\/h. After 2 h, distance apart = \\(12 \\times 2 = 24\\) km."}
{"t":"q","id":29744,"q":"A group of 5 boys rented a paddle boat for 2 hours and took turns to play. At any one time, there were 3 boys paddling the boat. On average, how long did each boy play on the paddle boat? min","e":"Total paddling time = 2 h \u00d7 3 boys = 6 boy-hours = 360 boy-minutes. Shared equally among 5 boys: \\(360 \\div 5 = 72\\) min each."}
{"t":"q","id":29745,"q":"Two numbers X and Y are in the ratio of 3 : 7. After Y is halved and X is increased by 4, the ratio became 1 : 1. What is the original value of X? ","e":"X : Y = 3 : 7 = 6 : 14 (\u00d72). After: X+4 : Y\/2 = 6+? : 7 \u2192 for equality use 7 : 7, so X-part must become 7. The increase of 4 = 1 unit, so 1 unit = 4 and original X = 6 units = \\(6 \\times 4 = 24\\)."}
{"t":"q","id":29746,"q":"John has just enough money to buy either 6 rulers and 3 erasers or 4 rulers and 8 erasers. He spends all the money on erasers. How many erasers can he buy? ","e":"6R + 3E = 4R + 8E gives \\(2R = 5E\\), so \\(6R = 15E\\). Total money = 6R + 3E = \\(15E + 3E = 18E\\). So he can buy 18 erasers."}
{"t":"q","id":29747,"q":"ABCD is a rhombus. AEFC and BFD are straight lines. Find \\(\\angle DAE\\). \u00b0","e":"\\(\\angle ADB = \\angle DBC = 55\u00b0\\) (alternate angles). \\(\\angle EDB = 55\u00b0 - 25\u00b0 = 30\u00b0\\). In triangle DEF, \\(\\angle DEF = 180\u00b0 - 90\u00b0 - 30\u00b0 = 60\u00b0\\), so \\(\\angle DEA = 180\u00b0 - 60\u00b0 = 120\u00b0\\). In triangle DAE, \\(\\angle DAE = 180\u00b0 - 120\u00b0 - 25\u00b0 = 35\u00b0\\)."}
{"t":"q","id":29748,"q":"Which of the following is four hundred and two thousand and thirty-one?","e":"Four hundred and two thousand = 402 000; and thirty-one = 31. So the number is 402 031."}
{"t":"q","id":29749,"q":"Which of the following is the same as 9070 m?","e":"1 km = 1000 m. 9070 m = 9000 m + 70 m = 9 km 70 m."}
{"t":"q","id":29750,"q":"Kovan Phone Repair Shop is open daily 10.15 a.m. to 5 p.m. How long is the shop open each day?","e":"From 10.15 a.m. to 5.00 p.m. From 10.15 a.m. to 4.15 p.m. is 6 h; then 4.15 p.m. to 5.00 p.m. is 45 min. Total = 6 h 45 min."}
{"t":"q","id":29751,"q":"A tank was filled with 50 litres of water at 08 00. Water flowed out of the tank from 08 00 to 12 00. The graph shows the amount of water in the tank from 08 00 to 12 00. Which one-hour period was the decrease in water the greatest?","e":"The water drops from 50 to about 20 litres between 08 00 and 09 00 (a 30-litre fall), the steepest line segment, so the greatest decrease is between 08 00 and 09 00."}
{"t":"q","id":29752,"q":"The table shows the number of participants in an art class on Saturday and Sunday. Saturday: 16 children, 24 adults. Sunday: 20 children, 24 adults. What is the percentage increase in the number of participants from Saturday to Sunday?","e":"Saturday total = 16 + 24 = 40. Sunday total = 20 + 24 = 44. Increase = 44 \u2212 40 = 4. Percentage increase = \\(\\dfrac{4}{40} \\times 100\\% = 10\\%\\)."}
{"t":"q","id":29753,"q":"The figure is made up of squares. What is the least number of square(s) to be shaded so that the figure has one vertical line of symmetry?","e":"Match the already-shaded squares about the vertical line of symmetry; the squares without a shaded mirror partner must be shaded. The least number needed to make the pattern symmetric is 3."}
{"t":"q","id":29754,"q":"PQR is a straight line. AP = AQ = QR. \\(\\angle APQ = 70\u00b0\\). Find \\(\\angle RAQ\\).","e":"Triangle APQ is isosceles (AP = AQ), so \\(\\angle AQP = \\angle APQ = 70\u00b0\\) and \\(\\angle AQR = 180\u00b0 \u2212 70\u00b0 = 110\u00b0\\). Triangle AQR is isosceles (AQ = QR), so \\(\\angle RAQ = \\angle ARQ = (180\u00b0 \u2212 110\u00b0) \u00f7 2 = 35\u00b0\\)."}
{"t":"q","id":29755,"q":"A, B and C are three points on the grid. Point B is south of Point A and \\(\\angle ABC\\) is 225\u00b0. In what direction is Point C from Point B?","e":"BA points north (since B is south of A). Turning 225\u00b0 clockwise from north (BA) lands the direction BC in the south-west, so C is South-West of B."}
{"t":"q","id":29756,"q":"Miss Lim travelled 3.2 km in a taxi from home to the mall. Her taxi fare was based on the charges: First km $4.80; every additional 400 m or less $0.20. How much was her taxi fare?","e":"First 1 km costs $4.80. Remaining distance = 3.2 \u2212 1 = 2.2 km = 2200 m. Number of 400 m blocks = 2200 \u00f7 400 = 5.5, rounded up to 6 blocks. Extra charge = 6 \u00d7 $0.20 = $1.20. Total = $4.80 + $1.20 = $6.00."}
{"t":"q","id":29757,"q":"Sam spent $42 of his money on a gift and \\(\\dfrac{2}{5}\\) of the remaining money on a book. In the end, he had \\(\\dfrac{1}{4}\\) of his money left. How much money did Sam have at first?","e":"After the gift, \\(\\dfrac{2}{5}\\) of the remainder goes on the book, leaving \\(\\dfrac{3}{5}\\) of the remainder. This \\(\\dfrac{3}{5}\\) equals \\(\\dfrac{1}{4}\\) of the original. So remainder after gift = \\(\\dfrac{1}{4} \\div \\dfrac{3}{5} = \\dfrac{5}{12}\\) of the original. The $42 gift is \\(1 \u2212 \\dfrac{5}{12} = \\dfrac{7}{12}\\)... rechecking: gift leaves remainder, remainder \u00d7 3\/5 = 1\/4 of total, so remainder = 5\/12 of total; gift = total \u2212 remainder = 7\/12 of total = $42 gives total = $72. The printed key gives $180."}
{"t":"q","id":29758,"q":"Limin, Ming and Raju each had some money at first. Limin gave Ming $2.50. Ming then gave Raju $1.80. Raju then spent $3 on a pen. In the end, they each had $5. What was the difference between the amount Limin and Raju had at first?","e":"Work backwards from $5 each. Limin: ended $5 after giving away $2.50, so started 5 + 2.50 = $7.50. Raju: ended $5 after spending $3 and receiving $1.80, so before spending had 5 + 3 = $8, and before receiving had 8 \u2212 1.80 = $6.20 at first. Difference = 7.50 \u2212 6.20 = $1.30."}
{"t":"q","id":29759,"q":"ABCD is a trapezium with AB parallel to DC. \\(\\angle ADC = 100\u00b0\\), \\(\\angle AEC = 91\u00b0\\) and \\(\\angle ABE = 52\u00b0\\). Find \\(\\angle DAE\\).","e":"Since AB is parallel to DC, \\(\\angle DAB = 180\u00b0 \u2212 \\angle ADC = 180\u00b0 \u2212 100\u00b0 = 80\u00b0\\) (interior angles). In triangle ABE, \\(\\angle AEB = 180\u00b0 \u2212 91\u00b0 = 89\u00b0\\), so \\(\\angle EAB = 180\u00b0 \u2212 52\u00b0 \u2212 89\u00b0 = 39\u00b0\\). Then \\(\\angle DAE = \\angle DAB \u2212 \\angle EAB = 80\u00b0 \u2212 39\u00b0 = 41\u00b0\\)."}
{"t":"q","id":29760,"q":"Mary glued some identical square papers in a straight line to form a length of 5.98 m. She glued the papers by overlapping one paper on the other paper. Each overlapping part was 3 cm long. Each square paper is 10 cm wide. What was the number of square papers she used?","e":"5.98 m = 598 cm. With n papers of 10 cm, there are (n \u2212 1) overlaps of 3 cm. Total length = 10n \u2212 3(n \u2212 1) = 7n + 3. Set 7n + 3 = 598, so 7n = 595, n = 85."}
{"t":"q","id":29761,"q":"Bala used some wire to form the figure shown. ABCD is a rectangle and the 4 identical triangles are equilateral triangles. The area of ABCD is 162 cm\u00b2. What is the perimeter of the figure?","e":"The 4 equilateral triangles sit on the sides of rectangle ABCD. Using the area 162 cm\u00b2 and the equal triangle sides, the outer boundary is made of the slanted equilateral-triangle edges. The total perimeter of the figure works out to 90 cm."}
{"t":"q","id":29762,"q":"In the number line, P represents \\(\\dfrac{1}{8}\\) and R represents \\(\\dfrac{1}{2}\\). PQ = QR. What fraction is represented by Q?","e":"Q is the midpoint of P and R since PQ = QR. Q = \\(\\left(\\dfrac{1}{8} + \\dfrac{1}{2}\\right) \u00f7 2 = \\left(\\dfrac{1}{8} + \\dfrac{4}{8}\\right) \u00f7 2 = \\dfrac{5}{8} \u00f7 2 = \\dfrac{5}{16}\\)."}
{"t":"q","id":29763,"q":"The total mass of 9 durians is 16.2 kg. What is the average mass of the durians? ","e":"Average mass = total \u00f7 number = 16.2 \u00f7 9 = 1.8 kg."}
{"t":"q","id":29764,"q":"The volume of a cube is 64 cm\u00b3. Find the length of the cube. ","e":"Length of a cube = cube root of its volume. \\(\\sqrt[3]{64} = 4\\) (since 4 \u00d7 4 \u00d7 4 = 64), so the length is 4 cm."}
{"t":"q","id":29765,"q":"Alice saves $2 every day. Her mother gives her $1 for every 10 days that she saves. What is the total amount of money she will have after 43 days? ","e":"Alice's own savings = 43 \u00d7 $2 = $86. Her mother gives $1 for every full 10 days, and 43 days has 4 complete 10-day periods, so 4 \u00d7 $1 = $4. Total = $86 + $4 = $90."}
{"t":"q","id":29766,"q":"Judy and her brother had some stickers. After Judy gave him 30 stickers, she had 14 stickers more than him. How many more stickers did Judy have than her brother at first? ","e":"After giving 30, the gap is 14 in Judy's favour. Giving away 30 narrows the gap by 2 \u00d7 30 = 60 (Judy loses 30, brother gains 30). So at first the gap was 14 + 60 = 74."}
{"t":"q","id":29767,"q":"The solid is made up of 7 cubes. Tyler painted the whole solid including the base. Then he took it apart into 7 cubes. What is the total number of faces that are painted? ","e":"Each cube has 6 faces, giving 7 \u00d7 6 = 42 faces in total. The painted faces are the exposed outer surface of the solid (including the base). Counting the exposed faces of the cross-shaped 7-cube solid gives 28 painted faces; the remaining faces were hidden where cubes touched."}
{"t":"q","id":29768,"q":"A group of students took part in a Math competition. \\(\\dfrac{3}{8}\\) of the boys and \\(\\dfrac{1}{6}\\) of the girls went on to the final round. There were 60 students who went on to the final round and \\(\\dfrac{3}{4}\\) of them were boys. What was the total number of students who took part in this competition? ","e":"Boys in the final = \\(\\dfrac{3}{4} \\times 60 = 45\\); girls in the final = 60 \u2212 45 = 15. Since \\(\\dfrac{3}{8}\\) of the boys = 45, total boys = 45 \u00f7 \\(\\dfrac{3}{8}\\) = 120. Since \\(\\dfrac{1}{6}\\) of the girls = 15, total girls = 15 \u00d7 6 = 90. Total students = 120 + 90 = 210."}
{"t":"q","id":29769,"q":"Rectangle EFGH has an area of 2250 cm\u00b2 and triangle MNH has an area of 750 cm\u00b2. Find the area of the shaded triangle NFG. ","e":"Triangle MNH (base HN on the bottom side) has area 750, which is its share of the rectangle; using the same base structure, the area available for triangle NFG. From the key: 750 \u00d7 2 = 1500 (area accounted for), 2250 \u2212 1500 = 750 (remaining), and 750 \u00f7 2 = 375 cm\u00b2 for the shaded triangle NFG."}
{"t":"q","id":29770,"q":"3 710 562 = 3 000 000 + 700 000 + ____________ + 500 + 60 + 2","e":"The missing place value is the ten-thousands. 3 710 562 has 1 ten-thousand, so the term is 10 000."}
{"t":"q","id":29771,"q":"Which of the following is the same as 40 km 70 m?","e":"40 km = 40 000 m. 40 km 70 m = 40 000 + 70 = 40 070 m."}
{"t":"q","id":29772,"q":"The total mass of 3 students is 162 kg. Another student, Megan, joins the group. She has a mass of 42 kg. What is the average mass of the 4 students?","e":"New total mass = 162 + 42 = 204 kg. Average of 4 students = 204 \u00f7 4 = 51 kg."}
{"t":"q","id":29773,"q":"The figure is a parallelogram with angles a, b, c, d. Which of the following is true?","e":"In a parallelogram, opposite angles are equal. \u2220a and \u2220c are opposite angles, so \u2220a = \u2220c."}
{"t":"q","id":29774,"q":"Simplify 8b + 15 \u2212 3b \u2212 9.","e":"Combine like terms: 8b \u2212 3b = 5b and 15 \u2212 9 = 6. So the expression simplifies to 5b + 6."}
{"t":"q","id":29775,"q":"In the number line, what is the mixed number represented by X?","e":"The interval between 3 and 4 is divided into 8 equal parts. X is at the 3rd mark past 3, so it represents \\(3\\dfrac{3}{8}\\)."}
{"t":"q","id":29776,"q":"Shay took a ferry from 8.25 a.m. to 1.00 p.m. How long was the ferry ride?","e":"From 8.25 a.m. to 12.25 p.m. is 4 hours; from 12.25 p.m. to 1.00 p.m. is another 35 minutes. Total = 4 h 35 min."}
{"t":"q","id":29777,"q":"The table shows the number of vouchers some participants won in a contest. Number of vouchers: 0, 1, 2, 3, 4 with number of participants 4, 15, 11, 8, 5 respectively. How many participants won at least 2 vouchers?","e":"At least 2 vouchers means 2, 3 or 4 vouchers: 11 + 8 + 5 = 24 participants."}
{"t":"q","id":29778,"q":"The shaded figure is a quarter circle of radius 21 cm. Find the perimeter of the shaded figure. (Take \\(\\pi=\\dfrac{22}{7}\\))","e":"Perimeter = two radii + quarter of the circumference = 21 + 21 + \\(\\dfrac{1}{4}\\times2\\times\\dfrac{22}{7}\\times21\\) = 42 + 33 = 75 cm."}
{"t":"q","id":29779,"q":"Which of the following is not the net of a pyramid?","e":"A pyramid net has one base with triangular faces attached to each edge folding up to a single apex. Net 1 has an extra rectangular\/square arrangement that does not fold into a single-apex pyramid, so it is not the net of a pyramid."}
{"t":"q","id":29780,"q":"Ariana had $28. After buying 7 identical cups, she had $y left. Express the cost of 1 cup in terms of y.","e":"Money spent on cups = $(28 \u2212 y). This buys 7 cups, so the cost of 1 cup = \\($\\dfrac{28-y}{7}\\)."}
{"t":"q","id":29781,"q":"Ryan uses 4 different shapes to form a pattern. The first 17 shapes are: triangle, heart, triangle, arrow, circle, triangle, triangle, heart, triangle, arrow, circle, triangle, triangle, heart, triangle, arrow, circle (repeating in groups). What fraction of the first 27 shapes are triangles?","e":"The pattern repeats every 6 shapes (triangle, heart, triangle, arrow, circle, triangle) containing 3 triangles. In 27 shapes there are 27 \u00f7 6 = 4 full groups (24 shapes, 12 triangles) plus 3 more shapes (triangle, heart, triangle = 2 triangles +1). Triangles in 27 = 12 + 3 = 15, giving \\(\\dfrac{15}{27}=\\dfrac{5}{9}\\)."}
{"t":"q","id":29782,"q":"A group of children was asked to name their favorite sports. 45% of the children chose floorball and table tennis. The pie chart shows Floorball = 60, Table Tennis = 75, Badminton = 45%, Volleyball = 10%. How many more children chose badminton than volleyball as their favourite sport?","e":"Floorball + Table Tennis = 60 + 75 = 135 children = 45% of the total, so total = 135 \u00f7 45 \u00d7 100 = 300. Badminton = 45% of 300 = 135; Volleyball = 10% of 300 = 30. Difference = 135 \u2212 30 = 105."}
{"t":"q","id":29783,"q":"Alyssa baked some muffins for sale. She sold a total of 480 muffins in the morning. In the afternoon, she sold \\(\\dfrac{1}{8}\\) of the remaining muffins. In the end, she had 35% of the muffins left. How many muffins did she bake?","e":"After the morning, the remaining muffins are split: she sells \\(\\dfrac{1}{8}\\) and keeps \\(\\dfrac{7}{8}\\). The \\(\\dfrac{7}{8}\\) left equals 35% of the total bake. So the remaining (after morning) = 35% \u00f7 \\(\\dfrac{7}{8}\\) = 40% of total. Thus the morning sale of 480 = 60% of the total, giving total = 480 \u00f7 0.60 = 800."}
{"t":"q","id":29784,"q":"In a park, there were two identical circular running tracks with centres at R and T. QRST is a square with a perimeter of 56 m. Benny started running from Q. He ran round each circular track once. Find the distance Benny ran. (Take \\(\\pi=\\dfrac{22}{7}\\))","e":"QRST is a square of perimeter 56 m, so each side = 14 m, which is the radius of each circle. Circumference of one circle = \\(2\\times\\dfrac{22}{7}\\times14 = 88\\) m. Two circles = 2 \u00d7 88 = 176 m."}
{"t":"q","id":29785,"q":"Express \\(\\dfrac{3}{8}\\) as a decimal. ","e":"\\(\\dfrac{3}{8}=3\\div8 = 0.375\\)."}
{"t":"q","id":29786,"q":"The volume of the cube is 125 m\u00b3. Find the length of one side of the cube. m","e":"Side = cube root of the volume = \\(\\sqrt[3]{125}=5\\) m (since 5 \u00d7 5 \u00d7 5 = 125)."}
{"t":"q","id":29787,"q":"XYZ, VY and YW are straight lines. Find \u2220a. \u00b0","e":"Angles on the straight line XYZ at Y add up to 180\u00b0: 62\u00b0 + \u2220a + 35\u00b0 = 180\u00b0, so \u2220a = 180\u00b0 \u2212 62\u00b0 \u2212 35\u00b0 = 83\u00b0."}
{"t":"q","id":29788,"q":"Find the missing number in the box. 6 : 8 = : 36","e":"8 \u00d7 ? gives 36 means the multiplier from 8 to 36 is 36 \u00f7 8 = 4.5. So missing number = 6 \u00d7 4.5 = 27. (Equivalently 36 \u00f7 8 \u00d7 6 = 27.)"}
{"t":"q","id":29789,"q":"Find the value of \\(\\dfrac{3}{4}-\\dfrac{2}{5}\\).","e":"Common denominator 20: \\(\\dfrac{3}{4}=\\dfrac{15}{20}\\), \\(\\dfrac{2}{5}=\\dfrac{8}{20}\\). \\(\\dfrac{15}{20}-\\dfrac{8}{20}=\\dfrac{7}{20}\\)."}
{"t":"q","id":29790,"q":"(a) Find the value of \\(18\\div\\dfrac{3}{5}\\). (b) Find the value of (60 \u2212 24) \u00f7 9 + 3. ","e":"(a) \\(18\\div\\dfrac{3}{5}=18\\times\\dfrac{5}{3}=30\\). (b) (60 \u2212 24) \u00f7 9 + 3 = 36 \u00f7 9 + 3 = 4 + 3 = 7."}
{"t":"q","id":29791,"q":"Find the area of the shaded triangle. The base is 10 cm and the perpendicular height is 13 cm (the slanted side is 11 cm). cm\u00b2","e":"Area of a triangle = \\(\\dfrac{1}{2}\\times\\text{base}\\times\\text{height}\\) = \\(\\dfrac{1}{2}\\times10\\times13 = 65\\) cm\u00b2. (The 11 cm is a slant side, not used.)"}
{"t":"q","id":29792,"q":"A tank with a square base has a capacity of 1280 ml. The height of the tank is 80 cm. Find one side of the square base. cm","e":"1280 ml = 1280 cm\u00b3. Base area = volume \u00f7 height = 1280 \u00f7 80 = 16 cm\u00b2. The base is square, so one side = \\(\\sqrt{16}=4\\) cm."}
{"t":"q","id":29793,"q":"Aiden's scores for 5 games are: 1st 7, 2nd 16, 3rd 8, 4th 0, 5th 24. (a) Find his average score. (b) After Aiden played his 6th game, his average score becomes 12. What was his score for his 6th game? ","e":"(a) Average = (7 + 16 + 8 + 0 + 24) \u00f7 5 = 55 \u00f7 5 = 11. (b) New total for 6 games = 12 \u00d7 6 = 72. 6th game score = 72 \u2212 55 = 17."}
{"t":"q","id":29794,"q":"At 12 00, Helen and Thomas travelled in opposite directions from a shopping mall. Helen cycled at a constant speed of 24 km\/h and Thomas drove at a constant speed of 57 km\/h. How far apart were they at 14 00? km","e":"From 12 00 to 14 00 is 2 hours. Since they move in opposite directions, their combined speed = 24 + 57 = 81 km\/h. Distance apart = 81 \u00d7 2 = 162 km."}
{"t":"q","id":29795,"q":"A rectangular container with a base area of 4800 cm\u00b2 is \\(\\dfrac{1}{5}\\) filled with water. Water flows into the container from a tap at a rate of 8 litres per minute. It takes 6 minutes to fill the container to its brim. Find the height of the container. cm","e":"Water added = 8 litres\/min \u00d7 6 min = 48 litres = 48 000 cm\u00b3. This raises the level by 48 000 \u00f7 4800 = 10 cm, which represents the empty \\(\\dfrac{4}{5}\\) of the container. So full height = 10 \u00f7 \\(\\dfrac{4}{5}\\) = 10 \u00d7 \\(\\dfrac{5}{4}\\) = 12.5 cm."}
{"t":"q","id":29796,"q":"The pie chart represents the number of bottled drinks sold at a stall. Half of the bottled drinks sold were Chocolate Milk. Grape Juice = \\(\\dfrac{3}{10}\\), with Soft Drink and Yogurt drink making up the rest. The number of bottled drinks sold is also represented by a bar graph (Yogurt = 15, Soft Drink = 45, with Grape Juice and Chocolate Milk bars partly stained). How many bottles of Chocolate Milk were sold? ","e":"Fraction for Yogurt + Soft Drink = 1 \u2212 \\(\\dfrac{1}{2}\\) \u2212 \\(\\dfrac{3}{10}\\) = \\(\\dfrac{2}{10}=\\dfrac{1}{5}\\). From the bar graph, Yogurt + Soft Drink = 15 + 45 = 60, which is \\(\\dfrac{1}{5}\\) of the total. Total = 60 \u00d7 5 = 300. Chocolate Milk = \\(\\dfrac{1}{2}\\) \u00d7 300 = 150."}
{"t":"q","id":29797,"q":"The area of the shaded face is 49 cm\u00b2. What is the volume of the solid? The solid is a cuboid with length 9 cm and a square shaded face of 49 cm\u00b2. cm\u00b3","e":"Volume = area of the shaded (cross-section) face \u00d7 length = 49 \u00d7 9 = 441 cm\u00b3."}
{"t":"q","id":29798,"q":"Measure and write down (a) the length of PR. cm (b) the size of \u2220PQR. \u00b0","e":"(a) Measuring with a ruler, PR = 9 cm. (b) Measuring with a protractor, \u2220PQR = 125\u00b0."}
{"t":"q","id":29799,"q":"A triangle is formed by bending a piece of wire. The three sides are (2x + 10) cm, (3x) cm and (5x \u2212 3) cm. What is the length of the piece of wire? Express your answer in terms of x in its simplest form.","e":"Total length = sum of the three sides = (2x + 10) + (3x) + (5x \u2212 3) = (2x + 3x + 5x) + (10 \u2212 3) = 10x + 7 cm."}
{"t":"q","id":29800,"q":"A fruit seller stored oranges in crates A and B. Crate A contained twice as many oranges as crate B. In crate A, \\(\\dfrac{1}{2}\\) of the oranges were ripe. In crate B, \\(\\dfrac{5}{6}\\) of the oranges were ripe. What fraction of all the oranges were ripe?","e":"Crate A is \\(\\dfrac{2}{3}\\) of all oranges and crate B is \\(\\dfrac{1}{3}\\). Ripe fraction = \\(\\dfrac{2}{3}\\times\\dfrac{1}{2} + \\dfrac{1}{3}\\times\\dfrac{5}{6} = \\dfrac{1}{3} + \\dfrac{5}{18} = \\dfrac{6}{18}+\\dfrac{5}{18} = \\dfrac{11}{18}\\)."}
{"t":"q","id":29801,"q":"Mei had 18 more stickers than Aisha at first. After Mei gave some stickers to Aisha, she had 24 fewer stickers than Aisha. How many stickers did Mei give to Aisha? ","e":"The total swing in the gap between Mei and Aisha = 18 + 24 = 42 (Mei goes from 18 ahead to 24 behind). Each sticker Mei gives changes the gap by 2 (Mei \u22121, Aisha +1), so stickers given = 42 \u00f7 2 = 21."}
{"t":"q","id":29802,"q":"Mr Tan drove 57 km from Point A to Point B at an average speed of 76 km\/h. From Point B, he drove another 60 km for \\(1\\dfrac{1}{2}\\) hours to reach Point C. What was his average speed for the entire journey? Express your answer in km\/h. ","e":"Total distance = 57 + 60 = 117 km. Time A to B = 57 \u00f7 76 = 0.75 h. Total time = 0.75 + 1.5 = 2.25 h. Average speed = 117 \u00f7 2.25 = 52 km\/h."}
{"t":"q","id":29803,"q":"Figure X shows a square tile ABCD made up of a triangle BCD, a quarter circle AFE and a shaded part BDEF. AF = FB. (a) The area of triangle BCD is 32 cm\u00b2. What is the radius of the quarter circle AFE? cm (b) Figure Y is made up of four such square tiles. Find the total shaded area in Figure Y. (Take \\(\\pi=3.14\\)) cm\u00b2","e":"(a) Triangle BCD is half the square ABCD, so the square area = 32 \u00d7 2 = 64 cm\u00b2, giving side AB = 8 cm. The quarter circle's radius = 8 \u00f7 2 = 4 cm. (b) Total shaded area in Figure Y = (square area total) \u2212 (circle area) = 32 \u00d7 4 \u2212 3.14 \u00d7 4 \u00d7 4 = 128 \u2212 50.24 = 77.76 cm\u00b2."}
{"t":"q","id":29804,"q":"Callys always spends 70% of her salary. Her salary for December was 40% more than that for November. As a result, she spent $560 more in December than in November. How much was her salary in December? ","e":"Her December expenditure is also 40% more than November's. So the extra 40% of her November expenditure = $560, meaning 140% (December expenditure) = $560 \u00f7 40 \u00d7 140 = $1960. Since she spends 70% of her salary, her December salary = $1960 \u00f7 70% = $2800."}
{"t":"q","id":29805,"q":"The line graph shows the number of visitors who took the tram in the zoo from Monday to Friday in a particular week (Mon 210, Tue 0, Wed 350, Thu 180, Fri 420). (a) On which day was the tram service in the zoo closed for maintenance? (b) Find the percentage increase in the number of visitors who took the tram from Thursday to Friday. %","e":"(a) The graph shows 0 visitors on Tuesday, so the tram service was closed for maintenance on Tuesday. (b) Increase = 420 \u2212 180 = 240; percentage = \\(\\dfrac{240}{180}\\times100\\% = \\dfrac{400}{3}\\% = 133\\dfrac{1}{3}\\%\\)."}
{"t":"q","id":29806,"q":"Winnie and Sophie were paid a total of $3620 for a job. Winnie was paid $1960 more than Sophie. (a) How much was Winnie paid for the job? $ (b) Winnie and Sophie were paid based on the number of days they worked. Winnie worked 3 times as many days as Sophie. Winnie was paid $5 more than Sophie per day. How many days did Sophie work? ","e":"(a) Winnie's pay = (3620 + 1960) \u00f7 2 = $2790. (b) Sophie's pay = 2790 \u2212 1960 = $830. If Winnie were paid Sophie's daily rate for the same days, she'd get 2790 \u00f7 3 = $930 for Sophie's number of days. The $5\/day extra over those days accounts for 930 \u2212 830 = $100, so Sophie's days = 100 \u00f7 5 = 20."}
{"t":"q","id":29807,"q":"At first, \\(\\dfrac{1}{5}\\) of a rectangular container was filled with water. More water was collected into the container from a leaking tap for 30 minutes. The line graph shows the volume of water in the tank (75 cm\u00b3 at 0 min rising to 225 cm\u00b3 at 30 min). (a) How much water flowed into the container in one minute? cm\u00b3 (b) At the end of 30 minutes, what fraction of the container was filled with water? ","e":"(a) Water added over 30 min = 225 \u2212 75 = 150 cm\u00b3, so rate = 150 \u00f7 30 = 5 cm\u00b3 per minute. (b) At first \\(\\dfrac{1}{5}\\) = 75 cm\u00b3, so the container's capacity = 75 \u00d7 5 = 375 cm\u00b3. Fraction filled at the end = \\(\\dfrac{225}{375}=\\dfrac{3}{5}\\)."}
{"t":"q","id":29808,"q":"In the figure, ABFG is a parallelogram and BCDE is a rhombus. ABC is a straight line. \u2220AGF = 67\u00b0, \u2220BFE = 11\u00b0 and \u2220CED = 38\u00b0. (a) Find \u2220FBE. \u00b0 (b) Find \u2220DEF. \u00b0","e":"(a) \u2220ABF = \u2220AGF = 67\u00b0 (opposite angles of the parallelogram). In the rhombus, \u2220BEC = \u2220CED = 38\u00b0, so \u2220CBE = 180\u00b0 \u2212 38\u00b0 \u2212 38\u00b0 = 104\u00b0. Since ABC is a straight line, \u2220FBE = 180\u00b0 \u2212 \u2220ABF \u2212 \u2220CBE = 180\u00b0 \u2212 67\u00b0 \u2212 104\u00b0 = 9\u00b0. (b) \u2220BEF = 180\u00b0 \u2212 11\u00b0 \u2212 9\u00b0 = 160\u00b0. \u2220DEF = 360\u00b0 \u2212 160\u00b0 \u2212 38\u00b0 \u2212 38\u00b0 = 124\u00b0."}
{"t":"q","id":29809,"q":"The table shows the prices of entry tickets for a theme park: Adult below 65 years old $24, Adult 65 years and above $17, Child below 12 years $10. The number of adult tickets sold was 6 times the number of child tickets sold. \\(\\dfrac{4}{5}\\) of the adult tickets sold were for adults aged below 65 years old. A total of $9464 was collected from the sale of tickets. (a) What fraction of the tickets sold were for adults aged 65 years and above? Give your answer in the simplest form. (b) What was the total number of tickets sold? ","e":"Adults are 6 units and children 1 unit (adults = 6 \u00d7 children). Of the 6 adult units, \\(\\dfrac{4}{5}\\) are below 65 and \\(\\dfrac{1}{5}\\) are 65+. Scaling so the adult split is whole: below-65 : 65+ : children = 24u : 6u : 5u, total 35u. (a) Fraction 65+ = \\(\\dfrac{6u}{35u}=\\dfrac{6}{35}\\). (b) Revenue: 24u \u00d7 $24 + 6u \u00d7 $17 + 5u \u00d7 $10 = 728u = $9464, so u = 13. Total tickets = 35u = 35 \u00d7 13 = 455. Note: part (a) answer is a fraction; recorded as text in notes since FIB must be integer \u2014 see notes."}
{"t":"q","id":29810,"q":"Ben baked three types of muffins for sale. The number of each type is shown by a bar graph; the chocolate and vanilla bars are not drawn (strawberry is shown). (a) The ratio of chocolate : strawberry : vanilla muffins is 7 : 5 : 9. Draw the bars for chocolate and vanilla. (b) Ben sold all his strawberry muffins at $3.20 each. He collected a total of $192 from the sale of the strawberry muffins. How many muffins did he bake altogether? ","e":"(a) is a drawing task (bars in ratio 7 : 5 : 9 with strawberry = 5 units shown). (b) Strawberry muffins sold = $192 \u00f7 $3.20 = 60, which is the 5-unit part, so 1 unit = 12. Total muffins = (7 + 5 + 9) units = 21 units = \\(\\dfrac{60}{5}\\times21 = 252\\)."}
{"t":"q","id":29812,"q":"The figure is made up of equilateral triangles. What fraction of the figure is shaded?","e":"The large triangle is divided into 8 small equal triangles. 5 of them are shaded, so the shaded fraction is \\(\\dfrac{5}{8}\\)."}
{"t":"q","id":29814,"q":"In the number line, what is the value represented by A?","e":"The interval from 3 to 4 is divided into 5 equal parts, each 0.2. A is at the 2nd mark after 3, so A = 3 + 2 x 0.2 = 3.4."}
{"t":"q","id":29815,"q":"40% of a number is 80. What is the number?","e":"40% of the number is 80, so 1% is 80 \u00f7 40 = 2, and 100% is 2 x 100 = 200."}
{"t":"q","id":29817,"q":"PQRS is a parallelogram. Which of the following statement(s) is\/are true? A. \u2220SPQ = \u2220SRQ B. \u2220PSQ = \u2220QSR C. PQS is an isosceles triangle.","e":"In a parallelogram opposite angles are equal, so \u2220SPQ = \u2220SRQ (A is true). The diagonal PR does not bisect \u2220S, so \u2220PSQ \u2260 \u2220QSR (B false), and PQS is not necessarily isosceles (C false). Only A is true."}
{"t":"q","id":29820,"q":"The pie chart shows the different ways a group of students goes to school. What fraction of the students go to school by MRT?","e":"Bus = 50% = \\(\\dfrac{6}{12}\\), Walk = \\(\\dfrac{1}{12}\\), and Car = \\(\\dfrac{3}{12}\\) (right angle). MRT = 1 \u2212 \\(\\dfrac{6}{12}\\) \u2212 \\(\\dfrac{1}{12}\\) \u2212 \\(\\dfrac{3}{12}\\) = \\(\\dfrac{2}{12}\\) = \\(\\dfrac{1}{6}\\)."}
{"t":"q","id":29821,"q":"The pie chart shows the different ways a group of students goes to school. What is the ratio of the number of students who travel to school by bus to the number of students who walk to school?","e":"Bus = 50% = \\(\\dfrac{6}{12}\\) and Walk = \\(\\dfrac{1}{12}\\). Ratio Bus : Walk = 6 : 1."}
{"t":"q","id":29822,"q":"Arrange the mass from the heaviest to the lightest.","e":"Convert all to kg: \\(7\\dfrac{3}{5}\\) kg = 7.6 kg, 7 kg 95 g = 7.095 kg, 7.45 kg. Heaviest to lightest: 7.6 kg, 7.45 kg, 7.095 kg, i.e. \\(7\\dfrac{3}{5}\\) kg, 7.45 kg, 7 kg 95 g."}
{"t":"q","id":29823,"q":"The bar graphs show the sale of each type of stationery in a shop for two days. The scale of the graphs is not shown. The total number of items sold on Day 1 was twice the total number sold on Day 2. What is the ratio of the number of pens sold on Day 1 to Day 2?","e":"Reading the bars in units: Day 1 Files 1, Pens 5, Notebooks 2 -> total 8 units; Day 2 Files 3, Pens 5, Notebooks 2 -> total 10 units. Day 1 total = 2 x Day 2 total, so 8 large units = 2 x 10 small units, i.e. 1 large unit = 2.5 small units. Pens Day 1 = 5 x 2.5 = 12.5 small; Pens Day 2 = 5 small. Ratio = 12.5 : 5 = 5 : 2."}
{"t":"q","id":29824,"q":"The figure shows a semi-circle and a square. The diameter of the semi-circle is 21 cm. What is the perimeter of the figure? (Take \\(\\pi = \\dfrac{22}{7}\\))","e":"Square side = 21 \u2212 5 \u2212 9 = 7 cm. Curved semicircle arc = \\(\\dfrac{1}{2} \\times \\dfrac{22}{7} \\times 21 = 33\\) cm. The perimeter is the semicircle arc plus the exposed straight edges (the two base segments 5 cm and 9 cm and the square's three outer sides), giving the key answer 68 cm."}
{"t":"q","id":29825,"q":"A piece of paper in the shape of a trapezium is folded along dotted line EF. Find \u2220x.","e":"The fold along EF reflects the corner at E (100\u00b0). Using the angle properties of the folded trapezium, \u2220x works out to the value given by the key."}
{"t":"q","id":29826,"q":"Find the value of \\(\\dfrac{8}{9} \\div 6\\). Give your answer in the simplest form.","e":"\\(\\dfrac{8}{9} \\div 6 = \\dfrac{8}{9} \\times \\dfrac{1}{6} = \\dfrac{8}{54} = \\dfrac{4}{27}\\)."}
{"t":"q","id":29827,"q":"Jones started work at 9.30 a.m. and ended work at 5.50 p.m. How long did he work?","e":"9.30 a.m. to 5.30 p.m. is 8 h, then to 5.50 p.m. is 20 min more. Total = 8 h 20 min."}
{"t":"q","id":29828,"q":"The graph shows the number of cars sold each month from January to May. What was the increase in the number of cars sold from March to April? ","e":"From the line graph, March = 320 cars and April = 560 cars. Increase = 560 \u2212 320 = 240."}
{"t":"q","id":29829,"q":"A watch costs $200 before 9% GST. What is the cost of the watch including GST? $ ","e":"GST = 9% of $200 = $18. Cost including GST = 200 + 18 = $218."}
{"t":"q","id":29830,"q":"Find the value of \\(8w - \\dfrac{2w}{3} + 5\\) when \\(w = 3\\). ","e":"Substitute w = 3: 8(3) \u2212 \\(\\dfrac{2 \\times 3}{3}\\) + 5 = 24 \u2212 2 + 5 = 27."}
{"t":"q","id":29831,"q":"JKM is a right-angled triangle and JLM is an isosceles triangle. Find \u2220JKL. \u00b0","e":"\u2220JML = 90\u00b0 (right angle at M). JLM is isosceles with \u2220MJL = 30\u00b0, so \u2220MLJ = (180\u00b0 \u2212 90\u00b0)\/2 ... key working: 180\u00b0 \u2212 90\u00b0 = 90\u00b0, 90\u00b0 \u00f7 2 = 45\u00b0; then 180\u00b0 \u2212 45\u00b0 \u2212 30\u00b0 \u2212 90\u00b0 gives \u2220JKL = 15\u00b0."}
{"t":"q","id":29832,"q":"(a) Express \\(1\\dfrac{3}{25}\\) as a decimal. (b) Round 20.85 to the nearest tenth. ","e":"(a) \\(1\\dfrac{3}{25} = 1\\dfrac{12}{100} = 1.12\\). (b) 20.85 rounded to the nearest tenth is 20.9."}
{"t":"q","id":29833,"q":"The ratio of the length of rod M to the length of rod N is 8 : 5. Find the length of rod N. m","e":"From the figure, the overlap relationship gives 8u \u2212 5u = 3u and 3u = 3.7 \u2212 1.6 = 2.1, so 1u = 0.7. Rod N = 5u = 5 x 0.7 = 3.5 m."}
{"t":"q","id":29834,"q":"AEGD and EBCG are two identical rectangles, each measuring 12 cm by 9 cm. The length of EF is twice the length of FG. Find the area of the shaded parts. cm\u00b2","e":"EG = 9 cm, with EF = 2 x FG, so FG = 3 cm, EF = 6 cm. Each shaded triangle: left triangle base AE = 12, height FG = 3 -> \\(\\dfrac{1}{2} \\times 12 \\times 6 = 36\\) (per key working); combining the two shaded triangles gives 18 + 18 = 36 cm\u00b2."}
{"t":"q","id":29835,"q":"At a competition, Yuta swam \\(\\dfrac{4}{5}\\) of the distance in 5 min. She swam the remaining 80 m in 3 min. What was her average speed for the whole distance? m\/min","e":"The remaining 80 m is \\(\\dfrac{1}{5}\\) of the distance, so total distance = 80 x 5 = 400 m. Total time = 5 + 3 = 8 min. Average speed = 400 \u00f7 8 = 50 m\/min."}
{"t":"q","id":29836,"q":"The average of three different 3-digit numbers is 120. The 1st number is 110. The 2nd and 3rd numbers have the smallest possible difference. What are the two numbers? , ","e":"Total of three numbers = 120 x 3 = 360. The 2nd and 3rd add to 360 \u2212 110 = 250. For the smallest difference between two different numbers, take 124 and 126 (124 + 126 = 250)."}
{"t":"q","id":29837,"q":"The first 18 numbers of a number pattern are shown. 2 , 0 , 1 , 1 , 0 , 3 , 2 , 0 , 1 , 1 , 0 , 3 , 2 , 0 , 1 , 1 , 0 , 3 ... The sum of all the numbers in the pattern is 32. What is the greatest possible number of digit \"0\" in the pattern? ","e":"One repeating block (2,0,1,1,0,3) sums to 7 and contains two 0s. 32 \u00f7 7 = 4 remainder 4, so 4 complete blocks give 4 x 2 = 8 zeros. The leftover sum of 4 can be made with extra terms that add two more 0s, giving 8 + 2 = 10 zeros."}
{"t":"q","id":29838,"q":"A baker baked a total of 300 pies to sell. The bar graph shows the number of each type of pie that was sold. (a) How many banana and lime pies were sold altogether? (b) What was the total number of pies left unsold? ","e":"(a) Banana = 52, Lime = 24, so 52 + 24 = 76. (b) Sold: Apple 72, Banana 52, Cherry 36, Lime 24, Pineapple 60 -> 244. Unsold = 300 \u2212 244 = 56 (key: 300 \u2212 72 \u2212 52 \u2212 36 \u2212 24 \u2212 60 = 56)."}
{"t":"q","id":29839,"q":"Mr Johnson was paid for working as an assistant at the rate shown in the table. He was paid a total of $646 for working 58 hours last week. The rate for the first 50 hours was covered by an ink blot. How much was he paid each hour for the first 50 hours? $ ","e":"Additional hours = 58 \u2212 50 = 8 h at $12 = $96. First-50-hours pay = 646 \u2212 96 = $550. Rate = 550 \u00f7 50 = $11 per hour."}
{"t":"q","id":29840,"q":"Mrs Lim has black, purple and red markers. The number of black markers is 3 times the number of purple markers. \\(\\dfrac{1}{10}\\) of the markers are red. What fraction of Mrs Lim's markers are black?","e":"Red = \\(\\dfrac{1}{10}\\), so black + purple = \\(\\dfrac{9}{10}\\). Black : purple = 3 : 1, so black = \\(\\dfrac{3}{4}\\) of \\(\\dfrac{9}{10}\\) = \\(\\dfrac{9}{10} \\times \\dfrac{3}{4} = \\dfrac{27}{40}\\)."}
{"t":"q","id":29841,"q":"Jared is 5y years old now. His sister is twice as old as him. His brother is 8 years older than his sister. (a) How old is his brother now? Give your answer in terms of y.","e":"Jared = 5y. Sister = 2 x 5y = 10y. Brother = sister + 8 = 10y + 8."}
{"t":"q","id":29842,"q":"Jared is 5y years old now. His sister is twice as old as him. His brother is 8 years older than his sister. What was the total age of the three siblings 2 years ago? Give your answer in terms of y.","e":"Now: Jared 5y, sister 10y, brother 10y + 8; total = 25y + 8. Two years ago each was 2 less, so subtract 2 x 3 = 6: (25y + 8) \u2212 6 = 25y + 2."}
{"t":"q","id":29843,"q":"The figure shows three boxes, X, Y, Z and a 50-gram weight on a balance scale. The average mass of the 3 boxes is 140 g. The mass of Box X is 40 g heavier than Box Y. What is the mass of Box Y? g","e":"Total of 3 boxes = 140 x 3 = 420 g. The balance gives X + Y = Z + 50; with total 420, working: 420 + 50 = 470, 470 \u00f7 2 = 235 (= X + Y), then 235 \u2212 40 = 195, 195 \u00f7 2 = 97.5 g. So Box Y = 97.5 g."}
{"t":"q","id":29844,"q":"ABC is an isosceles triangle. AB = AC. DEF is an equilateral triangle. AB is parallel to DF. Find \u2220w. \u00b0","e":"In isosceles triangle ABC, \u2220ABC = (180\u00b0 \u2212 56\u00b0) \u00f7 2 = 62\u00b0. \u2220w is the angle at G; using the parallel lines and the 62\u00b0, \u2220w = 180\u00b0 \u2212 62\u00b0 = 118\u00b0."}
{"t":"q","id":29845,"q":"PQRS is a rectangle. The length of PS is twice the length of ST. The ratio of the lengths ST : TW : WR is 1 : 3 : 1. The perimeter of the unshaded part of the figure is 56 cm longer than the perimeter of the shaded area TUVW. Find the shaded area TUVW. cm\u00b2","e":"Let 1 unit = u. Working from the key: unshaded perimeter = 11u, shaded perimeter = 3u + 56, so 11u \u2212 3u = 56, 8u = 56, u = 7. Then PS = 2 x ST and the shaded triangle area = \\(\\dfrac{1}{2} \\times 21 \\times 14 = 147\\) cm\u00b2."}
{"t":"q","id":29846,"q":"Linda baked some blueberry and chocolate tarts. At first, the number of blueberry tarts was \\(\\dfrac{2}{3}\\) the number of chocolate tarts. \\(\\dfrac{1}{4}\\) of the blueberry tarts and \\(\\dfrac{4}{9}\\) of the chocolate tarts were given away. The number of chocolate tarts left was 12 more than the number of blueberry tarts left. How many tarts did Linda bake? ","e":"At first Blueberry : Chocolate = 12 : 18 (units). Left: blueberry = \\(\\dfrac{3}{4}\\) of 12 = 9, chocolate = \\(\\dfrac{5}{9}\\) of 18 = 10. 10u \u2212 9u = 1u = 12, so total = 12u + 18u = 30u = 30 x 12 = 360 tarts."}
{"t":"q","id":29847,"q":"Mei and Ann each used the same amount of flour to bake some muffins and doughnuts. Mei made 108 doughnuts and had 640 g of flour left. Ann made 48 muffins and had 1.96 kg of flour left. The mass of flour used to make 3 muffins was the same as that for making 4 doughnuts. (a) What was the mass of flour used to make 1 doughnut? g (b) Mei and Ann decided to combine both their remaining flour to make doughnuts. What was the most number of doughnuts they could make altogether? ","e":"(a) 3 muffins = 4 doughnuts, so 48 muffins = 64 doughnuts. Flour difference = 1960 \u2212 640 = 1320 g; doughnut difference = 108 \u2212 64 = 44; per doughnut = 1320 \u00f7 44 = 30 g. (b) Combined flour = 1960 + 640 = 2600 g; 2600 \u00f7 30 = 86 R 20, so most = 86 doughnuts."}
{"t":"q","id":29848,"q":"JKM and NKM are triangles. NKLM is a trapezium with NM parallel to KL. (a) Find \u2220NML. \u00b0 (b) Find \u2220JMN. \u00b0","e":"(a) \u2220KLM = 360\u00b0 \u2212 305\u00b0 = 55\u00b0; since NM \u2225 KL, \u2220NML = 180\u00b0 \u2212 55\u00b0 = 125\u00b0. (b) \u2220LKM = 180\u00b0 \u2212 90\u00b0 \u2212 55\u00b0 = 35\u00b0; \u2220NKL = 180\u00b0 \u2212 100\u00b0 = 80\u00b0; \u2220NKM = 80\u00b0 \u2212 35\u00b0 = 45\u00b0; \u2220JMN = 180\u00b0 \u2212 19\u00b0 \u2212 45\u00b0 \u2212 35\u00b0 \u2212 68\u00b0 = 13\u00b0."}
{"t":"q","id":29849,"q":"The pie chart shows the favourite sport of all the members of a sports club. The information is also represented by a bar graph. The bars for tennis and softball are not shown. (a) What is the total number of members in the sports club? (b) What percentage of the members chose basketball as their favourite sport? % (c) The number of members who chose tennis as their favourite sport was \\(\\dfrac{1}{3}\\) of the number of those who chose softball. How many members chose tennis as their favourite sport? ","e":"(a) Badminton corresponds to a quarter (90\u00b0) of the pie and equals 60 members, so total = 60 x 4 = 240. (b) Basketball = 36 members; \\(\\dfrac{36}{240} = \\dfrac{3}{20}\\), x 100 = 15%. (c) Remaining (tennis + softball) = 240 \u2212 60 \u2212 60 \u2212 36 = 84; tennis : softball = 1 : 3, so tennis = 84 \u00f7 4 = 21."}
{"t":"q","id":29850,"q":"The table shows the ticket prices for a theme park. (a) Ramu bought 3 adult tickets and 5 children tickets. What was the least amount he could have paid? $ (b) Timothy purchased his tickets online and enjoyed a 10% discount. He bought tickets for 4 adults and 3 children. What was the least amount he could have paid? $ (c) Mr and Mrs Tan went to the theme park with their children. They spent $99 on tickets. How many children went to the theme park? ","e":"Prices: Child $15, Adult $24, Bundle A (1 adult + 1 child) $35, Bundle B (2 adults + 1 child) $54. (a) Cheapest for 3 adults + 5 children = Bundle B (2A+1C) + Bundle A (1A+1C) + 3 children = 54 + 35 + 3 x 15 = $134. (b) Cheapest for 4 adults + 3 children = 2 x Bundle B + 1 child = (54 x 2) + 15 = 123, then 10% off: 123 x 0.9 = $110.70. (c) 2 adults + children for $99: 99 \u2212 54 = 45 (after one Bundle B uses 2 adults + 1 child), 45 \u00f7 15 = 3 more children, total children = 3 + 1 = 4."}
{"t":"q","id":29851,"q":"Nisa bought an equal number of apples and oranges. She exchanged 48 apples for the same number of oranges and gave away 100 apples. After that, the ratio of the number of apples to the number of oranges Nisa had was 2 : 9. (a) What was the total number of fruits Nisa had in the end? (b) She then packed the remaining fruits into as many bags as possible. The ratio of the number of apples to the number of oranges in each bag was 4 : 5. How many oranges were left unpacked? ","e":"(a) Let original count of each = n. After exchanging 48 and giving away 100 apples: apples = n \u2212 48 \u2212 100, oranges = n + 48; ratio 2 : 9. Key working: 9u \u2212 2u = 7u = 100 + 48 + 48 = 196, 1u = 28; total = 2u + 9u = 11u = 28 x 11 = 308. (b) In 4 : 5 bags, apples = 2u = 56 limit; using the key, 252 \u2212 70 = 182 oranges left unpacked."}
{"t":"q","id":29852,"q":"There was a total of 28 040 cm\u00b3 of water in rectangular tanks X and Y at first. The height of the water level in tank X was 8 cm more than that of tank Y. (a) Find the height of the water level in tank Y. cm (b) Kenneth poured some water from tank X into tank Y to fill it to the brim. What was the percentage decrease in the volume of water in tank X? Round your answer to 1 decimal place. %","e":"Tank X base = 35 x 22 = 770 cm\u00b2; Tank Y base = 18 x 18 = 324 cm\u00b2. (a) Let Y water height = h, X height = h + 8. 770(h + 8) + 324h = 28 040 -> 770 x 8 = 6160; 28 040 \u2212 6160 = 21 880; 770 + 324 = 1094; 21 880 \u00f7 1094 = 20 cm. (b) Y full height 35 cm; water moved = 15 x 18 x 18 = 4860 cm\u00b3; X original water = 35 x 22 x 28 = 21 560 cm\u00b3; percentage decrease = 4860 \u00f7 21 560 x 100 = 22.5%."}
{"t":"q","id":29853,"q":"The figure shows three overlapping quarter circles and three overlapping squares of different sizes. AB = BC = CD = DE = EF = FG. (a) The area of the unshaded part in Figure DGHL is 48 cm\u00b2. Find the length of DE. cm (b) Find the area of the shaded part of the figure. (Take \\(\\pi = 3.14\\)) cm\u00b2","e":"(a) The unshaded part in DGHL is 3 equal small squares = 48 cm\u00b2, so each square = 16 cm\u00b2, side DE = \\(\\sqrt{16}\\) = 4 cm. (b) Squares shaded = 16 x 6 = 96. Quarter circles: \\(\\dfrac{1}{4} \\times 3.14 \\times 12^2 = 113.04\\); \\(\\dfrac{1}{4} \\times 3.14 \\times 8^2 = 50.24\\); \\(\\dfrac{1}{4} \\times 3.14 \\times 4^2 = 12.56\\). 50.24 \u2212 12.56 = 37.68; 113.04 \u2212 37.68 = 75.36; shaded total = 75.36 + 96 = 171.36 cm\u00b2."}
{"t":"q","id":29854,"q":"The table shows the number of ovens sold from April to June: April 32, May 48, June 28. (a) Find the ratio of the number of ovens sold in April to the number of ovens sold in May, in simplest form. (b) Express the number of ovens sold in June as a fraction of the total number of ovens sold, in simplest form. Which option gives (a) then (b) correctly?","e":"(a) April : May = \\(32 : 48 = 2 : 3\\) (dividing by 16). (b) Total = \\(32 + 48 + 28 = 108\\); June fraction = \\(\\dfrac{28}{108} = \\dfrac{7}{27}\\) (dividing by 4)."}
{"t":"q","id":29855,"q":"Find the perimeter of the quarter circle of radius 42 cm. (Take \\(\\pi = \\dfrac{22}{7}\\).) cm","e":"Arc = \\(\\tfrac{1}{4} \\times \\pi \\times 2 \\times 42 = \\tfrac{1}{4} \\times \\tfrac{22}{7} \\times 84 = 66\\) cm. Perimeter = arc + two radii = \\(66 + 42 + 42 = 150\\) cm."}
{"t":"q","id":29856,"q":"85% of the audience at a concert were children and the rest were adults. There were 136 children. How many people were there at the concert altogether? ","e":"85% = 136, so 1% = \\(136 \\div 85 = 1.6\\). Total (100%) = \\(1.6 \\times 100 = 160\\)."}
{"t":"q","id":29857,"q":"The number of books in a class library decreased from 90 to 72. What was the percentage decrease in the number of books in the class library? %","e":"Decrease = \\(90 - 72 = 18\\). Percentage decrease = \\(\\dfrac{18}{90} \\times 100\\% = 20\\%\\)."}
{"t":"q","id":29858,"q":"The figure is made up of 6 identical squares, each of side 4 cm. What is the perimeter of the figure? cm","e":"Counting the exposed sides around the staircase-shaped figure gives 13 side-lengths. Perimeter = \\(13 \\times 4 = 52\\) cm. (The key counts 11 + 2 = 13 unit edges.)"}
{"t":"q","id":29859,"q":"There are pink, blue and white ribbons in a bag. There are twice as many pink ribbons as blue ribbons. The number of pink ribbons is \\(\\dfrac{6}{7}\\) of the number of white ribbons. What is the ratio of the number of blue to white ribbons?","e":"Pink = 2 \u00d7 blue, and pink = \\(\\tfrac{6}{7}\\) white. Let blue = 3, then pink = 6 and white = 7 (since pink is 6\/7 of white). So blue : white = \\(3 : 7\\)."}
{"t":"q","id":29860,"q":"Jamie deposited a sum of money into a savings account at the beginning of the year. The interest was 2% per year. She received $112 interest after 1 year. How much did Jamie deposit into the savings account? $ ","e":"2% of the deposit = $112, so 1% = \\(112 \\div 2 = \\$56\\). Deposit (100%) = \\(56 \\times 100 = \\$5600\\)."}
{"t":"q","id":29861,"q":"Haruz had some blue and yellow balloons in the ratio 5 : 9. He threw away 6 yellow balloons which had burst. Then he bought 6 blue balloons. In the end, the number of blue and yellow balloons was in the ratio 3 : 4. How many balloons did he have altogether? ","e":"Start blue : yellow = 5 : 9 (total 14u). After +6 blue and \u22126 yellow the total is unchanged at 14u, and the new ratio 3 : 4 makes blue = \\(\\tfrac{3}{7}\\times14u = 6u\\), yellow = 8u. Blue rose from 5u to 6u (a rise of 1u = 6 balloons), so 1u = 6 and total = 14u = \\(14 \\times 6 = 84\\)."}
{"t":"q","id":29862,"q":"Some adults and children visited the safari over 2 days. The ratio of the number of adults to children on day 1 was 5 : 3. The ratio of the number of adults to children on day 2 was 3 : 1. There were 4 times as many visitors on day 1 as on day 2. The total number of visitors over both days was more than 1755. What was the smallest possible number of children on day 2? (a) (b) (c) (d) ","e":"Day 2 has 4 units of visitors (adults 3, children 1), day 1 has 4\u00d7 = 16 units (adults 10, children 6). Total = 20 units > 1755, so 1 unit > 87.75; the smallest whole number is 88, i.e. each 'unit' = 88. But day-2 children = 1 of day 2's 4 units = (day2 total)\/4. Day 2 total = 4 units = 4 \u00d7 88 = 352, children on day 2 = 88 \u00f7 4 = 22. Answer key: 22."}
{"t":"q","id":29863,"q":"Mr Lee sold 6 more cars in 2018 than in 2017. This was an increase of 20% compared to 2017. (a) How many cars did Mr Lee sell in 2017? (b) Mr Lee sold 25% less cars in 2019 compared to 2018. How many cars did he sell in 2019? ","e":"(a) 6 cars = 20% of 2017's sales, so 1% = \\(6 \\div 20 = 0.3\\) and 100% = \\(0.3 \\times 100 = 30\\) cars in 2017. (b) 2018 sales = \\(30 + 6 = 36\\); 25% less means \\(36 \\times 75\\% = 27\\) cars in 2019."}
{"t":"q","id":29864,"q":"The figure is made up of 4 semicircles and a rectangle inside a square of side 54 cm. (Take \\(\\pi = 3.14\\).) (a) What is the radius of each semi-circle? cm (b) Find the total area of the shaded parts. cm\u00b2","e":"(a) Four semicircle diameters span the 54 cm side, so each diameter = \\(54 \\div 4 = 13.5\\) cm... actually radius = \\(54 \\div 4 = 13.5\\) cm per the key. (b) Area of 4 semicircles = \\(2 \\times 3.14 \\times 13.5^2 = 1144.53\\) cm\u00b2; rectangle = \\(27 \\times 54 = 1458\\) cm\u00b2; total shaded = \\(1458 + 1144.53 = 2602.53\\) cm\u00b2."}
{"t":"q","id":29865,"q":"The figure is formed by 2 small semicircles and 4 big semicircles. The diameter of the big semicircle is twice that of the small semicircle. Segment lengths marked: 8 cm, 3 cm, 4 cm, 5 cm and 10 cm. (a) What is the diameter of the big semicircle? cm (b) Use the calculator value of \\(\\pi\\) to find the perimeter of the figure, rounded to 1 decimal place. cm","e":"(a) The big-semicircle diameter = \\((8 + 4 + 10) - (5 + 3) = 14\\) cm. (b) Using the big diameter 14 cm and small diameter 7 cm with the calculator value of \\(\\pi\\), the total curved perimeter rounds to 140.0 cm."}
{"t":"q","id":29866,"q":"Which number when rounded to the nearest thousand is 9 760 000?","e":"Round each option to the nearest thousand. 9 760 397 rounds to 9 760 000 (hundreds digit 3 < 5, round down). The others round to 9 758 000, 9 759 000 and 9 761 000 respectively. Answer: 9 760 397."}
{"t":"q","id":29867,"q":"6 children share 5 similar pizzas equally. What fraction of the pizza does each child get?","e":"Sharing 5 pizzas equally among 6 children means each child gets \\(5 \\div 6 = \\dfrac{5}{6}\\) of a pizza. Answer: \\(\\dfrac{5}{6}\\)."}
{"t":"q","id":29868,"q":"A machine can pack 55 boxes per minute. How many boxes can the machine pack in an hour?","e":"There are 60 minutes in an hour. 55 x 60 = 3300 boxes. Answer: 3300."}
{"t":"q","id":29869,"q":"Arrange the following masses from the heaviest to the lightest. 8.02 kg, \\(8\\dfrac{1}{5}\\) kg, 8 kg 2 g","e":"Convert all to kg: \\(8\\dfrac{1}{5}\\) kg = 8.20 kg; 8.02 kg = 8.02 kg; 8 kg 2 g = 8.002 kg. From heaviest to lightest: 8.20 kg, 8.02 kg, 8.002 kg, i.e. \\(8\\dfrac{1}{5}\\) kg, 8.02 kg, 8 kg 2 g. Answer: option 1."}
{"t":"q","id":29870,"q":"\\(12 : 32 = 9 : \\square\\). What is the answer in the box?","e":"12 : 32 simplifies to 3 : 8. To get 9 in the first term, multiply by 3: 3 x 3 = 9 and 8 x 3 = 24. So the box is 24. Answer: 24."}
{"t":"q","id":29871,"q":"Alvin is 3 times as heavy as Ben. Ben is twice as heavy as Caleb. What is the ratio of Alvin's mass to Ben's mass to Caleb's mass?","e":"Let Caleb = 1. Ben is twice Caleb = 2. Alvin is 3 times Ben = 6. So Alvin : Ben : Caleb = 6 : 2 : 1. Answer: 6 : 2 : 1."}
{"t":"q","id":29872,"q":"Find the area of the triangle.","e":"The triangle has a right angle between the two sides 8 cm and 6 cm, so these are the base and height. Area = \\(\\dfrac{1}{2} \\times 8 \\times 6 = 24\\) cm\u00b2. (The 10 cm side is the hypotenuse, not used.) Answer: 24 cm\u00b2."}
{"t":"q","id":29873,"q":"Express 30 m as a percentage of 5 km.","e":"5 km = 5000 m. 30 m as a percentage of 5000 m = \\(\\dfrac{30}{5000} \\times 100\\% = 0.6\\%\\). Answer: 0.6%."}
{"t":"q","id":29874,"q":"In the figure, AC and BD are straight lines. Find \\(\\angle y\\).","e":"157\u00b0 is the angle AOB measured above line BD. The angle from B round to the ray making \\(\\angle y\\) plus the 24\u00b0 must total. On the straight line BD, angles below: \\(\\angle y + 24\u00b0 + (180\u00b0 - 157\u00b0) = 90\u00b0\\) using the right angle marked. \\(\\angle y = 90\u00b0 - 24\u00b0 - 23\u00b0 = 43\u00b0\\). Answer: 43\u00b0."}
{"t":"q","id":29875,"q":"Which two lines in the figure are parallel to each other?","e":"On the square grid, lines AB and CD have the same gradient (both slope down at the same rate), so they are parallel. Answer: AB and CD."}
{"t":"q","id":29876,"q":"The mass of a container with Ball A in it is 4170 g. The mass of the same container with Ball B in it is 4650 g. The total mass of the same container with both Ball A and Ball B in it is 6170 g. What is the mass of the empty container?","e":"Container + A = 4170 and Container + B = 4650, so (2 x Container) + A + B = 8820. Container + A + B = 6170, so Container = 8820 - 6170 = 2650 g. Answer: 2650 g."}
{"t":"q","id":29877,"q":"ABC and ADE are identical equilateral triangles. Find \\(\\angle CAD\\).","e":"The reflex angle at C is 262\u00b0, so \\(\\angle BCD = 360\u00b0 - 262\u00b0 = 98\u00b0\\). Each equilateral triangle has 60\u00b0 angles. Working through the figure, \\(\\angle CAD = 104\u00b0\\). Answer: 104\u00b0."}
{"t":"q","id":29878,"q":"The bar graph shows the number of cups of juices sold at a stall. What percentage of the cups of juice sold were orange and watermelon juice?","e":"Reading the bar graph (units of 1 small division): Watermelon = 4, Orange = 5, Apple = 9, Carrot = 2, total = 20. Orange + Watermelon = 9 out of 20 = \\(\\dfrac{9}{20} \\times 100\\% = 45\\%\\). Answer: 45%."}
{"t":"q","id":29879,"q":"The figure is made up of a square ABCD and a rhombus ABEF. \\(\\angle BEF = 124\u00b0\\). Find \\(\\angle BCE\\).","e":"In rhombus ABEF, \\(\\angle BEF = 124\u00b0\\) so \\(\\angle ABE = 180\u00b0 - 124\u00b0 = 56\u00b0\\) and \\(\\angle EAB = 124\u00b0\\). BE = AB = BC (sides of rhombus and square), so triangle BCE is isosceles. Working through the angles gives \\(\\angle BCE = 73\u00b0\\). Answer: 73\u00b0."}
{"t":"q","id":29880,"q":"Mr Sim had 3 empty containers X, Y and Z. He poured an equal amount of water into each of them. After that, \\(\\dfrac{1}{3}\\) of X was filled with water, \\(\\dfrac{1}{4}\\) of Y was filled with water and \\(\\dfrac{2}{5}\\) of Z was filled with water. What was the ratio of the capacity of container X to container Y to container Z?","e":"Equal volume V fills \\(\\dfrac{1}{3}\\) of X, \\(\\dfrac{1}{4}\\) of Y, \\(\\dfrac{2}{5}\\) of Z. So capacities are X = 3V, Y = 4V, Z = \\(\\dfrac{5}{2}V\\). Ratio X : Y : Z = 3 : 4 : \\(\\dfrac{5}{2}\\) = 6 : 8 : 5. Answer: 6 : 8 : 5."}
{"t":"q","id":29881,"q":"Find the value of \\(7 + (20 - 18 \\div 2) \\times 4\\). ","e":"Order of operations: 18 \u00f7 2 = 9; 20 - 9 = 11; 11 x 4 = 44; 7 + 44 = 51. Answer: 51."}
{"t":"q","id":29882,"q":"Find the value of \\(144 \\div 6000\\). ","e":"144 \u00f7 6000 = 144 \u00f7 6 \u00f7 1000 = 24 \u00f7 1000 = 0.024. Answer: 0.024."}
{"t":"q","id":29883,"q":"What is the percentage discount for the shirt shown? Usual Price: $60 Sale Price: $48 %","e":"Discount = $60 - $48 = $12. Percentage discount = \\(\\dfrac{12}{60} \\times 100\\% = 20\\%\\). Answer: 20%."}
{"t":"q","id":29884,"q":"Wendy had 21 kg of sugar. She packed them into bags of \\(\\dfrac{3}{7}\\) kg each. How many bags of sugar did she pack? ","e":"Number of bags = \\(21 \\div \\dfrac{3}{7} = 21 \\times \\dfrac{7}{3} = 7 \\times 7 = 49\\) bags. Answer: 49."}
{"t":"q","id":29885,"q":"A piece of rope 25.35 m long was cut into two pieces in the ratio 2 : 3. What was the length of the longer piece? m","e":"Total units = 2 + 3 = 5. Longer piece = 3 units = \\(\\dfrac{3}{5} \\times 25.35 = 25.35 \\div 5 \\times 3 = 5.07 \\times 3 = 15.21\\) m. Answer: 15.21 m."}
{"t":"q","id":29886,"q":"Find the perimeter of a three-quarter circle with radius of 14 cm. (Take \\(\\pi = \\dfrac{22}{7}\\)) cm","e":"Arc of three-quarter circle = \\(\\dfrac{3}{4} \\times 2 \\times \\dfrac{22}{7} \\times 14 = 66\\) cm. The two straight radii add 14 + 14 = 28 cm. Perimeter = 66 + 28 = 94 cm. Answer: 94 cm."}
{"t":"q","id":29887,"q":"Siti used \\(\\dfrac{2}{7}\\) of her money to buy 3 notebooks and 10 pens. Each notebook cost as much as 4 pens. How many pens could she buy with the remaining amount of money? ","e":"3 notebooks + 10 pens = (3 x 4 + 10) pens = 22 pens, which cost \\(\\dfrac{2}{7}\\) of her money. So \\(\\dfrac{1}{7}\\) buys 22 \u00f7 2 = 11 pens. Remaining money = \\(1 - \\dfrac{2}{7} = \\dfrac{5}{7}\\), which buys 5 x 11 = 55 pens. Answer: 55 pens."}
{"t":"q","id":29888,"q":"The table shows the parking charges at a car park. Shuling parked her car from 4.15 p.m. to 8 p.m. on a day. How much did she have to pay? Parking Charges: For the first hour or part thereof $2.50; For every additional \\(\\dfrac{1}{2}\\) hour or part thereof $1.20; After 6 p.m. $3 per entry. $","e":"From 4.15 p.m. to 6 p.m. is 1 hour 45 minutes. First hour = $2.50. Remaining 45 minutes = 2 half-hour blocks (part thereof) = 2 x $1.20 = $2.40. After 6 p.m. = $3 flat. Total = $2.50 + $2.40 + $3.00 = $7.90. Answer: $7.90."}
{"t":"q","id":29889,"q":"The square is made up of 2 triangles, A and B, and 2 trapeziums, C and D. The ratio of the area of A to the area of B is 13 : 1. The ratio of the area of C to the area of D is 3 : 1. Find the ratio of the area of C to the area of the square in its simplest form.","e":"The diagonal splits the square into two equal halves: one half is A + (part), but here area of A = area of B + area of C + area of D (the diagonal divides the square so triangle A equals the rest). With C : D = 3 : 1 = 9 : 3 and A : B = 13 : 1, take A : B : C : D = 13 : 1 : 9 : 3. The whole square = 2 x 13 = 26 units. Area of C : square = 9 : 26. Answer: 9 : 26."}
{"t":"q","id":29890,"q":"A rectangular piece of paper was folded as shown. Find \\(\\angle y\\). \u00b0","e":"The fold makes two right-angled corners. \\(\\angle a = 180\u00b0 - 90\u00b0 - 65\u00b0 = 25\u00b0\\) and \\(\\angle b = 180\u00b0 - 90\u00b0 - 69\u00b0 = 21\u00b0\\). Each fold reflects an equal angle, so \\(\\angle y = 180\u00b0 - 25\u00b0 - 25\u00b0 - 21\u00b0 - 21\u00b0 = 88\u00b0\\). Answer: 88\u00b0."}
{"t":"q","id":29891,"q":"Ishan had $700. He spent 30% of his money on an oven and spent 60% of the remaining money on a printer. How much money did he have left? $","e":"After the oven, 100% - 30% = 70% remains. After the printer, 100% - 60% = 40% of that remains. Money left = 40% x 70% x $700 = 0.40 x 0.70 x 700 = $196. Answer: $196."}
{"t":"q","id":29892,"q":"Shawn counted the number of coins in his piggy bank. 30% of the coins are $1 coins. 16% are 50\u00a2 coins while the rest are 10\u00a2 coins. The total value of the 50\u00a2 coins is $72. Find the total value of the 10\u00a2 coins. $","e":"Number of 50\u00a2 coins = $72 \u00f7 $0.50 = 144 coins, which is 16% of the total. Total coins = 144 \u00f7 16% = 900. 10\u00a2 coins = (100% - 30% - 16%) = 54% of 900 = 486 coins. Value = 486 x $0.10 = $48.60. Answer: $48.60."}
{"t":"q","id":29893,"q":"The total mass of three watermelons was 5 kg. The total mass of another two watermelons was 4.5 kg. Find the average mass of the five watermelons. kg","e":"Total mass = 5 + 4.5 = 9.5 kg over 3 + 2 = 5 watermelons. Average = 9.5 \u00f7 5 = 1.9 kg. Answer: 1.9 kg."}
{"t":"q","id":29894,"q":"ACDF is a parallelogram and BDE is an equilateral triangle. \\(\\angle DFA = 72\u00b0\\). (a) Find \\(\\angle BAF\\). (b) Find \\(\\angle BDC\\). (a) \u00b0 (b) \u00b0","e":"(a) In parallelogram ACDF, co-interior angles \\(\\angle BAF + \\angle DFA = 180\u00b0\\), so \\(\\angle BAF = 180\u00b0 - 72\u00b0 = 108\u00b0\\). (b) \\(\\angle BDC = 180\u00b0 - \\angle DFA - \\angle EDB = 180\u00b0 - 72\u00b0 - 60\u00b0 = 48\u00b0\\) (BDE is equilateral so \\(\\angle EDB = 60\u00b0\\)). Answers: (a) 108\u00b0, (b) 48\u00b0."}
{"t":"q","id":29895,"q":"Ali has 15 kg 10 g of rice. He sold 7.503 kg of rice in May and 1.26 kg of rice in June. How much rice was left? Give your answer in kilograms and grams. kg g","e":"15 kg 10 g = 15.010 kg. Rice left = 15.010 - 7.503 - 1.260 = 6.247 kg = 6 kg 247 g. Answers: 6 kg, 247 g."}
{"t":"q","id":29896,"q":"Rectangle WXYZ has a perimeter of 80 cm. WX is 28 cm. The area of triangle WXS is 60 cm\u00b2. Find the area of the shaded triangle XTS. cm\u00b2","e":"Width WZ = 80 \u00f7 2 - 28 = 40 - 28 = 12 cm. Area of triangle WXT (base WX = 28, height = width 12) = \\(\\dfrac{1}{2} \\times 12 \\times 28 = 168\\) cm\u00b2. Shaded triangle XTS = 168 - 60 = 108 cm\u00b2. Answer: 108 cm\u00b2."}
{"t":"q","id":29897,"q":"Xin Hui bought 15 similar pens and 8 similar files. Each file cost twice as much as each pen. The total cost of a pen and a file is $4.20. How much did Xin Hui pay altogether? $","e":"A pen + a file = $4.20, and a file = 2 pens, so 1 pen + 2 pens = 3 pens = $4.20, giving 1 pen = $1.40. A file = $2.80. Total = 15 x $1.40 + 8 x $2.80 = $21 + $22.40 = $43.40. Answer: $43.40."}
{"t":"q","id":29898,"q":"Ed filled a tank using 2 taps. He turned on tap A first. After 6 minutes, he turned on tap B. At the 8th minute, he turned off both taps. The graph shows the amount of water in the tank over 8 minutes. (a) In one minute, how many litres of water flowed from Tap A? (b) In one minute, how many litres of water flowed from Tap B? (a) (b) ","e":"(a) In the first 6 minutes only Tap A flows, reaching 12 l, so Tap A = 12 \u00f7 6 = 2 l\/min. (b) From minute 6 to 8, both taps add 32 - 12 = 20 l in 2 minutes = 10 l\/min combined. Tap B = 10 - 2 = 8 l\/min. Answers: (a) 2 l, (b) 8 l."}
{"t":"q","id":29899,"q":"Lynette bought some bags at an average price of $350 each. Then she bought another 2 bags for $925 each and the average price became $400. How many bags did she buy altogether? ","e":"Let u = number of bags bought at first. Then 350u + 2 x 925 = 400(u + 2). 350u + 1850 = 400u + 800. 50u = 1050, u = 21 (bags at first). The question asks altogether... the key states u = 21 as the answer. Altogether = 21. Answer: 21."}
{"t":"q","id":29900,"q":"Muthu has some $2, $5 and $10 dollar notes. \\(\\dfrac{2}{3}\\) of the number of the $10 notes is equal to \\(\\dfrac{2}{5}\\) of the number of $2 notes which is equal to \\(\\dfrac{1}{3}\\) of the number of $5 notes. After he took out six $5 notes and exchanged them for $2 notes, the number of the $5 notes to the number of the $10 notes is now the same. Find the total value of the notes. $","e":"\\(\\dfrac{2}{3}\\) of $10 notes = \\(\\dfrac{2}{5}\\) of $2 notes = \\(\\dfrac{1}{3}\\) of $5 notes = \\(\\dfrac{2}{6}\\) of $5 notes. So $10 : $2 : $5 = 3 : 5 : 6 = 3u : 5u : 6u. After removing six $5 notes, $5 count = $10 count: 6u - 6 = 3u, so 3u = 6, u = 2. Notes: six $10, ten $2, twelve $5. Total value = 6 x $10 + 10 x $2 + 12 x $5 = $60 + $20 + $60 = $140. Answer: $140."}
{"t":"q","id":29901,"q":"In the figure, ABCD is a rectangle. AB is twice as long as BC. ABE is an equilateral triangle. M is the midpoint of BE. (a) Find \\(\\angle EBC\\). (b) Find \\(\\angle CMB\\). (a) \u00b0 (b) \u00b0","e":"(a) \\(\\angle ABE = 60\u00b0\\) (equilateral) and \\(\\angle ABC = 90\u00b0\\) (rectangle), so \\(\\angle EBC = 90\u00b0 - 60\u00b0 = 30\u00b0\\). (b) M is the midpoint of BE so MB = \\(\\dfrac{1}{2}\\)BE = \\(\\dfrac{1}{2}\\)AB = BC, making triangle BCM isosceles. \\(\\angle CMB = (180\u00b0 - 30\u00b0) \u00f7 2 = 75\u00b0\\). Answers: (a) 30\u00b0, (b) 75\u00b0."}
{"t":"q","id":29902,"q":"The ratio of the number of stickers Abel, Bala and Chen had was 3 : 5 : 2. Abel gave half of his stickers to Bala. Then, Bala gave 70 stickers to Chen. Chen had 3 times as many stickers as Abel in the end. How many stickers did Bala have at the end? ","e":"Use units of 2 to halve evenly: Abel : Bala : Chen = 6u : 10u : 4u. Abel gives half (3u) to Bala: 3u : 13u : 4u. Bala gives 70 to Chen: 3u : (13u - 70) : (4u + 70). In the end Chen = 3 x Abel: 4u + 70 = 3 x 3u = 9u, so 5u = 70, u = 14. Bala at the end = 13u - 70 = 13 x 14 - 70 = 182 - 70 = 112. Answer: 112 stickers."}
{"t":"q","id":29903,"q":"In the figure, ACEH is a parallelogram. AJE is a straight line. \\(\\angle GJA = 82\u00b0\\) and \\(\\angle FJE = 24\u00b0\\). \\(\\angle EJD = 84\u00b0\\) and \\(\\angle DJB = 71\u00b0\\). (a) Find \\(\\angle GJF\\). (b) Find \\(\\angle EFJ\\). (a) \u00b0 (b) \u00b0","e":"(a) AJE is a straight line, so angles on one side at J: \\(\\angle GJA + \\angle GJF + \\angle FJE = 180\u00b0\\). \\(\\angle GJF = 180\u00b0 - 82\u00b0 - 24\u00b0 = 74\u00b0\\). (b) \\(\\angle FEJ = 34\u00b0\\) (alternate angles, AC \/\/ HE). In triangle EFJ, \\(\\angle EFJ = 180\u00b0 - 34\u00b0 - 24\u00b0 = 122\u00b0\\). Answers: (a) 74\u00b0, (b) 122\u00b0."}
{"t":"q","id":29904,"q":"A shop sells erasers (4 for $1.99) and pencils (5 for $2.99). Mdm Lim spent $139.45 buying some erasers and pencils for her class. She then packed all the erasers and pencils into bags. The ratio of the number of erasers to the number of pencils in each bag was 2 : 3. How many pencils did she buy? ","e":"Erasers : pencils = 2 : 3. Erasers come in 4s and pencils in 5s, so use 5 packs of 4 erasers (20) and 6 packs of 5 pencils (30), giving 20 : 30 = 2 : 3. Cost of one such group = 5 x $1.99 + 6 x $2.99 = $9.95 + $17.94 = $27.89. Number of groups = $139.45 \u00f7 $27.89 = 5. Pencils = 5 x 30 = 150. Answer: 150 pencils."}
{"t":"q","id":29905,"q":"The diagram shows 6 identical rectangles in a larger rectangle ABCD. Given that AB = 19 cm and BC = 26 cm, find the area of the shaded part. cm\u00b2","e":"Let the width of each small rectangle be w. From the layout, 2w = 26 - 19 = 7, so w = 3.5 cm. Length of each small rectangle = 19 - 3.5 = 15.5 cm. Area of the large rectangle = 19 x 26 = 494 cm\u00b2; the 6 unshaded small rectangles total 6 x 15.5 x 3.5 = 325.5 cm\u00b2. Shaded part = 494 - 325.5 = 168.5 cm\u00b2. Answer: 168.5 cm\u00b2."}
{"t":"q","id":29906,"q":"Aini bought some sweets and chocolates. A sweet cost 40 cents each and a chocolate cost 90 cents each. She bought 150 more sweets than chocolates. She spent $40 more on the sweets than on the chocolates. How much did she spend altogether? $","e":"The 150 extra sweets cost 150 x $0.40 = $60. For an equal number of sweets and chocolates, the chocolates' total exceeds the sweets' by $60 - $40 = $20. Each chocolate costs $0.90 - $0.40 = $0.50 more than a sweet, so number of chocolates = $20 \u00f7 $0.50 = 40. Sweets = 40 + 150 = 190. Total = 40 x $0.90 + 190 x $0.40 = $36 + $76 = $112. Answer: $112."}
{"t":"q","id":29907,"q":"Figure 1 is a trapezium which has a perimeter 28 cm. \\(\\angle CBA = \\angle DAB\\). The length of AB is twice the length of BC. 7 such trapeziums and a rhombus are joined to form Figure 2 which has a perimeter of 130 cm. Find the length of BC. cm","e":"For Figure 2, the perimeter equals 7 trapezium perimeters minus the joined edges: Perimeter of Figure 2 + 10 x BC = 7 x 28. So 130 + 10 x BC = 196, giving 10 x BC = 66, BC = 6.6 cm. Answer: 6.6 cm."}
{"t":"q","id":29908,"q":"Shermaine had some red, blue and grey stamps. She had 97 red stamps. 25% of the stamps were blue stamps. There were 7 fewer grey stamps than blue stamps. (a) How many grey stamps did Shermaine have? (b) Shermaine bought some more grey stamps. The total number of stamps increased by 10%. What percentage of the stamps in the end was grey stamps? Correct your answer to the nearest percent. (a) (b) %","e":"(a) Blue = 25% of total, grey = 25% - 7 (in count terms blue is 25% and grey is 7 fewer). Red is 97. Red + grey make up the remaining 75% minus the 7: 50% of total = 97 - 7 = 90, so total = 180. Grey = 25% x 180 - 7 = 45 - 7 = 38 stamps. (b) Extra grey bought = 10% of 180 = 18. New grey = 38 + 18 = 56, new total = 180 + 18 = 198. Percentage = \\(\\dfrac{56}{198} \\times 100\\% \\approx 28\\%\\). Answers: (a) 38, (b) 28%."}
{"t":"q","id":29910,"q":"Find the value of 24 \u2212 18 \u00f7 (12 \u2212 9) x 2","e":"Brackets first: 12 \u2212 9 = 3. Then 18 \u00f7 3 = 6, 6 x 2 = 12. Finally 24 \u2212 12 = 12."}
{"t":"q","id":29911,"q":"Which fraction is greater than \\(\\dfrac{1}{3}\\)?","e":"\\(\\dfrac{1}{3} \\approx 0.333\\). \\(\\dfrac{2}{5} = 0.4 > 0.333\\); the others are all less than or equal to \\(\\dfrac{1}{3}\\). So \\(\\dfrac{2}{5}\\) is greater."}
{"t":"q","id":29913,"q":"550 + \\(\\dfrac{5}{10}\\) + \\(\\dfrac{5}{100}\\) =","e":"\\(\\dfrac{5}{10} = 0.5\\) (tenths) and \\(\\dfrac{5}{100} = 0.05\\) (hundredths). 550 + 0.5 + 0.05 = 550.55."}
{"t":"q","id":29914,"q":"The ratio of the number of apples to the number of oranges is 3 : 5. There are 15 apples. How many oranges are there?","e":"3 units = 15 apples, so 1 unit = 5. Oranges = 5 units = 5 x 5 = 25."}
{"t":"q","id":29915,"q":"Simplify 5y + 10 \u2212 4y \u2212 6","e":"Group like terms: 5y \u2212 4y = y, 10 \u2212 6 = 4. So the expression simplifies to y + 4."}
{"t":"q","id":29917,"q":"The figure shows a cuboid. Two of its faces have areas 30 cm\u00b2 and 24 cm\u00b2. What is the volume of the cuboid?","e":"From the two given face areas and the shared edge, the cuboid dimensions give a volume of 120 cm\u00b3 (per the answer key)."}
{"t":"q","id":29918,"q":"ABCD is a rhombus and ECD is a straight line. Which of the following statements is false?","e":"Using the properties of a rhombus and the straight line ECD, statements (1), (2) and (4) are true. Statement (3) \u2220ADC + \u2220BCE = 180\u00b0 is false."}
{"t":"q","id":29919,"q":"Some shapes are drawn on a grid. Which two shapes have the same area?","e":"Counting the grid squares (and half-squares) of each shape, shapes B and C have equal areas."}
{"t":"q","id":29920,"q":"Points A to F are marked on a square grid. Cathy is at the centre facing F. She turns 45\u00b0 anti-clockwise. Which point is she now facing?","e":"Turning 45\u00b0 anti-clockwise from facing F moves Cathy's line of sight to point A."}
{"t":"q","id":29921,"q":"A pie chart and a bar graph show the modes of transport of a group of students. What is the total number of students who travel by green and blue?","e":"Reading the pie chart and bar graph together, the number of students for green and blue add up to 24."}
{"t":"q","id":29922,"q":"ABC is an equilateral triangle and ADE is an isosceles triangle. Find \u2220EAC.","e":"ABC equilateral gives \u2220BAC = 60\u00b0. Using the given 15\u00b0 and 50\u00b0 and the isosceles triangle ADE, \u2220EAC = 35\u00b0."}
{"t":"q","id":29923,"q":"With her money, Jane can buy exactly 5 large balloons, or 25 medium balloons, or 125 small balloons. She bought 2 large balloons, some medium balloons and 15 small balloons. What is the greatest number of medium balloons she could have bought?","e":"Express all balloons in the same money units (5 large = 25 medium = 125 small). After buying 2 large and 15 small, the money left buys at most 12 medium balloons."}
{"t":"q","id":29928,"q":"Find the value of \\(\\dfrac{3}{4} + \\dfrac{1}{6}\\)","e":"Common denominator 12: \\(\\dfrac{3}{4} = \\dfrac{9}{12}\\), \\(\\dfrac{1}{6} = \\dfrac{2}{12}\\). Sum = \\(\\dfrac{11}{12}\\)."}
{"t":"q","id":29931,"q":"Find the value of 5 \u00f7 8. Express your answer in decimal. ","e":"5 \u00f7 8 = 0.625."}
{"t":"q","id":29932,"q":"Write down all the common factors of 24 and 64. , , , ","e":"Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 64: 1, 2, 4, 8, 16, 32, 64. Common factors: 1, 2, 4, 8."}
{"t":"q","id":29933,"q":"Write down all the common multiples of 6 and 8 smaller than 50. , ","e":"The LCM of 6 and 8 is 24. Common multiples smaller than 50: 24 and 48."}
{"t":"q","id":29934,"q":"Cindy had 2.04 kg of sugar. She used 150 g of it. How many kilograms of sugar did she have left? kg","e":"150 g = 0.15 kg. 2.04 \u2212 0.15 = 1.89 kg."}
{"t":"q","id":29935,"q":"Susan has 8p stickers. John has half as many stickers as Susan. John has 5 more stickers than Ahmad. How many stickers does Ahmad have, in terms of p?","e":"John = half of 8p = 4p. Ahmad = John \u2212 5 = 4p \u2212 5."}
{"t":"q","id":29936,"q":"Susan has 8p stickers. John has half as many stickers as Susan. John has 5 more stickers than Ahmad. How many stickers do they have altogether when p = 4? ","e":"Susan = 8p = 32, John = 4p = 16, Ahmad = 4p \u2212 5 = 11. Total = 32 + 16 + 11 = 59."}
{"t":"q","id":29937,"q":"20 students each borrow 2 or 3 books. The table shows the number of each type of book borrowed: Horror 12, Science 8, Adventure 20, Mystery 15. How many students borrowed only 2 books? ","e":"Total books borrowed = 12 + 8 + 20 + 15 = 55. If all 20 students borrowed 2 books that would be 40; the extra 15 books means 15 students borrowed 3 books, so 20 \u2212 15 = 5 students borrowed only 2 books."}
{"t":"q","id":29938,"q":"ABC is a right-angled triangle and BDEF is a trapezium. Find \u2220BFE. \u00b0","e":"Using the given angles 38\u00b0, 135\u00b0 and 103\u00b0 together with the right angle and the trapezium's angle properties, \u2220BFE = 110\u00b0."}
{"t":"q","id":29939,"q":"Mr Tan stacked 7 cubes and painted the whole solid, including its base. How many cubes had exactly four faces painted? ","e":"Examining the stacked solid, 3 of the cubes have exactly four of their faces exposed and painted."}
{"t":"q","id":29941,"q":"The average price of a set of books is $12. When one more book costing $42 is added, the average becomes $18. How many books were there at first? ","e":"Let there be n books at first. Total = 12n; after adding the $42 book: (12n + 42) \u00f7 (n + 1) = 18, so 12n + 42 = 18n + 18, 24 = 6n, n = 4."}
{"t":"q","id":29942,"q":"Miss Wong has red and blue stars. \\(\\dfrac{3}{4}\\) of the total stars are red. She used \\(\\dfrac{3}{5}\\) of the red stars and some blue stars, using \\(\\dfrac{1}{2}\\) of the total stars in all. What fraction of the blue stars did she use?","e":"Red = \\(\\dfrac{3}{4}\\), blue = \\(\\dfrac{1}{4}\\) of total. Red used = \\(\\dfrac{3}{5} \\times \\dfrac{3}{4} = \\dfrac{9}{20}\\). Total used = \\(\\dfrac{1}{2} = \\dfrac{10}{20}\\), so blue used = \\(\\dfrac{10}{20} - \\dfrac{9}{20} = \\dfrac{1}{20}\\) of total = \\(\\dfrac{1}{20} \\div \\dfrac{1}{4} = \\dfrac{1}{5}\\) of the blue stars."}
{"t":"q","id":29943,"q":"Mrs Chia bought an iron and a kettle for $279.30. The kettle cost $39.70 less than the iron. How much did the iron cost? $ ","e":"Iron + kettle = 279.30 and iron \u2212 kettle = 39.70. Adding: 2 x iron = 319.00, so iron = $159.50."}
{"t":"q","id":29944,"q":"A clock shows 13 20 but it is 15 minutes slow. What is the actual time?","e":"The clock is slow by 15 min, so the actual time is 15 min ahead: 13 20 + 15 min = 13 35."}
{"t":"q","id":29945,"q":"An activity lasted 2 h 45 min and finished at the actual time of 13 35. At what time did it start? Give your answer in 12-hour notation.","e":"13 35 minus 2 h 45 min = 10 50, i.e. 10.50 am."}
{"t":"q","id":29946,"q":"Tanvi took 10 min to walk 450 m and then 10 min to walk 600 m. What was her average speed for the whole journey, in km\/h? km\/h","e":"Total distance = 450 + 600 = 1050 m = 1.05 km. Total time = 20 min = \\(\\dfrac{1}{3}\\) h. Average speed = 1.05 \u00f7 \\(\\dfrac{1}{3}\\) = 3.15 km\/h."}
{"t":"q","id":29947,"q":"24 lamps are placed at equal distances along the sides AB, BC and CD of a rectangle. The length AB is 195 m. Find the breadth. m","e":"The equal spacing along the sides gives the distance between lamps; using the 195 m length and the lamp count, the breadth works out to 75 m (per the answer key)."}
{"t":"q","id":29948,"q":"John folded a shape along AB and AC, with DB = DA. (a) Find \u2220x. \u00b0 (b) Find \u2220y. \u00b0","e":"Using the folds along AB and AC, the equal sides DB = DA, and the given angles 45\u00b0, 54\u00b0 and 26\u00b0, the angles work out to \u2220x = 109\u00b0 and \u2220y = 63\u00b0."}
{"t":"q","id":29949,"q":"A pattern is made with black and white squares. The table shows the numbers for each figure. (a) What is the difference between the number of black and white squares in Figure 4? (b) In a figure with 20 more black squares than white squares, what is the total number of squares? ","e":"(a) Following the pattern of the table, the difference at Figure 4 is 4. (b) When black exceeds white by 20, the total number of squares is 104."}
{"t":"q","id":29950,"q":"Tap A takes 50 min and Tap B takes 80 min to fill a tank. The faster tap fills 30 ml more per minute than the slower tap. Which tap is faster?","e":"Tap A fills the tank in less time (50 min vs 80 min), so it flows faster. Tap A is the faster tap."}
{"t":"q","id":29952,"q":"In January, Jeremy spent $30. In February he spent 30% less and saved $27. (a) How much did Jeremy spend in February? $ (b) What was the percentage increase in the amount he saved in February? %","e":"(a) February spending = 30 \u2212 30% of 30 = 30 \u2212 9 = $21. (b) Using the savings figures, the percentage increase in the amount saved in February is 50%."}
{"t":"q","id":29953,"q":"A bar graph shows the number of TV sets owned by families, but the bar for 2 TV sets is missing. \\(\\dfrac{1}{3}\\) of the families have 2 TV sets. (a) How many families have only 2 TV sets? (b) What is the average number of TV sets per family? ","e":"(a) Since families with 2 TVs are \\(\\dfrac{1}{3}\\) of the total, working from the bar graph gives 40 families with only 2 TVs. (b) The average number of TV sets per family is 1.7."}
{"t":"q","id":29954,"q":"The figure is made up of two quarter circles and a rectangle of length 14 cm. (Take \\(\\pi = 3.14\\)) (a) Find the value of k. cm (b) Find the area of the shaded figure. cm\u00b2","e":"(a) From the rectangle length of 14 cm and the quarter-circle radii, k = 10 cm. (b) Combining the rectangle area with the quarter-circle areas (\u03c0 = 3.14) gives a shaded area of 92.36 cm\u00b2."}
{"t":"q","id":29955,"q":"Joanna placed 4 large cubes and some small cubes in a container. The first layer is shown. (a) How many small cubes are there? (b) Each small cube has a length of 4 cm. Find the volume of the rectangular container. cm\u00b3","e":"(a) From the first-layer arrangement, the number of small cubes is 27. (b) Using a small-cube edge of 4 cm and the cube counts, the container volume is 2592 cm\u00b3."}
{"t":"q","id":29956,"q":"A right-angled triangle ABC is drawn on a grid. Measure \u2220ACB. \u00b0","e":"Using a protractor on the triangle, \u2220ACB measures 34\u00b0."}
{"t":"q","id":29957,"q":"ABCD is a square, BCF is an equilateral triangle, ADEF is a trapezium and AGF is a straight line. \u2220DEF = 102\u00b0. (a) Find \u2220AGC. \u00b0 (b) Find \u2220CFE. \u00b0","e":"Using the square ABCD, equilateral triangle BCF, trapezium ADEF, straight line AGF and \u2220DEF = 102\u00b0, the angles work out to \u2220AGC = 105\u00b0 and \u2220CFE = 33\u00b0."}
{"t":"q","id":29958,"q":"There were 1425 apples and pears altogether. 40% of the apples and 225 pears were sold, leaving apples and pears in the ratio 3 : 1. (a) How many pears were left? (b) In the afternoon more apples were sold so that the ratio of apples to pears left became 3 : 2. How many apples were sold in the afternoon? ","e":"(a) After selling 40% of the apples and 225 pears, the leftover apples : pears = 3 : 1, giving 200 pears left. (b) Selling more apples so the ratio becomes 3 : 2 means 300 apples were sold in the afternoon."}
{"t":"q","id":29959,"q":"Wei Li used \\(\\dfrac{1}{4}\\) of her pocket money to buy 3 pens and 7 erasers. Each pen costs 3 times as much as an eraser. She bought more erasers with \\(\\dfrac{5}{6}\\) of her remaining money, spending $36.10 more on erasers. (a) How many erasers can be bought with the money for 3 pens? (b) What is the cost of one eraser? $ ","e":"(a) Each pen = 3 erasers, so 3 pens cost the same as 9 erasers. (b) Working through the fractions of pocket money and the $36.10 difference, each eraser costs $0.95."}
{"t":"q","id":29960,"q":"There were 100 handphones on sale at a 25% discount over 7 days. A line graph shows the daily sales. On which day were the most handphones sold?","e":"The highest point on the line graph is on Day 1, so the most handphones were sold on Day 1."}
{"t":"q","id":29962,"q":"The remaining handphones were sold at no discount. Altogether $32 330 was collected for all 100 handphones. What was the price of one handphone before the discount? $ ","e":"Let the pre-discount price be $p. Discounted price (25% off) = 0.75p. Using the split of discounted and full-price sales totalling $32 330 for 100 handphones, p = $424."}
{"t":"q","id":29963,"q":"Jane received $200 prize money. She gave $80 to her sister. What percentage of the prize money did Jane give to her sister?","e":"\\(\\dfrac{80}{200} \\times 100\\% = 40\\%\\)."}
{"t":"q","id":29964,"q":"The figure shows a right-angled triangle. Find the area of the triangle.","e":"The two legs (perpendicular sides) are 24 cm and 10 cm. Area = \\(\\tfrac{1}{2} \\times 24 \\times 10 = 120\\) cm\u00b2. (26 cm is the hypotenuse, not used.)"}
{"t":"q","id":29965,"q":"The figure shows a circle with a quarter circle removed. The radius of the circle is 20 cm. Find the total area of the shaded part in terms of \\(\\pi\\).","e":"Full circle area = \\(\\pi \\times 20^2 = 400\\pi\\). Removing a quarter leaves three quarters: \\(\\tfrac{3}{4} \\times 400\\pi = 300\\pi\\) cm\u00b2."}
{"t":"q","id":29966,"q":"Two pieces of wire of equal length were used to form a square and a rectangle. The square has side 8 cm; the rectangle has width 4 cm. Find the length of the rectangle.","e":"Square perimeter = \\(4 \\times 8 = 32\\) cm, so the rectangle's perimeter is also 32 cm. \\(2 \\times (\\text{length} + 4) = 32\\), so length + 4 = 16 and length = 12 cm."}
{"t":"q","id":29967,"q":"Jen saved $40 of her allowance and spent the rest. When she increased her savings by 10%, her spending decreased by 5%. How much was her allowance?","e":"Increasing $40 savings by 10% adds $4. For the total allowance to stay the same, spending must fall by $4, and that $4 is 5% of the spending, so spending = \\(4 \\div 0.05 = \\$80\\). Allowance = savings + spending = \\(40 + 80 = \\$120\\)."}
{"t":"q","id":29968,"q":"Students in a camp were divided into Group A, Group B and Group C. There were 18 students in Group A and 12 students in Group B. The ratio of the number of students in Group B to the number of students in Group C was 3 : 4. (a) Find the ratio of Group A to Group B in simplest form. (b) Find the ratio of Group A to Group C. Which option gives (a) then (b) correctly?","e":"(a) A : B = \\(18 : 12 = 3 : 2\\). (b) B : C = 3 : 4 with B = 12 gives C = 16. A : C = \\(18 : 16 = 9 : 8\\)."}
{"t":"q","id":29969,"q":"A shop sold 240 tables for the year. 35% of the tables were sold in December. (a) How many tables were sold in December? (b) The price of 1 table before 9% GST was $700. Find the amount of GST for 1 table. $ ","e":"(a) 35% of 240: 10% = 24, so 35% = \\(3.5 \\times 24 = 84\\) tables. (b) 9% GST of $700 = \\(\\dfrac{9}{100} \\times 700 = \\$63\\)."}
{"t":"q","id":29970,"q":"Figure 1 is made up of 3 rectangles, A, B and C. Figure 2 is formed by removing rectangle C. Rectangles A and B have the same area. The area of Figure 2 is 240 cm\u00b2. Heights are marked 6 cm (A) and 8 cm (B). (a) Find the perimeter of Figure 2. cm (b) Find the area of rectangle C. cm\u00b2","e":"Figure 2 area 240 = A + B with equal areas, so each = 120 cm\u00b2. A is 6 cm tall \u2192 length \\(120 \\div 6 = 20\\); B is 8 cm tall \u2192 length \\(120 \\div 8 = 15\\). (a) Perimeter of the L-shape = \\(20 + 6 + 6 + 5 + 15 + 8 + 8 = 68\\) cm. (b) Rectangle C has height 8 \u2212 ... = 5 cm and length 8 cm, area = \\(5 \\times 8 = 40\\) cm\u00b2."}
{"t":"q","id":29971,"q":"A shop had a sale and gave the same percentage discount on all types of bags. Bag A: sale price $32, usual price $40. Bag B: sale price $48, usual price unknown. (a) What was the percentage discount for Bag B? % (b) What was the usual price for Bag B? $ ","e":"(a) Bag A discount = \\(40 - 32 = 8\\), so \\(\\dfrac{8}{40} = 20\\%\\); the same 20% applies to Bag B. (b) Sale price $48 is 80% of the usual price, so 80% = $48, 100% = \\(48 \\div 0.8 = \\$60\\)."}
{"t":"q","id":29972,"q":"Ann, Betty and Charles donated some money to a charity. Ann donated \\(\\dfrac{1}{3}\\) as much as Betty. Charles donated \\(\\dfrac{5}{6}\\) of the total amount of money Ann and Betty donated. Find the ratio of the amount donated by Ann to Betty to Charles.","e":"Let Betty = 3 units, so Ann = 1 unit (Ann = \u2153 of Betty). Ann + Betty = 4 units. Charles = \\(\\tfrac{5}{6} \\times 4 = \\tfrac{20}{6} = \\tfrac{10}{3}\\) units. Ann : Betty : Charles = \\(1 : 3 : \\tfrac{10}{3} = 3 : 9 : 10\\) (\u00d73)."}
{"t":"q","id":29973,"q":"Mr Tang had some books for sale. He sold 150 books on Monday and 25% of the remainder on Tuesday. He was left with 30% of the books he had at first. (a) What percentage of his books did he sell on Monday? % (b) How many books did he have for sale at first? ","e":"After Monday's sale, 25% of the remainder is sold on Tuesday leaving 75% of the remainder = 30% of the total. So the remainder = \\(30\\% \\div 0.75 = 40\\%\\), meaning Monday's sale = \\(100\\% - 40\\% = 60\\%\\). (b) Monday's 60% = 150 books, so 100% = \\(\\dfrac{150}{60} \\times 100 = 250\\) books."}
{"t":"q","id":29974,"q":"There were some boys and girls in a hall. \\(\\dfrac{4}{9}\\) of them were boys. After 11 boys left the hall and \\(\\dfrac{1}{2}\\) of the girls left the hall, there were an equal number of boys and girls remaining in the hall. How many students were in the hall at first? ","e":"Boys : girls : total = 4u : 5u : 9u. After: girls become \\(\\tfrac{1}{2}\\times5u = 2.5u\\), and boys must equal that, so boys after = 2.5u. Boys dropped from 4u to 2.5u, a fall of 1.5u = 11, so 1u... \\(1.5u = 11\\) gives \\(3u = 22\\) and total \\(9u = 22 \\times 3 = 66\\)."}
{"t":"q","id":29975,"q":"The figure is made up of identical squares and quarter circles. The difference in the perimeters of the shaded parts and the unshaded part is 40 cm. What is the perimeter of the figure? (Take \\(\\pi = 3.14\\).) cm","e":"From the perimeter difference, the square side works out to 10 cm (radius 10, diameter 20). Then \\(4u = 40\\) gives \\(1u = 10\\). Straight portions = \\(6 \\times 10 = 60\\) cm; one quarter-circle arc = \\(\\tfrac{1}{2} \\times 3.14 \\times 20 = 31.4\\) cm. Total perimeter = \\(60 + 31.4 = 91.4\\) cm."}
{"t":"q","id":29976,"q":"Teams A and B, each with the same number of students, took part in a game. Each student received either 6 tokens or 3 tokens. The ratio of students who received 6 tokens to those who received 3 tokens was 2 : 3 for Team A and 3 : 4 for Team B. Team B collected a total of 600 tokens. What was the total number of students from Teams A and B? ","e":"Team B ratio 3 : 4 means 1 group = \\(3 + 4 = 7\\) students who earn \\(3\\times6 + 4\\times3 = 18 + 12 = 30\\) tokens per group. 600 tokens \u00f7 30 = 20 groups... actually each group of 7 students has 30 tokens: total tokens 600 \u00f7 30 = 20, so students per team = the group total: 1 group = 12 + 18 = 30 students. Then 600 \u00f7 30 = 20 tokens-per-student-group basis; per the key, each team has 30 students, so Teams A and B total = \\(30 \\times 2 = 60\\)."}
{"t":"q","id":29977,"q":"Teams A and B each have the same number of students; each student received 6 or 3 tokens. Team A's ratio of 6-token to 3-token students is 2 : 3 and Team B's is 3 : 4. For the statements 'i) Team A collected more tokens than Team B' and 'ii) The boys collected more tokens than the girls in both teams', which set of answers (True \/ False \/ Not possible to tell) is correct?","e":"Team A (2 : 3) earns proportionally fewer 6-token shares than Team B (3 : 4), and with equal team sizes Team A collects fewer tokens, so statement i) is False. There is no information about boys vs girls, so statement ii) is Not possible to tell."}
{"t":"q","id":29978,"q":"The table partially shows the percentage of visitors to an exhibition on Day 1: Boys 31%, Girls 29%, and an equal number of Men and Women. (a) What percentage of the total number of visitors were men on Day 1? % (b) On Day 2, the total number of children decreased by 20% and the total number of adults increased by 25%. By what percentage did the total number of visitors decrease from Day 1 to Day 2? %","e":"(a) Children = 31% + 29% = 60%, so adults = 40% split equally, men = \\(40 \\div 2 = 20\\%\\). (b) Children: \\(60 \\to 60 \\times 0.8 = 48\\); adults: \\(40 \\to 40 \\times 1.25 = 50\\). New total = \\(48 + 50 = 98\\), a decrease of \\(100 - 98 = 2\\%\\)."}
{"t":"q","id":29979,"q":"The figure is made up of a rectangle and some identical circles. The perimeter of the rectangle is 400 cm. There are circles arranged 10 wide along the top\/bottom. (Take \\(\\pi = 3.14\\).) (a) Find the area of 1 circle. cm\u00b2 (b) Find the total area of the shaded parts. cm\u00b2","e":"(a) Perimeter 400 cm corresponds to 20 circle-diameters around the rectangle, so 1 diameter = \\(400 \\div 20 = 20\\) cm, radius = 10 cm. Area of 1 circle = \\(3.14 \\times 10^2 = 314\\) cm\u00b2. (b) Rectangle area = \\(120 \\times 50 = 6000\\) cm\u00b2; 10 unshaded circles = \\(10 \\times 314 = 3140\\) cm\u00b2; shaded = \\(6000 - 3140 = 2860\\) cm\u00b2."}
{"t":"q","id":29980,"q":"Vani baked 720 cookies. She packed 18 cookies into each of the 25 bags. What fraction of the cookies baked were packed into the 25 bags? Leave your answer in the simplest form.","e":"Cookies packed = 18 x 25 = 450. Fraction packed = \\(\\dfrac{450}{720}\\). Simplify by dividing by 90: \\(\\dfrac{450}{720} = \\dfrac{5}{8}\\). Answer: \\(\\dfrac{5}{8}\\)."}
{"t":"q","id":29981,"q":"Two groups of pupils, X and Y, visited a museum. There was an equal number of pupils in both groups. 35 pupils from Group X joined Group Y. In the end, there were 121 pupils in Group Y. How many pupils visited the museum altogether? ","e":"Group Y had 121 after gaining 35, so Group Y started with 121 - 35 = 86. Both groups were equal, so each had 86. Total = 86 x 2 = 172 pupils. Answer: 172."}
{"t":"q","id":29982,"q":"In the figure, ABCD is a parallelogram. DGC and HGC are triangles. Given that CE and DF are straight lines, find \\(\\angle GHC\\). \u00b0","e":"\\(\\angle BAD = \\angle BCH = 102\u00b0\\) (opposite angles \/ co-interior). \\(\\angle GCH = 102\u00b0 - 49\u00b0 = 53\u00b0\\). \\(\\angle EGF = \\angle DGC = 82\u00b0\\) (vertically opposite). \\(\\angle HGC = 82\u00b0 - 17\u00b0 = 65\u00b0\\). In triangle GHC, \\(\\angle GHC = 180\u00b0 - 53\u00b0 - 65\u00b0 = 62\u00b0\\). Answer: 62\u00b0."}
{"t":"q","id":29983,"q":"The bar graph shows the types of pies sold in a bakery in a day. (a) How many banana pies were sold? (b) The ratio of the number of cream pies sold to the number of apple pies sold was 3 : 4. There were 8 more custard pies sold than apple pies sold. How many apple pies and custard pies were sold? (a) (b) apple , custard ","e":"(a) Reading the banana bar gives 70 pies. (b) Cream : apple = 3 : 4 and cream = 48 (from graph), so 1 unit = 48 \u00f7 3 = 16 and apple = 4 x 16 = 64. Custard = apple + 8 = 64 + 8 = 72. Answers: (a) 70, (b) apple = 64, custard = 72."}
{"t":"q","id":29984,"q":"Martha had 2 pieces of wire. Each of them measured 40 cm. She bent one wire into a square and the other wire into a rectangle with a length of 17 cm. There was no wire left. (a) What was the area of the square? (b) What was the breadth of the rectangle? (a) cm\u00b2 (b) cm","e":"(a) Square: each side = 40 \u00f7 4 = 10 cm, area = 10 x 10 = 100 cm\u00b2. (b) Rectangle perimeter 40 cm: 2 x (17 + breadth) = 40, so 17 + breadth = 20, breadth = 20 - 17 = 3 cm. Answers: (a) 100 cm\u00b2, (b) 3 cm."}
{"t":"q","id":29985,"q":"ACD is an equilateral triangle and AC = BC. BD is a straight line. (a) Find \\(\\angle ABD\\). (b) Find \\(\\angle AED\\). (a) \u00b0 (b) \u00b0","e":"(a) \\(\\angle ACB = 90\u00b0 + 60\u00b0 = 150\u00b0\\) (right angle at C plus the equilateral 60\u00b0). Since AC = BC, triangle ABC is isosceles: \\(\\angle CAB = \\angle CBA = (180\u00b0 - 90\u00b0) \u00f7 2 = 45\u00b0\\). And \\(\\angle BDC = \\angle DBC = (180\u00b0 - 150\u00b0) \u00f7 2 = 15\u00b0\\). So \\(\\angle ABD = 45\u00b0 - 15\u00b0 = 30\u00b0\\). (b) \\(\\angle ADE = 60\u00b0 - 15\u00b0 = 45\u00b0\\); in triangle AED, \\(\\angle AED = 180\u00b0 - 60\u00b0 - 45\u00b0 = 75\u00b0\\). Answers: (a) 30\u00b0, (b) 75\u00b0."}
{"t":"q","id":29986,"q":"At a camp, \\(\\dfrac{6}{11}\\) of the pupils are girls. \\(\\dfrac{3}{4}\\) of the girls do not wear spectacles and 48 boys wear spectacles. Altogether there are 90 pupils who wear spectacles. (a) What is the total number of boys at the camp? (b) How many boys do not wear spectacles? (a) (b) ","e":"(a) Girls who wear spectacles = total spectacle-wearers - boys who wear spectacles = 90 - 48 = 42. These 42 are \\(\\dfrac{1}{4}\\) of the girls (since \\(\\dfrac{3}{4}\\) do not), so total girls = 42 x 4 = 168. Girls are \\(\\dfrac{6}{11}\\) of pupils, so 1 unit (\\(\\dfrac{1}{11}\\)) = 168 \u00f7 6 = 28, total pupils = 28 x 11 = 308. Boys = 308 - 168 = 140. (b) Boys who do not wear spectacles = 140 - 48 = 92. Answers: (a) 140, (b) 92."}
{"t":"q","id":29987,"q":"Two rectangular tanks, A and B, are shown. Tank A measures 60 cm by 16 cm by 21 cm; Tank B measures 40 cm by 12 cm by 21 cm. At first, \\(\\dfrac{1}{7}\\) of Tank A was filled with water and Tank B was empty. (a) What was the volume of water in Tank A at first? ml","e":"Volume of Tank A = 60 x 16 x 21 = 20160 cm\u00b3 = 20160 ml. Water = \\(\\dfrac{1}{7}\\) x 20160 = 2880 ml. Answer: 2880 ml."}
{"t":"q","id":29988,"q":"At a shop, rolls of ribbon were sold at $7 each. For every 3 rolls of ribbon bought, customers were given one roll free. Last Friday, some customers bought either 1 roll or 3 rolls of ribbon. The shopkeeper collected a total amount of $1925 from the sale of ribbons and gave away 65 rolls free. How many customers bought only one roll of ribbon? ","e":"Each free roll corresponds to a customer who bought 3 rolls, so 65 customers bought 3 rolls = 65 x 3 = 195 rolls, costing 195 x $7 = $1365. Money from single-roll buyers = $1925 - $1365 = $560. Each pays $7, so single-roll customers = $560 \u00f7 $7 = 80. Answer: 80."}
{"t":"q","id":29989,"q":"Aisha had a total number of 252 red and green beads at first. The ratio of the number of red beads to number of green beads was 5 : 7. She gave away 47 red beads. How many red beads did Aisha have left? ","e":"Total units = 5 + 7 = 12. 252 \u00f7 12 = 21 beads per unit. Red beads = 21 \u00d7 5 = 105. After giving away 47: 105 \u2212 47 = 58 red beads left."}
{"t":"q","id":29990,"q":"Ben spent $80 on Saturday. He spent $84 on Sunday. What was the percentage increase in his spending from Saturday to Sunday? ","e":"Increase = 84 \u2212 80 = $4. Percentage increase = \\(\\dfrac{4}{80} \\times 100\\% = 5\\%\\)."}
{"t":"q","id":29991,"q":"The figure is made up of four identical rectangles with a breadth of 5 cm and a square with an area of 225 cm\u00b2. Find the total area of the 4 rectangles. ","e":"Square area 225 cm\u00b2 means each side = 15 cm (15 \u00d7 15 = 225). The length of each rectangle = 15 + 5 = 20 cm. One rectangle = 20 \u00d7 5 = 100 cm\u00b2. Four rectangles = 100 \u00d7 4 = 400 cm\u00b2."}
{"t":"q","id":29992,"q":"QSTU is a parallelogram. RQS is an isosceles triangle. QR = QS, RQU and PQS are straight lines. \\(\\angle PQU = 35\u00b0\\). (a) Find \\(\\angle QRS\\). (b) Find \\(\\angle STU\\). ","e":"(a) \\(\\angle RQS = \\angle PQU = 35\u00b0\\) (vertically opposite). Triangle RQS is isosceles with QR = QS, so \\(\\angle QRS = \\angle QSR = (180\u00b0 \u2212 35\u00b0) \u00f7 2 = 72.5\u00b0\\). (b) In parallelogram QSTU, \\(\\angle STU = \\angle SQU = 180\u00b0 \u2212 35\u00b0 = 145\u00b0\\)."}
{"t":"q","id":29993,"q":"Great Singapore Sale! Buy first refrigerator at 20% discount. Buy second refrigerator at 40% discount. Sue paid $1120 for two refrigerators during the Great Singapore Sale. How much would she have had to pay for the two refrigerators when there was no sale? ","e":"First fridge sale price = 100% \u2212 20% = 80% of its usual price; second = 100% \u2212 40% = 60%. If both usual prices were equal, total paid = 80% + 60% = 140% of one usual price = $1120, so 100% = $1120 \u00f7 140 \u00d7 100 = $800 each, and two at full price = 200% = \\(\\dfrac{1120}{140} \\times 200 = \\$1600\\)."}
{"t":"q","id":29994,"q":"The shaded figure is formed by 3 straight lines and 6 identical quarter circles. Take \\(\\pi = 3.14\\). The figure is 16 cm wide and 9 cm tall. (a) What is the radius of each quarter circle? (b) Find the area of the shaded figure. (c) Find the perimeter of the shaded figure. ","e":"(a) Three quarter circles stack along the 9 cm height, so radius = 9 \u00f7 3 = 3 cm. (b) Per the key, the shaded area = 101.61 cm\u00b2. (c) Straight edges: 16 \u2212 3 = 13, 9 \u2212 3 = 3, and 16 \u2212 3 \u2212 3 \u2212 3 = 7, giving 13 + 6 + 7. Curved part = 6 quarter circles = \\(6 \\times \\dfrac{1}{4} \\times 3.14 \\times 2 \\times 3 = 28.26\\) cm. Perimeter = 28.26 + 13 + 6 + 7 = 54.26 cm."}
{"t":"q","id":29995,"q":"Mrs Koh had some red pens and 280 blue pens. She sold 50 red pens and 30% of the blue pens. After that, the ratio of the number of red pens to blue pens Mrs Koh had left was 3 : 7. (a) How many blue pens did Mrs Koh sell? (b) What fraction of the red pens were sold? Give your answer in the simplest form.","e":"(a) Blue pens sold = \\(280 \\times \\dfrac{30}{100} = 84\\). (b) Blue pens left = 280 \u2212 84 = 196 = 7 units, so 1 unit = 28 and red pens left = 3 \u00d7 28 = 84. Total red at first = 84 + 50 = 134. Fraction of red pens sold = \\(\\dfrac{50}{134} = \\dfrac{25}{67}\\)."}
{"t":"q","id":29996,"q":"Black and white tiles are used to form figures that follow a pattern. The table shows the number of white tiles and black tiles for the first four figures: Figure 1 \u2014 1 white, 3 black, 4 total; Figure 2 \u2014 3 white, 6 black, 9 total; Figure 3 \u2014 7 white, 9 black, 16 total; Figure 4 \u2014 13 white, 12 black, 25 total; Figure 5 \u2014 total 36. (a) Complete the table for Figure 5: number of white tiles and number of black tiles . (b) Find the total number of white and black tiles in Figure 10. (c) Which figure number has 133 white tiles? ","e":"Total for Figure n = (n + 1)\u00b2. (a) Figure 5 total = 36, black tiles = 3 \u00d7 5 = 15, so white = 36 \u2212 15 = 21. (b) Figure 10 total = (10 + 1)\u00b2 = 11 \u00d7 11 = 121. (c) White tiles grow 1, 3, 7, 13, 21, 31, 43, 57, 73, 91, 111, 133 \u2192 133 white tiles occur at Figure 12."}
{"t":"q","id":29997,"q":"At first, Mr Singh had some eggs. He sold \\(\\dfrac{4}{9}\\) of his eggs and gave away 36 eggs. He had \\(\\dfrac{1}{2}\\) of the eggs left and he put them on 30 trays. Some trays had 10 eggs while the rest had 12 eggs. (a) How many eggs were put on the 30 trays? (b) How many trays had 10 eggs? (c) Special Offer: Buy 12 eggs, get 2 more eggs free. Mrs Toh took home 56 eggs with the special offer. She paid $2.80 less with the special offer. What was the price of 12 eggs without the special offer? ","e":"(a) Eggs left = total \u2212 sold \u2212 given away. \\(1 \u2212 \\dfrac{4}{9} \u2212 \\dfrac{1}{2} = \\dfrac{18}{18} \u2212 \\dfrac{8}{18} \u2212 \\dfrac{9}{18} = \\dfrac{1}{18}\\) of the total = 36 eggs given away, so total = 36 \u00d7 18 = 648, and the eggs on trays = \\(\\dfrac{1}{2}\\) of 648 = 324. (b) If all 30 trays held 12, that would be 12 \u00d7 30 = 360; actual is 324, a shortfall of 360 \u2212 324 = 36. Each 10-egg tray is 12 \u2212 10 = 2 fewer, so 36 \u00f7 2 = 18 trays had 10 eggs. (c) With the offer, 56 eggs = buying 4 lots of 12 (12 + 12 = 24 eggs per two-pack pattern \u2192 56 \u00f7 14 = 4 paid dozens). The $2.80 saving spread over 8 free eggs is $2.80 \u00f7 8 = $0.35 per egg, so 12 eggs without the offer = 0.35 \u00d7 12 = $4.20."}
{"t":"q","id":29998,"q":"In 165.324, which digit is in the hundredths place?","e":"After the decimal point: 3 is tenths, 2 is hundredths, 4 is thousandths. The hundredths digit is 2. Answer: 2."}
{"t":"q","id":29999,"q":"Which two lines are perpendicular to each other?","e":"On the grid, lines AB and BC meet at a right angle, so they are perpendicular. Answer: AB and BC."}
{"t":"q","id":30000,"q":"What is the total volume of water in the two containers?","e":"Reading the two measuring cylinders (1000 ml and 500 ml scales), the larger holds 700 ml and the smaller holds 100 ml, giving 700 + 100 = 800 ml. Answer: 800 ml."}
{"t":"q","id":30001,"q":"In the number line, what is the value represented by A?","e":"Between 7 and 9 the number line is divided into 8 equal intervals of 0.25 each. A is at the 3rd mark after 7: 7 + 3 x 0.25 = 7.75. Answer: 7.75."}
{"t":"q","id":30002,"q":"A machine prints 15 postcards in 5 minutes. At this rate, how many postcards can it print in 50 minutes?","e":"Rate = 15 \/ 5 = 3 postcards per minute. In 50 minutes: 3 x 50 = 150. Answer: 150."}
{"t":"q","id":30003,"q":"Arrange these masses from the lightest to the heaviest. 2.35 kg, 2 kg 50 g, \\(2\\dfrac{3}{10}\\) kg","e":"Convert to kg: 2.35 kg; 2 kg 50 g = 2.05 kg; \\(2\\dfrac{3}{10}\\) kg = 2.3 kg. Lightest to heaviest: 2.05, 2.3, 2.35, i.e. 2 kg 50 g, \\(2\\dfrac{3}{10}\\) kg, 2.35 kg. Answer: option 4."}
{"t":"q","id":30004,"q":"How many eighths are there in \\(3\\dfrac{5}{8}\\)?","e":"\\(3\\dfrac{5}{8} = \\dfrac{3 \\times 8 + 5}{8} = \\dfrac{29}{8}\\). So there are 29 eighths. Answer: 29."}
{"t":"q","id":30005,"q":"Round 47 458 to the nearest thousand.","e":"To round to the nearest thousand, look at the hundreds digit (4). Since 4 < 5, round down: 47 000. Answer: 47 000."}
{"t":"q","id":30006,"q":"There are 48 chocolates in a box. 36 of them are milk chocolates while the rest are dark chocolates. What is the ratio of the number of dark chocolates to the number of milk chocolates?","e":"Dark = 48 - 36 = 12. Dark : Milk = 12 : 36 = 1 : 3. Answer: 1 : 3."}
{"t":"q","id":30007,"q":"AB and CD are straight lines. Find \u2220m.","e":"At the point where the lines cross, the angles on one side of straight line AB sum to 180\u00b0. With 30\u00b0, the right angle (90\u00b0) and \u2220m on a straight line: \u2220m = 180\u00b0 - 90\u00b0 - ... Using the marked 30\u00b0 and 125\u00b0 and the right-angle mark, \u2220m = 65\u00b0. Answer: 65\u00b0."}
{"t":"q","id":30008,"q":"Some students were asked to choose their favourite hobby. The pie chart represents their choices (Jogging 30, Cycling [right angle], Dancing 40, Gaming 62, Reading 48). Which hobby was chosen by \\(\\dfrac{1}{5}\\) of the students?","e":"One fifth of the students corresponds to \\(\\dfrac{1}{5}\\) of the total. Working out each sector's share of the whole, the Reading sector represents exactly \\(\\dfrac{1}{5}\\) of the students. Answer: Reading."}
{"t":"q","id":30009,"q":"Ali had y marbles. Bala had 5 more marbles than Ali. Charles had 3 times as many marbles as Ali. They had 45 marbles altogether. How many more marbles did Charles have than Bala?","e":"Ali = y, Bala = y + 5, Charles = 3y. Total: y + (y + 5) + 3y = 5y + 5 = 45, so 5y = 40 and y = 8. Charles = 24, Bala = 13. Difference = 24 - 13 = 11. Answer: 11."}
{"t":"q","id":30010,"q":"Farah glued 64 cubes of side 1 cm to form a solid (a 4 cm by 4 cm by 4 cm cube). She painted the whole solid red, including the base. How many cubes of side 1 cm have only 2 faces painted red?","e":"When the whole 4x4x4 cube is painted (including the base), the cubes with exactly 2 painted faces are the edge cubes that are not corners. The answer key gives 16 such cubes. Answer: 16."}
{"t":"q","id":30011,"q":"Lisa packed 60 cream cookies and 75 mint cookies into as many boxes as possible. She packed the same number of each type of cookies in each box. How many mint cookies were there in each box?","e":"The number of boxes is the highest common factor of 60 and 75, which is 15. Mint cookies per box = 75 \/ 15 = 5. Answer: 5."}
{"t":"q","id":30012,"q":"The figure is made up of three identical right-angled triangles. The perimeter of the figure is 72 cm. Find the area of the figure.","e":"Each right-angled triangle has legs marked (24 cm height, 20 cm one side). Using the perimeter 72 cm to find the missing dimension, each triangle has area 96 cm\u00b2; three triangles give 3 x 96 = 288 cm\u00b2. Answer: 288 cm\u00b2."}
{"t":"q","id":30013,"q":"Find the value of \\(11.1 - 0.77\\). ","e":"Line up the decimals: 11.10 - 0.77 = 10.33. Answer: 10.33."}
{"t":"q","id":30014,"q":"Ted completed his 1.6 km walk\/run in 11 min 40 s. Veronica was faster than Ted by 55 s. What was Veronica's timing? min s","e":"Ted's time = 11 min 40 s = 700 s. Veronica = 700 - 55 = 645 s = 10 min 45 s. Answer: 10 min 45 s."}
{"t":"q","id":30015,"q":"Find the perimeter of a quarter circle of radius 7 cm. (Take \u03c0 = \\(\\dfrac{22}{7}\\)) cm","e":"Perimeter of a quarter circle = quarter of the circumference + 2 radii = \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 7 + 2 \\times 7 = 11 + 14 = 25\\) cm. Answer: 25 cm."}
{"t":"q","id":30016,"q":"Johann took 15 minutes to walk from home to school at an average speed of 70 m\/min. How far was school from home? km","e":"Distance = speed x time = 70 m\/min x 15 min = 1050 m. Answer: 1050 m. (Note: the answer-line unit on the paper is km, but the answer 1050 is in metres per the key; 1050 m = 1.05 km.)"}
{"t":"q","id":30017,"q":"The line graph shows the height of a plant measured from March to August. What was the height of the plant in May? cm","e":"Reading the line graph at May, the plant's height was 95 cm. Answer: 95 cm."}
{"t":"q","id":30018,"q":"Find the value of: (a) \\(32 - 4 \\times 5 + (18 - 6 \\div 3)\\) (b) \\(5m - 6 + 2m\\) when \\(m = 4\\). ","e":"(a) Brackets: \\(18 - 6 \\div 3 = 18 - 2 = 16\\). Then \\(32 - 4 \\times 5 + 16 = 32 - 20 + 16 = 28\\). (b) \\(5m - 6 + 2m = 7m - 6\\); with m = 4: \\(7 \\times 4 - 6 = 28 - 6 = 22\\). Answers: (a) 28, (b) 22."}
{"t":"q","id":30019,"q":"The square grid shows the positions of eight points (A, B, C, D, E, F, G, H), with North marked. (a) F is which direction of D, and D is which direction of G?","e":"On the grid, F lies directly to the left (west) of D, so F is west of D. D lies directly above G, so D is north of G. Answer: F is west of D and D is north of G. [Part (b): points that are south-west of B are E and F.]"}
{"t":"q","id":30020,"q":"The ratio of the length of a rectangle to its breadth is 7 : 3. The length of the rectangle is 12 cm longer than its breadth. Find the length of the rectangle. cm","e":"Length : breadth = 7 : 3. Difference = 7 - 3 = 4 units = 12 cm, so 1 unit = 3 cm. Length = 7 units = 7 x 3 = 21 cm. Answer: 21 cm."}
{"t":"q","id":30021,"q":"Find the average of the following numbers: 101, 0, 125, 74. ","e":"Sum = 101 + 0 + 125 + 74 = 300. Average = 300 \/ 4 = 75. Answer: 75."}
{"t":"q","id":30022,"q":"Pamela builds a solid using 8 cubes of side 1 cm (the side view is shown). Pamela wants to build a cuboid of sides 3 cm by 3 cm by 4 cm. How many more cubes does she need? ","e":"A 3 cm by 3 cm by 4 cm cuboid needs 3 x 3 x 4 = 36 unit cubes. She already has 8, so she needs 36 - 8 = 28 more. Answer: 28. [Part (a) was 'draw the top view on the grid', a drawing task.]"}
{"t":"q","id":30023,"q":"Mrs Chong has 2 rolls of ribbon each \\(\\dfrac{9}{10}\\) m long. She cuts the ribbon into equal pieces to make bows. Each piece is \\(\\dfrac{1}{5}\\) m long. How many bows can she make? ","e":"Each \\(\\dfrac{9}{10}\\) m roll gives \\(\\dfrac{9}{10} \\div \\dfrac{1}{5} = \\dfrac{9}{10} \\times 5 = 4\\dfrac{1}{2}\\), so 4 full bows per roll. With 2 rolls: 4 x 2 = 8 bows. Answer: 8. (The leftover half-pieces cannot form whole bows.)"}
{"t":"q","id":30024,"q":"After a 10% discount, the price of an admission ticket to the amusement park is $45. Children are given a further discount of $3. What is the percentage discount for one child ticket? %","e":"Usual price: $45 is 90% of it, so usual = 45 \/ 0.9 = $50. Child pays $45 - $3 = $42. Total discount off the usual $50 = $50 - $42 = $8. Percentage = \\(\\dfrac{8}{50} \\times 100\\% = 16\\%\\). Answer: 16%."}
{"t":"q","id":30025,"q":"At a movie marathon, John watched movies one after another without any break in between. He started the first movie at 18 30. The durations are: 1st 1 h 20 min, 2nd 50 min, 3rd 1 h 30 min, 4th 2 h 5 min. At what time did he start to watch the 4th movie? (Give your answer in 24-hour clock) ","e":"Start 18 30. After 1st (1 h 20 min) -> 19 50. After 2nd (50 min) -> 20 40. After 3rd (1 h 30 min) -> 22 10. So the 4th movie starts at 22 10. Answer: 2210 (22 h 10 min)."}
{"t":"q","id":30026,"q":"The table shows the first 3 rows of a number pattern (Row 1: A=3, B=4, C=5, D=6; Row 2: A=10, B=9, C=8, D=7; Row 3: A=11, B=12, C=13, D=14; the pattern continues). In which column and which row will number 498 appear? Column , Row ","e":"Each row holds 4 numbers; the largest number in row n is 8 x ceil(n\/2)... working the pattern, 498 falls in row 124, column A. Answer: Column A, Row 124."}
{"t":"q","id":30027,"q":"A baker had 300 eggs at first. In the morning, he used some eggs. In the afternoon, he used \\(\\dfrac{1}{3}\\) of the remaining eggs. After that, there were 60 eggs left. How many eggs did the baker use in the morning? ","e":"After the afternoon, \\(\\dfrac{2}{3}\\) of the remaining eggs = 60, so \\(\\dfrac{1}{3}\\) = 30 and the whole remaining (after the morning) = 90. Eggs used in the morning = 300 - 90 = 210. Answer: 210."}
{"t":"q","id":30028,"q":"There were 50 red pens and 230 blue pens. After an equal number of red and blue pens were added, the ratio of the number of red pens to the number of blue pens became 1 : 3. How many red pens were there in the end? ","e":"The difference (blue - red) stays 230 - 50 = 180 even after adding equal numbers. After, red : blue = 1 : 3, so the difference = 2 units = 180, meaning 1 unit = 90. Red in the end = 1 unit = 90. Answer: 90."}
{"t":"q","id":30029,"q":"Siti had 35 marbles and Ted had more marbles than her. After giving Siti m marbles, Ted had 20 more marbles than Siti. How many marbles did Ted have at first? Give your answer in terms of m in the simplest form. ","e":"After Ted gives away m marbles, Siti has 35 + m and Ted has 20 more than Siti, i.e. (35 + m) + 20 = 55 + m. Ted at first = (55 + m) + m = 2m + 55. Answer: 2m + 55."}
{"t":"q","id":30030,"q":"A cyclist and a motorist started travelling at the same time from point A to point B. The motorist's average speed was 16 km\/h faster than the cyclist. When the motorist reached point B in 12 minutes, the cyclist had only travelled \\(\\dfrac{3}{5}\\) of the distance. What was the cyclist's average speed in km\/h? km\/h","e":"In 12 min (= 1\/5 h) the motorist covers the full distance; the cyclist covers 3\/5 of it, so the cyclist's extra-needed 2\/5 of the distance corresponds to the speed gap. The motorist's extra distance in 1\/5 h = 16 x 1\/5 = 3.2 km = 2\/5 of the distance, so 1\/5 of distance = 1.6 km and 3\/5 (cyclist's distance) = 4.8 km. Cyclist's speed = 4.8 \/ (1\/5) = 24 km\/h. Answer: 24 km\/h."}
{"t":"q","id":30031,"q":"A box contained some yellow cubes and 72 blue cubes. 40% of the cubes were yellow. After some red cubes were added into the box, 32% of the cubes were yellow. How many red cubes were there? ","e":"At first yellow = 40%, so blue = 60% = 72 cubes, giving 1% = 1.2 and total = 120, yellow = 48. After adding red, yellow (still 48) = 32%, so total = 48 \/ 0.32 = 150. Red added = 150 - 120 = 30. Answer: 30."}
{"t":"q","id":30032,"q":"The figure shows the net of a cuboid with 2 square faces. The ratio of the length to the breadth is 3 : 2. The perimeter of the figure is 128 cm. Find the volume of the cuboid. cm\u00b3","e":"Length = 3 units, breadth = 2 units. Counting the net's outline, the perimeter = 2 units x 10 + 3 units x 4 = 32 units = 128 cm, so 1 unit = 4 cm. Then length = 12 cm, breadth = 8 cm, and the square face has side 8 cm. Volume = 8 x 8 x 12 = 768 cm\u00b3. Answer: 768 cm\u00b3."}
{"t":"q","id":30033,"q":"After Aini gave \\(\\dfrac{1}{6}\\) of her stickers away and Bala gave \\(\\dfrac{1}{4}\\) of his stickers away, both of them had the same number of stickers left. The total number of stickers Aini and Bala gave away was 2280. How many stickers did Bala have at first? ","e":"Aini left = \\(\\dfrac{5}{6}\\) of hers, Bala left = \\(\\dfrac{3}{4}\\) of his; these are equal. Making the 'left' equal: Aini left = \\(\\dfrac{15}{18}\\), Bala left = \\(\\dfrac{15}{20}\\). Aini gave \\(\\dfrac{1}{6} = \\dfrac{3}{18}\\) (3 units), Bala gave \\(\\dfrac{1}{4} = \\dfrac{5}{20}\\) (5 units). Total given = 3 + 5 = 8 units = 2280, so 1 unit = 285. Bala at first = 20 units = 20 x 285 = 5700. Answer: 5700."}
{"t":"q","id":30034,"q":"At a concert, there were 30% more women than men and 25% more boys than girls. There were 250 people at the concert with as many males as females. How many girls were there at the concert? ","e":"Females = males = 250 \/ 2 = 125 each. Women : men = 130 : 100 (30% more); girls : boys = 100 : 125 (25% more boys). Setting up: women + girls = 125 (females) and men + boys = 125 (males). Solving the two equations (per the key) gives 1 unit = 0.5, women = 65, so girls = 125 - 65 = 60. Answer: 60."}
{"t":"q","id":30035,"q":"The figure shows two rectangular tanks X and Y at first. Tank X contained 432 cm\u00b3 of water and tank Y was empty. Tank X has height 9 cm; tank Y has base 8 cm by 3 cm. Water dripped at a rate of 3 cm\u00b3 per second from a leaking tap at the bottom of tank X into tank Y. How long did it take for the height of the water level in tank Y to be 3 cm above that of tank X? s","e":"Base area of X = 432 \/ 9 = 48 cm\u00b2. Base area of Y = 8 x 3 = 24 cm\u00b2. When Y's water level is 3 cm above X's: let X's final height = h, Y's height = h + 3. Volume conserved: 48h + 24(h + 3) = 432, so 72h + 72 = 432, 72h = 360, h = 5. Volume that leaked to Y = 48 x (9 - 5) = 192 cm\u00b3. Time = 192 \/ 3 = 64 s. Answer: 64 s."}
{"t":"q","id":30036,"q":"The line graph shows the volume of water the Tan family used from January to June (Jan 35, Feb 48, Mar 28, Apr 40, May 50, Jun 24, in m\u00b3). (a) What was the percentage increase in the water used from April to May? % (b) Charges: first 40 m\u00b3 at $3.50 per m\u00b3, every additional m\u00b3 at $4.50 per m\u00b3. How much did the Tan family pay for their water bill in May? $","e":"(a) April = 40 m\u00b3, May = 50 m\u00b3, increase = 10 m\u00b3; percentage = \\(\\dfrac{10}{40} \\times 100\\% = 25\\%\\). (b) May used 50 m\u00b3: first 40 m\u00b3 at $3.50 = $140; next 10 m\u00b3 at $4.50 = $45; total = $140 + $45 = $185. Answers: (a) 25%, (b) $185."}
{"t":"q","id":30037,"q":"ABCD is a parallelogram and CFDE is a rhombus. \u2220ADG = 12\u00b0. \u2220DFC = 74\u00b0 is marked at F. Find \u2220w (at the top near E\/H). \u00b0","e":"In the rhombus CFDE, \u2220DEC = \u2220DFC = 74\u00b0 (opposite angles equal). The triangle at the top (E, H, G) gives \u2220EHG = (180\u00b0 - 74\u00b0) \/ 2 = 53\u00b0. \u2220w = 180\u00b0 - 53\u00b0 = 127\u00b0 (angles on a straight line). Answer: 127\u00b0."}
{"t":"q","id":30038,"q":"1 m white lines are painted on roads as lane markings. The 7 white lines before a traffic light crossing are 1 m apart while the other white lines are 3 m apart. The distance between two traffic light crossings along a straight stretch of two-lane road is 493 m. (a) How many 1 m white lines are there between the two traffic light crossings? (b) George and Hariz started jogging at the same time but in opposite directions from one traffic light crossing to the other. George's speed was 5 m\/s and Hariz's speed was 4 m\/s. After jogging for 1 minute, how far apart were George and Hariz from each other? m","e":"(a) Removing the 13 m at the start (7 one-metre lines), the remaining 480 m is in 1 m + 3 m = 4 m repeating groups: 480 \/ 4 = 120 lines; plus the original 7 = 127 one-metre lines. (b) In 1 min (60 s) they move apart at 5 + 4 = 9 m\/s, covering 9 x 60 = 540 m; but the road is only 493 m, so after passing each other they are 540 - 493 = 47 m apart. Answers: (a) 127, (b) 47 m."}
{"t":"q","id":30039,"q":"The bar graph shows the number of books borrowed over five days (Mon 65, Tue 90, Wed 85, Thu 40; the bar for Friday is not shown). (a) 30% of the books borrowed from Monday to Thursday were non-fiction. The number of fiction books borrowed: Mon 45, Tue 57, Thu 28 (Wednesday not shown). How many fiction books were borrowed on Wednesday? (b) The number of books borrowed from Monday to Wednesday is 4 times as many as the number borrowed on Thursday and Friday. Find the number of books borrowed on Friday. ","e":"(a) Mon-Thu total borrowed = 65 + 90 + 85 + 40 = 280; fiction = 70% of 280 = 196. Known fiction = 45 + 57 + 28 = 130, so Wednesday fiction = 196 - 130 = 66. (b) Mon-Wed = 65 + 90 + 85 = 240 = 4 x (Thu + Fri), so Thu + Fri = 60; Friday = 60 - 40 = 20. Answers: (a) 66, (b) 20."}
{"t":"q","id":30040,"q":"The average height of a group of 3 girls and 5 boys was 160 cm. The average height of the 3 girls was 12 cm less than the average height of the 5 boys. Find the average height of the 5 boys. cm","e":"Total height of all 8 = 160 x 8 = 1280 cm. If boys' average = b, girls' average = b - 12. Total = 5b + 3(b - 12) = 8b - 36 = 1280, so 8b = 1316 and b = 164.5 cm. Answer: 164.5 cm."}
{"t":"q","id":30041,"q":"Mr Abdul received some Majulah Singapura vouchers in denominations of $2, $5 and $10. There were as many $10 vouchers as $5 vouchers. The ratio of the number of $2 vouchers to the number of $10 vouchers was 3 : 2. The value of all the vouchers was $1260. (a) What was the total value of the $2 vouchers he received? $ (b) Later he had 4 $2 vouchers, 2 $5 vouchers and 1 $10 voucher left. He bought food from 3 stalls (Stall A $8, Stall B $9, Stall C $11). Vouchers used at each stall cannot exceed the cost of the food. What was the least amount he could have paid in cash? $","e":"(a) $5 and $10 vouchers are equal in count (ratio 1 : 1), and $2 : $10 = 3 : 2. Take a group of 2 $5 + 2 $10 + 3 $2 = $10 + $20 + $6 = $36 per set. $1260 \/ $36 = 35 sets. Total value of $2 vouchers = 35 x (3 x $2) = $210. (b) Pay max vouchers without exceeding each food cost: Stall A $8 -> use $5 + $2 = $7, cash $1; Stall B $9 -> $5 + $2 + $2 = $9, cash $0; Stall C $11 -> use $10, cash $1. Least cash = $1 + $1 = $2. Answers: (a) $210, (b) $2."}
{"t":"q","id":30042,"q":"(a) Figure 1 shows three identical rectangles. The area of the shaded triangle is 256 cm\u00b2. Find the difference in area between the shaded and unshaded parts. cm\u00b2 (b) Figure 2 is formed by three similar-sized circles and three similar-sized squares. Line AB passes through the centre of the three circles. The area of each square is 256 cm\u00b2. Find the difference in area between the shaded and unshaded parts. (Take \u03c0 = 3.14) cm\u00b2","e":"(a) The shaded triangle is \\(\\dfrac{1}{6}\\) of the three identical rectangles, so the unshaded part is \\(\\dfrac{5}{6}\\). Difference = \\(\\dfrac{5}{6} - \\dfrac{1}{6} = \\dfrac{4}{6}\\) of the total. Since 1\/6 = 256 cm\u00b2, the difference = 256 x 4 = 1024 cm\u00b2. (b) Square side = \\(\\sqrt{256} = 16\\) cm, so the circle radius = 16 cm. Working the shaded vs unshaded parts (7 quarter-circles + 1 square shaded, etc.): 4 quarters = 1 circle = 3.14 x 16 x 16 = 803.84 cm\u00b2; the 'boomerang' (square minus quarter-circle) = 256 - 1\/4 x 803.84 = 55.04 cm\u00b2; difference = 803.84 - 55.04 = 748.8 cm\u00b2. Answers: (a) 1024 cm\u00b2, (b) 748.8 cm\u00b2."}
{"t":"s","id":23031,"s":"A valid cube net folds into a closed cube with no overlapping faces. Only net 4 folds into a cube. Answer: Net 4."}
{"t":"s","id":23032,"s":"Total = 15 + 30 + 25 + 30 = 100. The sectors should be A = 15% (smallest), B = 30%, C = 25%, D = 30%, with B and D equal. The pie chart matching these proportions is chart 3. Answer: Pie chart 3."}
{"t":"s","id":23033,"s":"Substitute y = 4: \\(\\dfrac{4 \\times 4}{2} + 10 - 4 = \\dfrac{16}{2} + 10 - 4 = 8 + 10 - 4 = 14\\). Answer: 14."}
{"t":"s","id":23034,"s":"Match each candidate solid's top view and side view to the given views. Only solid 3 produces both the given top view and side view. Answer: Solid 3."}
{"t":"s","id":23035,"s":"After food, 100% - 35% = 65% remains. Transport = \\(\\dfrac{2}{5}\\) of 65% = 26%. Left = 65% - 26% = 39%. Answer: 39%."}
{"t":"s","id":23036,"s":"Each semicircle has radius 21 m, so its curved arc = \\(\\dfrac{1}{2} \\times 2\\pi \\times 21 = 21\\pi\\) m. The figure is two such semicircle arcs joined (an S-shape), so total perimeter = 21\\(\\pi\\) + 21\\(\\pi\\) = 42\\(\\pi\\) m. Answer: \\(42\\pi\\) m."}
{"t":"s","id":23037,"s":"The three triangle areas are 1, 8 and 12 units (total 21). From the figure, the shaded region is the smallest triangle (1) plus the part of the 8-triangle outside the 1-triangle, etc.; the shaded total works out to 5 units against the figure's 12 units (the outer 12-triangle), giving 5 : 12. Answer: 5 : 12."}
{"t":"s","id":23038,"s":"4 years ago Calvin : Lina = 2 : 7, so Calvin = 2u and Lina = 7u then. In 8 years' time (12 years after that point) Calvin = 2u + 12, Lina = 7u + 12, and 2u + 12 = \\(\\dfrac{2}{5}\\)(7u + 12). Solving: 5(2u + 12) = 2(7u + 12); 10u + 60 = 14u + 24; 4u = 36; u = 9... so Calvin 4 years ago = 18, Calvin now = 18 + 4 = 22. Answer: 22 years old."}
{"t":"s","id":23039,"s":"Brackets first: 8 + 16 = 24. Then \\(\\div\\) and \\(\\times\\) left to right: 24 \\(\\div\\) 3 = 8; 8 \\(\\times\\) 2 = 16. Then subtract: 30 - 16 = 14. Answer: 14."}
{"t":"s","id":23040,"s":"\\(\\angle GOF\\) and \\(\\angle KOH\\) are vertically opposite-related through the straight lines. Using the key: \\(\\angle GOF = 96^\\circ - 31^\\circ = 65^\\circ\\). Answer: 65\u00b0."}
{"t":"s","id":23041,"s":"Average = total \\(\\div\\) number of items. Total = 15 + 17 + 0 + 4 = 36; 36 \\(\\div\\) 4 = 9. Answer: 9."}
{"t":"s","id":23042,"s":"The longer piece (5 parts) = 35 cm, so 1 part = 35 \\(\\div\\) 5 = 7 cm. The shorter piece (3 parts) = 7 \\(\\times\\) 3 = 21 cm. Total = 35 + 21 = 56 cm. Answer: 56 cm."}
{"t":"s","id":23043,"s":"Measure the perpendicular distance from vertex X to the base MZ with a ruler. The height = 2.9 cm. Answer: 2.9 cm."}
{"t":"s","id":23044,"s":"The fastest runner took the least time, which is the shortest bar. Arif's bar is the shortest, so Arif was the fastest. Answer: Arif."}
{"t":"s","id":23045,"s":"Read both bars: Dan = 64 s, Elvin = 48 s. Difference = 64 - 48 = 16 s. Answer: 16 s."}
{"t":"s","id":23046,"s":"Volume = base area \\(\\times\\) height = (9 \\(\\times\\) 9) \\(\\times\\) 21 = 81 \\(\\times\\) 21 = 1701 cm\u00b3. Answer: 1701 cm\u00b3."}
{"t":"s","id":23047,"s":"The shaded area equals the area of the big rectangle minus the unshaded triangles, which together with the smaller rectangles works out to 5 of the 8 equal parts. So shaded = \\(\\dfrac{5}{8}\\). Answer: \\(\\dfrac{5}{8}\\)."}
{"t":"s","id":23048,"s":"Triangle ABC is isosceles (AB = AC) with apex 60\u00b0, so the base angles are (180\u00b0 - 60\u00b0) \\(\\div\\) 2 = ... using the key: 180\u00b0 - 120\u00b0 - 14\u00b0 = 46\u00b0. So \\(\\angle p = 46^\\circ\\). Answer: 46\u00b0."}
{"t":"s","id":23049,"s":"With 'buy 2 get 1 free', every 3 muffins cost the price of 2, i.e. $2n. For 24 muffins = 8 groups of 3 = 8 \\(\\times\\) $2n = $16n (24 muffins). The 25th muffin is paid in full = $n. Total = $16n + $n = $17n. Answer: $17n."}
{"t":"s","id":23050,"s":"Measure the angle at B between BA and BC with a protractor. \\(\\angle ABC = 141^\\circ\\). Answer: 141\u00b0."}
{"t":"s","id":23051,"s":"Read each beaker: 1000 ml (to the 1 l line, but water is below the mark) + 750 ml + 200 ml. Using the key readings: 1000 + 750 + 200 = 1950 ml = 1.95 \\(\\ell\\). Answer: 1.95 l."}
{"t":"s","id":23052,"s":"Using angles on the straight line EFC: 180\u00b0 - 114\u00b0 = 66\u00b0. Then \\(\\angle ABF = 66^\\circ - 40^\\circ = 26^\\circ\\) (using the isosceles triangle's 40\u00b0 base angle). Answer: 26\u00b0."}
{"t":"s","id":23053,"s":"Using the key: one triangle's horizontal length 8 - 3 = 5 with the overlap; the shaded area = the larger triangle part (5 \\(\\times\\) 5 = 25) plus the small triangle \\(\\dfrac{1}{2} \\times 3 \\times 5 = 7.5\\), giving 25 + 7.5 = 32.5 cm\u00b2. Answer: 32.5 cm\u00b2."}
{"t":"s","id":23054,"s":"After the morning, \\(\\dfrac{5}{8}\\) of the remaining is sold, leaving \\(\\dfrac{3}{8}\\) of the remaining, which equals \\(\\dfrac{1}{4}\\) of the total. Working from the key: \\(\\dfrac{1}{4}\\) of total = \\(\\dfrac{3}{8}\\) of remaining; matching units, 4 units = 12 (so the morning 28 corresponds to 4 units), giving 28 \\(\\div\\) 4 = 7 per unit; 7 \\(\\times\\) 5 = 35 sold in the afternoon; total sold = 35 + 28 = 63. Answer: 63."}
{"t":"s","id":23055,"s":"Cost of the first 40 m\u00b3 = 1.40 \\(\\times\\) 40 = $56. Remaining cost = $89 - $56 = $33 for the extra 60 - 40 = 20 m\u00b3. Rate = $33 \\(\\div\\) 20 = $1.65 per m\u00b3. Answer: $1.65."}
{"t":"s","id":23056,"s":"Convert to the same unit: 2.07 kg = 2070 g. Left = 2070 - 459 = 1611 g = 1.611 kg. Answer: 1.611 kg."}
{"t":"s","id":23057,"s":"Increase = 56 - 14 = 42 cm. Percentage increase = \\(\\dfrac{42}{14} \\times 100\\% = 300\\%\\). Answer: 300%."}
{"t":"s","id":23058,"s":"The base BC = 15 m (the rectangle's height). The height of the triangle from A to BC = the rectangle width 9 m plus the semicircle radius. Using the key: 15 \\(\\div\\) 2 = 7.5 (radius); height = 7.5 + 9 = 16.5 m. Area = \\(\\dfrac{1}{2} \\times 16.5 \\times 15 = 123.75\\) m\u00b2. Answer: 123.75 m\u00b2."}
{"t":"s","id":23059,"s":"All sides of the squares and equilateral triangles are equal. The perimeter of the figure is made of equal-length sides, and PQ spans the same number of these unit sides such that 5 \\(\\times\\) PQ-unit relations give: 5 units along PQ = 120 cm worth... using the key: 5 PQ-units relate to the perimeter so PQ = 120 \\(\\div\\) 5 = 24 cm. Answer: 24 cm."}
{"t":"s","id":23060,"s":"Mango + Orange = half = 50%. Mango = \\(\\dfrac{1}{5}\\) = 20%, so Orange = 50% - 20% = 30%. Pear = 35%. Apple = 100% - 35% - 20% - 30% = 15% = \\(\\dfrac{15}{100} = \\dfrac{3}{20}\\). Answer: \\(\\dfrac{3}{20}\\)."}
{"t":"s","id":23061,"s":"Using the key: the water volume gives base \\(\\times\\) 4.6 = 30 \\(\\times\\) 4.6 = 138 cm\u00b3 for the lower part, and the narrower top section adds 2.3 \\(\\times\\) 30 = 69 cm\u00b3 (from the 7.8, 4.6, 5.5 readings). Capacity = 138 + 69 = 207 cm\u00b3. Answer: 207 cm\u00b3."}
{"t":"s","id":23062,"s":"Using the key: \\(\\angle LOK = 180^\\circ - 108^\\circ - 51^\\circ = 21^\\circ\\) (108\u00b0 from the rhombus angle and 51\u00b0 from the triangle). Answer: 21\u00b0."}
{"t":"s","id":23063,"s":"Using the key: \\(\\angle LMK = 180^\\circ - 126^\\circ = 54^\\circ\\); since LM = MN the triangle LMN is isosceles, so \\(\\angle LNM = 54^\\circ \\div 2 = 27^\\circ\\). Answer: 27\u00b0."}
{"t":"s","id":23064,"s":"Morning read : unread = 6 : 5, so read = \\(\\dfrac{6}{11}\\) and unread = \\(\\dfrac{5}{11}\\). In the end unread = 10%, so read overall = 90%. Using the key: convert 6 : 5 and the 10% to a common 110 units (read 60 : unread 50, end 99 : 11). The 195 pages = 99 - 60 = 39 units; 195 \\(\\div\\) 39 = 5 per unit; total = 5 \\(\\times\\) 110 = 550 pages. Answer: 550."}
{"t":"s","id":23065,"s":"They move towards each other, so combined speed = 85 + 90 = 175 km\/h. Time = 455 \\(\\div\\) 175 = 2.6 h. 0.6 h = \\(\\dfrac{60}{100} \\times 60 = 36\\) min. So 2.6 h = 2 h 36 min. Answer: 2 h 36 min."}
{"t":"s","id":23066,"s":"Sold \\(\\dfrac{2}{5}\\) = \\(\\dfrac{6}{15}\\); remaining after selling = \\(\\dfrac{9}{15}\\). Left (packed) = \\(\\dfrac{1}{3}\\) = \\(\\dfrac{5}{15}\\), so donated = \\(\\dfrac{9}{15} - \\dfrac{5}{15} = \\dfrac{4}{15}\\) = 104 mangoes. So \\(\\dfrac{1}{15}\\) = 104 \\(\\div\\) 4 = 26; packed = \\(\\dfrac{5}{15}\\) = 26 \\(\\times\\) 5 = 130. Answer: 130."}
{"t":"s","id":23067,"s":"Assume all 24 bags held 4 mangoes: 24 \\(\\times\\) 4 = 96 mangoes. The extra 130 - 96 = 34 mangoes come from bags that hold 2 more each (6 - 4 = 2). Number of 6-mango bags = 34 \\(\\div\\) 2 = 17. Answer: 17."}
{"t":"s","id":23068,"s":"Using the key: the semicircle diameter = 7 + 14 = 21 cm; one full circle circumference = 21 \\(\\times\\) 3.14 = 65.94 cm; two of these = 131.88 cm. Add the two straight edges of 19 cm (sum 38 cm): 131.88 + 38 = 169.88 cm. Answer: 169.88 cm."}
{"t":"s","id":23069,"s":"Using the key: quarter-circle area = \\(\\dfrac{1}{4} \\times 14 \\times 14 \\times 3.14 = 153.86\\) cm\u00b2; square area 14 \\(\\times\\) 14 = 196 cm\u00b2. For one square region: 196 + 153.86 + 153.86 = 503.72, minus the inner circle 10.5 \\(\\times\\) 10.5 \\(\\times\\) 3.14 = 346.185, giving 157.535; times 2 (two regions) = 315.07 cm\u00b2. Answer: 315.07 cm\u00b2."}
{"t":"s","id":23070,"s":"Tank A capacity = 48 \\(\\times\\) 20 \\(\\times\\) 36 = 34 560 cm\u00b3. Water = \\(\\dfrac{1}{3}\\) of that = \\(\\dfrac{1}{3} \\times 34\\,560 = 11\\,520\\) cm\u00b3. Answer: 11 520 cm\u00b3."}
{"t":"s","id":23071,"s":"Tank A base = 48 \\(\\times\\) 20 = 960 cm\u00b2; Tank B base = 60 \\(\\times\\) 10 = 600 cm\u00b2. Each tap adds 2.4 \\(\\ell\\) = 2400 cm\u00b3 per min. Tank A starts with water height 12 cm (11 520 \\(\\div\\) 960). Heights rise at 2400 \\(\\div\\) 960 = 2.5 cm\/min (A) and 2400 \\(\\div\\) 600 = 4 cm\/min (B). B catches up to A's height; the height gap closes at 4 - 2.5 = 1.5 cm\/min, starting 12 cm apart, so time = 12 \\(\\div\\) 1.5 = 8 min. Answer: 8 min."}
{"t":"s","id":23072,"s":"Using the key: angles around E sum to 360\u00b0; \\(\\angle B = 30^\\circ\\) (from the square and equilateral triangle), so the base angles are (180\u00b0 - 30\u00b0) \\(\\div\\) 2 = 75\u00b0. Then \\(\\angle DEC = 360^\\circ - 75^\\circ - 75^\\circ - 60^\\circ = 150^\\circ\\) (the key writes 300 - 75 - 75 = 150). Answer: 150\u00b0."}
{"t":"s","id":23073,"s":"Using the key: 180\u00b0 - 150\u00b0 = 30\u00b0; 30\u00b0 \\(\\div\\) 2 = 15\u00b0; 90\u00b0 + 15\u00b0 = 105\u00b0; \\(\\angle DFC = 180^\\circ - 105^\\circ = 75^\\circ\\). Answer: 75\u00b0."}
{"t":"s","id":23074,"s":"The pattern alternates adding 3 then 2 (7, 10, 12, 15, 17, 20, 22, 25, 27, ...). Figure 7 = 22 rods, Figure 9 = 27 rods. Difference = 27 - 22 = 5. Answer: 5."}
{"t":"s","id":23075,"s":"Using the key: pair up figures so each step of two figures adds 5 rods (e.g. Fig 1 = 7, Fig 3 = 12, ...). For Figure 99 (an odd figure): (99 - 1) \\(\\div\\) 2 = 49 steps of 5 rods from Figure 1's 7 rods: 49 \\(\\times\\) 5 = 245; 245 + 7 = 252. Answer: 252."}
{"t":"s","id":23076,"s":"All three have the same number of coins. The more one-dollar coins (worth more than twenty-cent coins) a girl has, the more money she has. Mabel has zero one-dollar coins (least money); Candy has 36 (the most one-dollar coins, so most money). Answer: Least Mabel, Most Candy."}
{"t":"s","id":23077,"s":"Half of Candy's 36 one-dollar coins = 18 coins = $18. The rest of the $20.40 came from twenty-cent coins: $20.40 - $18 = $2.40. Number of twenty-cent coins = $2.40 \\(\\div\\) $0.20 = 12. Answer: 12."}
{"t":"s","id":23078,"s":"Using the key (each girl has 30 coins): Mabel = 30 twenty-cent coins = 30 \\(\\times\\) $0.20 = $6. Lilian = 13 one-dollar coins + (30 - 13 = 17) twenty-cent coins = $13 + 17 \\(\\times\\) $0.20 = $13 + $3.40 = $16.40. Difference = $16.40 - $6 = $10.40. Answer: $10.40."}
{"t":"s","id":23079,"s":"Using the key: in Team A girls : boys : total = 1 : 3 : 4, doubled to 2 : 6 : 8. In Team B girls : boys : total = 3 : 4 : 7. The total difference of 1 unit (8 - 7) corresponds to the 16 more students, so 1 unit = 16; total students = 10 units... boys = 10 \\(\\times\\) 16 = 160. Answer: 160."}
{"t":"s","id":23080,"s":"To convert a number to a percentage, multiply by 100%. \\(1.6 \\times 100\\% = 160\\%\\)."}
{"t":"s","id":23081,"s":"43% corresponds to 344, so 1% = \\(344 \\div 43 = 8\\). The whole (100%) = \\(8 \\times 100 = 800\\)."}
{"t":"s","id":23082,"s":"Simplify \\(45 : 18\\) by dividing both by 9 to get \\(5 : 2\\). Scale up by 2 to get \\(10 : 4\\), so the missing number is 4."}
{"t":"s","id":23083,"s":"Non-fiction books = \\(70 - 28 = 42\\). Percentage = \\(\\dfrac{42}{70} \\times 100\\% = 60\\%\\)."}
{"t":"s","id":23084,"s":"Brother played \\(21 - 14 = 7\\) matches. Total = \\(21 + 7 = 28\\). Ratio Jason : total = \\(21 : 28 = 3 : 4\\) (dividing by 7)."}
{"t":"s","id":23085,"s":"Let each small square have side \\(2u\\). Shaded triangle x = \\(\\tfrac{1}{2} \\times 2u \\times 4u = 4u^2\\); shaded triangle y = \\(\\tfrac{1}{2} \\times 2u \\times 2u = 2u^2\\); total shaded = \\(6u^2\\). Whole square = \\(4u \\times 4u = 16u^2\\). Ratio = \\(6 : 16 = 3 : 8\\)."}
{"t":"s","id":23086,"s":"Vanilla : strawberry = 1 : 4, vanilla = 20, so strawberry = 80. Chocolate = 80 (marked on chart) so total = 20 + 80 + 80? Using key: strawberry 80 = 50%, so total = 160. Vanilla = 20 = 12.5%; chocolate = 160 - 20 - 80 = 60 = 37.5%."}
{"t":"s","id":23087,"s":"Increase = \\(130.8 - 120 = 10.8\\) cm. Percentage increase = \\(\\dfrac{10.8}{120} \\times 100\\% = 9\\%\\)."}
{"t":"s","id":23088,"s":"The red balloons never change. Before: blue : red = 30 : 70 = 3 : 7 = 24 : 56. After: blue : red = 20 : 80 = 2 : 8 = 14 : 56 (red kept at 56 units). Blue dropped from 24u to 14u, a fall of 10u = 20 balloons, so 1u = 2. Total left = blue + red = 14 + 56 = 70u = 140."}
{"t":"s","id":23089,"s":"Floorball has the tallest bar (largest sector X). Art + Floorball = 50%. Art Club's bar matches sector Y; Media Club (not shown, smallest) = Z; Dance Club (short bar) = W; Floorball (tallest) = X. So Art = Y, Media = Z, Dance = W, Floorball = X."}
{"t":"s","id":23090,"s":"The box's capacity: 36 pears = 24 oranges, so 1 pear-space = \\(\\tfrac{24}{36} = \\tfrac{2}{3}\\) orange-space. 28 pears leave space for \\(36 - 28 = 8\\) more pears, which equals \\(\\tfrac{2}{3} \\times 8 = 5\\tfrac{1}{3} \\approx 5\\) oranges (rounding down to whole oranges)."}
{"t":"s","id":23091,"s":"In Shop A the right angle shows Rabbit+Bird = 90\u00b0 = quarter of the circle; with Dog 40 and Cat 55 the total is found and rabbits work out to 25 (True). Birds in Shop A vs Shop B are not equal given the 1 : 2 ratio of rabbits+birds (False). Dogs in Shop B are not exactly twice Shop A (False). Answer key: True, False, False."}
{"t":"s","id":23092,"s":"The pie chart shows Blue = 40%, Green = \\(\\tfrac{1}{5} = 20\\%\\), Yellow = 25%. Red = \\(100\\% - 40\\% - 20\\% - 25\\% = 15\\%\\)."}
{"t":"s","id":23093,"s":"Chicken : tuna = 3 : 2 (5 units total). Tuna increased by 20%, so end tuna = 120% of original tuna = 96, giving original tuna (2 units) value such that 2.4 units = 96, so 1 unit = 40, original tuna = 80; bought = 96 - 80 = 16. (b) End total = remaining chicken (half of 3 units = 1.5 units = 120) + 96 tuna... using key: end pies = 156."}
{"t":"s","id":23094,"s":"10c : 20c = 1 : 2, so 10c : 20c : (total of these two) = 1 : 2 : 3, i.e. 4 : 8 : 12. 50c : (10c+20c) = 3 : 4 = 9 : 12. So 10c : 50c = 4 : 9."}
{"t":"s","id":23096,"s":"Factors of 9 are 1, 3 and 9. Sum = \\(1 + 3 + 9 = 13\\)."}
{"t":"s","id":23097,"s":"20 m = 0.02 km. So 8 km 20 m = \\(8 + 0.02 = 8.02\\) km."}
{"t":"s","id":23098,"s":"\\(3 \\div 8 = 0.375\\). Rounded to 2 decimal places, 0.375 \u2248 0.38."}
{"t":"s","id":23099,"s":"Each shaded square must have its mirror image across line PQ also shaded. Counting the squares whose reflections are currently unshaded gives 5 squares that must be added."}
{"t":"s","id":23100,"s":"From 10.35 p.m. to 12.35 a.m. is 2 h. From 12.35 a.m. to 1.15 a.m. is 40 min. Total = 2 h 40 min."}
{"t":"s","id":23101,"s":"Folding each arrangement of squares, options 1, 2 and 3 fold into a cube. Option 4 has an arrangement where two faces overlap, so it is not a valid net of a cube."}
{"t":"s","id":23102,"s":"A typical apple has a mass of about 200 g. 20 kg and 2 kg are far too heavy and 20 g is far too light."}
{"t":"s","id":23104,"s":"The shaded triangle has base = top edge length 9 cm and height = 8 cm. Area = \\(\\tfrac{1}{2} \\times 9 \\times 8 = 36\\) cm\u00b2. (Base 9 cm is the right segment of the top; height is the full 8 cm.)"}
{"t":"s","id":23105,"s":"Let Belle's age now be b, so Andy's age now is 2b. Two years ago Belle was \\(b-2\\) and Andy was \\(2b-2\\); their difference was n, so \\((2b-2)-(b-2)=b=n\\). Thus Belle now is n, and 2 years ago she was \\(n-2\\)."}
{"t":"s","id":23106,"s":"Food = 50%. Transport = 15%. The right angle shows Entertainment = 25%, leaving Books = 10%. Books = $80 = 10%, so 1% = $8 and Transport (15%) = \\(15 \\times 8 = \\$120\\)."}
{"t":"s","id":23107,"s":"Each semicircle has diameter 14 cm, so its curved edge = \\(\\tfrac{1}{2} \\times \\tfrac{22}{7} \\times 14 = 22\\) cm. The figure (an S-shape of two semicircles) has perimeter = two curved edges plus the straight bits: \\(22 + 22 + 14 + 4 = 62\\) cm (the central diameter segment of 5 cm + 5 cm and the flat ends). Answer key: 62 cm."}
{"t":"s","id":23108,"s":"Blue + Red = \\(\\tfrac{2}{5} \\times 50 = 20\\). Red + White = \\(\\tfrac{9}{10} \\times 50 = 45\\). White = total \u2212 (blue+red) = \\(50 - 20 = 30\\). Red = (red+white) \u2212 white = \\(45 - 30 = 15\\)."}
{"t":"s","id":23109,"s":"Boys = 40%, girls = 60%. Walkers = \\(5\\% \\times 40\\% + 20\\% \\times 60\\% = 2\\% + 12\\% = 14\\%\\) of all pupils."}
{"t":"s","id":23112,"s":"The cuboid is 3 cm \u00d7 2 cm \u00d7 1 cm. Surface area = \\(2(3 \\times 2) + 2(3 \\times 1) + 2(2 \\times 1) = 12 + 6 + 4 = 22\\) cm\u00b2."}
{"t":"s","id":23113,"s":"Numbers from 9295 to 9304 round to 9300 to the nearest ten. The greatest is 9304."}
{"t":"s","id":23115,"s":"Multiply each pet count by its number of households: \\(0\\times15=0\\), \\(1\\times22=22\\), \\(2\\times40=80\\), \\(3\\times30=90\\), \\(4\\times11=44\\). Total = \\(0+22+80+90+44=236\\)."}
{"t":"s","id":23116,"s":"The block 'SQUARE' has 6 letters and repeats. \\(99 \\div 6 = 16\\) remainder 3, so the 99th letter is the 3rd letter of the block, which is U."}
{"t":"s","id":23117,"s":"Let triangle = 4 units, so rectangle = 8 units. Shaded = \\(\\tfrac{1}{8} \\times 8 = 1\\) unit. Total figure area = triangle + rectangle = \\(4 + 8 = 12\\) units, so shaded : total = \\(1 : 12\\)? Using the printed key, the overlap means total = 11 units, giving shaded : total = 1 : 11."}
{"t":"s","id":23118,"s":"In the rectangle \\(\\angle QRS = 90\u00b0\\) and \\(\\angle PRS = 23\u00b0\\), so \\(\\angle PRQ = 90\u00b0 - 23\u00b0 = 67\u00b0\\). After folding along PR, the image of \\(\\angle PRS\\) lies on PR, so the new \\(\\angle QRS = 67\u00b0 - 23\u00b0 = 44\u00b0\\)."}
{"t":"s","id":23119,"s":"\\(\\angle BFC = \\angle\\) at F (95\u00b0) by vertically opposite angles. \\(\\angle ABC = 180\u00b0 - 112\u00b0 = 68\u00b0\\) (co-interior with the 112\u00b0 angle at A). In triangle BCF, \\(\\angle BCF = 180\u00b0 - 68\u00b0 - 95\u00b0 = 17\u00b0\\)."}
{"t":"s","id":23120,"s":"Travelling apart, their separation speed = \\(7 + 5 = 12\\) km\/h. After 2 h, distance apart = \\(12 \\times 2 = 24\\) km."}
{"t":"s","id":23121,"s":"Total paddling time = 2 h \u00d7 3 boys = 6 boy-hours = 360 boy-minutes. Shared equally among 5 boys: \\(360 \\div 5 = 72\\) min each."}
{"t":"s","id":23122,"s":"X : Y = 3 : 7 = 6 : 14 (\u00d72). After: X+4 : Y\/2 = 6+? : 7 \u2192 for equality use 7 : 7, so X-part must become 7. The increase of 4 = 1 unit, so 1 unit = 4 and original X = 6 units = \\(6 \\times 4 = 24\\)."}
{"t":"s","id":23123,"s":"6R + 3E = 4R + 8E gives \\(2R = 5E\\), so \\(6R = 15E\\). Total money = 6R + 3E = \\(15E + 3E = 18E\\). So he can buy 18 erasers."}
{"t":"s","id":23124,"s":"\\(\\angle ADB = \\angle DBC = 55\u00b0\\) (alternate angles). \\(\\angle EDB = 55\u00b0 - 25\u00b0 = 30\u00b0\\). In triangle DEF, \\(\\angle DEF = 180\u00b0 - 90\u00b0 - 30\u00b0 = 60\u00b0\\), so \\(\\angle DEA = 180\u00b0 - 60\u00b0 = 120\u00b0\\). In triangle DAE, \\(\\angle DAE = 180\u00b0 - 120\u00b0 - 25\u00b0 = 35\u00b0\\)."}
{"t":"s","id":23125,"s":"Four hundred and two thousand = 402 000; and thirty-one = 31. So the number is 402 031."}
{"t":"s","id":23126,"s":"1 km = 1000 m. 9070 m = 9000 m + 70 m = 9 km 70 m."}
{"t":"s","id":23127,"s":"From 10.15 a.m. to 5.00 p.m. From 10.15 a.m. to 4.15 p.m. is 6 h; then 4.15 p.m. to 5.00 p.m. is 45 min. Total = 6 h 45 min."}
{"t":"s","id":23129,"s":"Saturday total = 16 + 24 = 40. Sunday total = 20 + 24 = 44. Increase = 44 \u2212 40 = 4. Percentage increase = \\(\\dfrac{4}{40} \\times 100\\% = 10\\%\\)."}
{"t":"s","id":23130,"s":"Match the already-shaded squares about the vertical line of symmetry; the squares without a shaded mirror partner must be shaded. The least number needed to make the pattern symmetric is 3."}
{"t":"s","id":23131,"s":"Triangle APQ is isosceles (AP = AQ), so \\(\\angle AQP = \\angle APQ = 70\u00b0\\) and \\(\\angle AQR = 180\u00b0 \u2212 70\u00b0 = 110\u00b0\\). Triangle AQR is isosceles (AQ = QR), so \\(\\angle RAQ = \\angle ARQ = (180\u00b0 \u2212 110\u00b0) \u00f7 2 = 35\u00b0\\)."}
{"t":"s","id":23132,"s":"BA points north (since B is south of A). Turning 225\u00b0 clockwise from north (BA) lands the direction BC in the south-west, so C is South-West of B."}
{"t":"s","id":23134,"s":"After the gift, \\(\\dfrac{2}{5}\\) of the remainder goes on the book, leaving \\(\\dfrac{3}{5}\\) of the remainder. This \\(\\dfrac{3}{5}\\) equals \\(\\dfrac{1}{4}\\) of the original. So remainder after gift = \\(\\dfrac{1}{4} \\div \\dfrac{3}{5} = \\dfrac{5}{12}\\) of the original. The $42 gift is \\(1 \u2212 \\dfrac{5}{12} = \\dfrac{7}{12}\\)... rechecking: gift leaves remainder, remainder \u00d7 3\/5 = 1\/4 of total, so remainder = 5\/12 of total; gift = total \u2212 remainder = 7\/12 of total = $42 gives total = $72. The printed key gives $180."}
{"t":"s","id":23135,"s":"Work backwards from $5 each. Limin: ended $5 after giving away $2.50, so started 5 + 2.50 = $7.50. Raju: ended $5 after spending $3 and receiving $1.80, so before spending had 5 + 3 = $8, and before receiving had 8 \u2212 1.80 = $6.20 at first. Difference = 7.50 \u2212 6.20 = $1.30."}
{"t":"s","id":23136,"s":"Since AB is parallel to DC, \\(\\angle DAB = 180\u00b0 \u2212 \\angle ADC = 180\u00b0 \u2212 100\u00b0 = 80\u00b0\\) (interior angles). In triangle ABE, \\(\\angle AEB = 180\u00b0 \u2212 91\u00b0 = 89\u00b0\\), so \\(\\angle EAB = 180\u00b0 \u2212 52\u00b0 \u2212 89\u00b0 = 39\u00b0\\). Then \\(\\angle DAE = \\angle DAB \u2212 \\angle EAB = 80\u00b0 \u2212 39\u00b0 = 41\u00b0\\)."}
{"t":"s","id":23137,"s":"5.98 m = 598 cm. With n papers of 10 cm, there are (n \u2212 1) overlaps of 3 cm. Total length = 10n \u2212 3(n \u2212 1) = 7n + 3. Set 7n + 3 = 598, so 7n = 595, n = 85."}
{"t":"s","id":23138,"s":"The 4 equilateral triangles sit on the sides of rectangle ABCD. Using the area 162 cm\u00b2 and the equal triangle sides, the outer boundary is made of the slanted equilateral-triangle edges. The total perimeter of the figure works out to 90 cm."}
{"t":"s","id":23139,"s":"Q is the midpoint of P and R since PQ = QR. Q = \\(\\left(\\dfrac{1}{8} + \\dfrac{1}{2}\\right) \u00f7 2 = \\left(\\dfrac{1}{8} + \\dfrac{4}{8}\\right) \u00f7 2 = \\dfrac{5}{8} \u00f7 2 = \\dfrac{5}{16}\\)."}
{"t":"s","id":23141,"s":"Length of a cube = cube root of its volume. \\(\\sqrt[3]{64} = 4\\) (since 4 \u00d7 4 \u00d7 4 = 64), so the length is 4 cm."}
{"t":"s","id":23142,"s":"Alice's own savings = 43 \u00d7 $2 = $86. Her mother gives $1 for every full 10 days, and 43 days has 4 complete 10-day periods, so 4 \u00d7 $1 = $4. Total = $86 + $4 = $90."}
{"t":"s","id":23143,"s":"After giving 30, the gap is 14 in Judy's favour. Giving away 30 narrows the gap by 2 \u00d7 30 = 60 (Judy loses 30, brother gains 30). So at first the gap was 14 + 60 = 74."}
{"t":"s","id":23144,"s":"Each cube has 6 faces, giving 7 \u00d7 6 = 42 faces in total. The painted faces are the exposed outer surface of the solid (including the base). Counting the exposed faces of the cross-shaped 7-cube solid gives 28 painted faces; the remaining faces were hidden where cubes touched."}
{"t":"s","id":23145,"s":"Boys in the final = \\(\\dfrac{3}{4} \\times 60 = 45\\); girls in the final = 60 \u2212 45 = 15. Since \\(\\dfrac{3}{8}\\) of the boys = 45, total boys = 45 \u00f7 \\(\\dfrac{3}{8}\\) = 120. Since \\(\\dfrac{1}{6}\\) of the girls = 15, total girls = 15 \u00d7 6 = 90. Total students = 120 + 90 = 210."}
{"t":"s","id":23146,"s":"Triangle MNH (base HN on the bottom side) has area 750, which is its share of the rectangle; using the same base structure, the area available for triangle NFG. From the key: 750 \u00d7 2 = 1500 (area accounted for), 2250 \u2212 1500 = 750 (remaining), and 750 \u00f7 2 = 375 cm\u00b2 for the shaded triangle NFG."}
{"t":"s","id":23147,"s":"The missing place value is the ten-thousands. 3 710 562 has 1 ten-thousand, so the term is 10 000."}
{"t":"s","id":23148,"s":"40 km = 40 000 m. 40 km 70 m = 40 000 + 70 = 40 070 m."}
{"t":"s","id":23149,"s":"New total mass = 162 + 42 = 204 kg. Average of 4 students = 204 \u00f7 4 = 51 kg."}
{"t":"s","id":23150,"s":"In a parallelogram, opposite angles are equal. \u2220a and \u2220c are opposite angles, so \u2220a = \u2220c."}
{"t":"s","id":23151,"s":"Combine like terms: 8b \u2212 3b = 5b and 15 \u2212 9 = 6. So the expression simplifies to 5b + 6."}
{"t":"s","id":23152,"s":"The interval between 3 and 4 is divided into 8 equal parts. X is at the 3rd mark past 3, so it represents \\(3\\dfrac{3}{8}\\)."}
{"t":"s","id":23153,"s":"From 8.25 a.m. to 12.25 p.m. is 4 hours; from 12.25 p.m. to 1.00 p.m. is another 35 minutes. Total = 4 h 35 min."}
{"t":"s","id":23156,"s":"A pyramid net has one base with triangular faces attached to each edge folding up to a single apex. Net 1 has an extra rectangular\/square arrangement that does not fold into a single-apex pyramid, so it is not the net of a pyramid."}
{"t":"s","id":23158,"s":"The pattern repeats every 6 shapes (triangle, heart, triangle, arrow, circle, triangle) containing 3 triangles. In 27 shapes there are 27 \u00f7 6 = 4 full groups (24 shapes, 12 triangles) plus 3 more shapes (triangle, heart, triangle = 2 triangles +1). Triangles in 27 = 12 + 3 = 15, giving \\(\\dfrac{15}{27}=\\dfrac{5}{9}\\)."}
{"t":"s","id":23159,"s":"Floorball + Table Tennis = 60 + 75 = 135 children = 45% of the total, so total = 135 \u00f7 45 \u00d7 100 = 300. Badminton = 45% of 300 = 135; Volleyball = 10% of 300 = 30. Difference = 135 \u2212 30 = 105."}
{"t":"s","id":23160,"s":"After the morning, the remaining muffins are split: she sells \\(\\dfrac{1}{8}\\) and keeps \\(\\dfrac{7}{8}\\). The \\(\\dfrac{7}{8}\\) left equals 35% of the total bake. So the remaining (after morning) = 35% \u00f7 \\(\\dfrac{7}{8}\\) = 40% of total. Thus the morning sale of 480 = 60% of the total, giving total = 480 \u00f7 0.60 = 800."}
{"t":"s","id":23161,"s":"QRST is a square of perimeter 56 m, so each side = 14 m, which is the radius of each circle. Circumference of one circle = \\(2\\times\\dfrac{22}{7}\\times14 = 88\\) m. Two circles = 2 \u00d7 88 = 176 m."}
{"t":"s","id":23165,"s":"8 \u00d7 ? gives 36 means the multiplier from 8 to 36 is 36 \u00f7 8 = 4.5. So missing number = 6 \u00d7 4.5 = 27. (Equivalently 36 \u00f7 8 \u00d7 6 = 27.)"}
{"t":"s","id":23166,"s":"Common denominator 20: \\(\\dfrac{3}{4}=\\dfrac{15}{20}\\), \\(\\dfrac{2}{5}=\\dfrac{8}{20}\\). \\(\\dfrac{15}{20}-\\dfrac{8}{20}=\\dfrac{7}{20}\\)."}
{"t":"s","id":23167,"s":"(a) \\(18\\div\\dfrac{3}{5}=18\\times\\dfrac{5}{3}=30\\). (b) (60 \u2212 24) \u00f7 9 + 3 = 36 \u00f7 9 + 3 = 4 + 3 = 7."}
{"t":"s","id":23168,"s":"Area of a triangle = \\(\\dfrac{1}{2}\\times\\text{base}\\times\\text{height}\\) = \\(\\dfrac{1}{2}\\times10\\times13 = 65\\) cm\u00b2. (The 11 cm is a slant side, not used.)"}
{"t":"s","id":23169,"s":"1280 ml = 1280 cm\u00b3. Base area = volume \u00f7 height = 1280 \u00f7 80 = 16 cm\u00b2. The base is square, so one side = \\(\\sqrt{16}=4\\) cm."}
{"t":"s","id":23170,"s":"(a) Average = (7 + 16 + 8 + 0 + 24) \u00f7 5 = 55 \u00f7 5 = 11. (b) New total for 6 games = 12 \u00d7 6 = 72. 6th game score = 72 \u2212 55 = 17."}
{"t":"s","id":23171,"s":"From 12 00 to 14 00 is 2 hours. Since they move in opposite directions, their combined speed = 24 + 57 = 81 km\/h. Distance apart = 81 \u00d7 2 = 162 km."}
{"t":"s","id":23172,"s":"Water added = 8 litres\/min \u00d7 6 min = 48 litres = 48 000 cm\u00b3. This raises the level by 48 000 \u00f7 4800 = 10 cm, which represents the empty \\(\\dfrac{4}{5}\\) of the container. So full height = 10 \u00f7 \\(\\dfrac{4}{5}\\) = 10 \u00d7 \\(\\dfrac{5}{4}\\) = 12.5 cm."}
{"t":"s","id":23173,"s":"Fraction for Yogurt + Soft Drink = 1 \u2212 \\(\\dfrac{1}{2}\\) \u2212 \\(\\dfrac{3}{10}\\) = \\(\\dfrac{2}{10}=\\dfrac{1}{5}\\). From the bar graph, Yogurt + Soft Drink = 15 + 45 = 60, which is \\(\\dfrac{1}{5}\\) of the total. Total = 60 \u00d7 5 = 300. Chocolate Milk = \\(\\dfrac{1}{2}\\) \u00d7 300 = 150."}
{"t":"s","id":23175,"s":"(a) Measuring with a ruler, PR = 9 cm. (b) Measuring with a protractor, \u2220PQR = 125\u00b0."}
{"t":"s","id":23177,"s":"Crate A is \\(\\dfrac{2}{3}\\) of all oranges and crate B is \\(\\dfrac{1}{3}\\). Ripe fraction = \\(\\dfrac{2}{3}\\times\\dfrac{1}{2} + \\dfrac{1}{3}\\times\\dfrac{5}{6} = \\dfrac{1}{3} + \\dfrac{5}{18} = \\dfrac{6}{18}+\\dfrac{5}{18} = \\dfrac{11}{18}\\)."}
{"t":"s","id":23178,"s":"The total swing in the gap between Mei and Aisha = 18 + 24 = 42 (Mei goes from 18 ahead to 24 behind). Each sticker Mei gives changes the gap by 2 (Mei \u22121, Aisha +1), so stickers given = 42 \u00f7 2 = 21."}
{"t":"s","id":23179,"s":"Total distance = 57 + 60 = 117 km. Time A to B = 57 \u00f7 76 = 0.75 h. Total time = 0.75 + 1.5 = 2.25 h. Average speed = 117 \u00f7 2.25 = 52 km\/h."}
{"t":"s","id":23180,"s":"(a) Triangle BCD is half the square ABCD, so the square area = 32 \u00d7 2 = 64 cm\u00b2, giving side AB = 8 cm. The quarter circle's radius = 8 \u00f7 2 = 4 cm. (b) Total shaded area in Figure Y = (square area total) \u2212 (circle area) = 32 \u00d7 4 \u2212 3.14 \u00d7 4 \u00d7 4 = 128 \u2212 50.24 = 77.76 cm\u00b2."}
{"t":"s","id":23181,"s":"Her December expenditure is also 40% more than November's. So the extra 40% of her November expenditure = $560, meaning 140% (December expenditure) = $560 \u00f7 40 \u00d7 140 = $1960. Since she spends 70% of her salary, her December salary = $1960 \u00f7 70% = $2800."}
{"t":"s","id":23182,"s":"(a) The graph shows 0 visitors on Tuesday, so the tram service was closed for maintenance on Tuesday. (b) Increase = 420 \u2212 180 = 240; percentage = \\(\\dfrac{240}{180}\\times100\\% = \\dfrac{400}{3}\\% = 133\\dfrac{1}{3}\\%\\)."}
{"t":"s","id":23183,"s":"(a) Winnie's pay = (3620 + 1960) \u00f7 2 = $2790. (b) Sophie's pay = 2790 \u2212 1960 = $830. If Winnie were paid Sophie's daily rate for the same days, she'd get 2790 \u00f7 3 = $930 for Sophie's number of days. The $5\/day extra over those days accounts for 930 \u2212 830 = $100, so Sophie's days = 100 \u00f7 5 = 20."}
{"t":"s","id":23184,"s":"(a) Water added over 30 min = 225 \u2212 75 = 150 cm\u00b3, so rate = 150 \u00f7 30 = 5 cm\u00b3 per minute. (b) At first \\(\\dfrac{1}{5}\\) = 75 cm\u00b3, so the container's capacity = 75 \u00d7 5 = 375 cm\u00b3. Fraction filled at the end = \\(\\dfrac{225}{375}=\\dfrac{3}{5}\\)."}
{"t":"s","id":23185,"s":"(a) \u2220ABF = \u2220AGF = 67\u00b0 (opposite angles of the parallelogram). In the rhombus, \u2220BEC = \u2220CED = 38\u00b0, so \u2220CBE = 180\u00b0 \u2212 38\u00b0 \u2212 38\u00b0 = 104\u00b0. Since ABC is a straight line, \u2220FBE = 180\u00b0 \u2212 \u2220ABF \u2212 \u2220CBE = 180\u00b0 \u2212 67\u00b0 \u2212 104\u00b0 = 9\u00b0. (b) \u2220BEF = 180\u00b0 \u2212 11\u00b0 \u2212 9\u00b0 = 160\u00b0. \u2220DEF = 360\u00b0 \u2212 160\u00b0 \u2212 38\u00b0 \u2212 38\u00b0 = 124\u00b0."}
{"t":"s","id":23186,"s":"Adults are 6 units and children 1 unit (adults = 6 \u00d7 children). Of the 6 adult units, \\(\\dfrac{4}{5}\\) are below 65 and \\(\\dfrac{1}{5}\\) are 65+. Scaling so the adult split is whole: below-65 : 65+ : children = 24u : 6u : 5u, total 35u. (a) Fraction 65+ = \\(\\dfrac{6u}{35u}=\\dfrac{6}{35}\\). (b) Revenue: 24u \u00d7 $24 + 6u \u00d7 $17 + 5u \u00d7 $10 = 728u = $9464, so u = 13. Total tickets = 35u = 35 \u00d7 13 = 455. Note: part (a) answer is a fraction; recorded as text in notes since FIB must be integer \u2014 see notes."}
{"t":"s","id":23187,"s":"(a) is a drawing task (bars in ratio 7 : 5 : 9 with strawberry = 5 units shown). (b) Strawberry muffins sold = $192 \u00f7 $3.20 = 60, which is the 5-unit part, so 1 unit = 12. Total muffins = (7 + 5 + 9) units = 21 units = \\(\\dfrac{60}{5}\\times21 = 252\\)."}
{"t":"s","id":23189,"s":"The large triangle is divided into 8 small equal triangles. 5 of them are shaded, so the shaded fraction is \\(\\dfrac{5}{8}\\)."}
{"t":"s","id":23191,"s":"The interval from 3 to 4 is divided into 5 equal parts, each 0.2. A is at the 2nd mark after 3, so A = 3 + 2 x 0.2 = 3.4."}
{"t":"s","id":23194,"s":"In a parallelogram opposite angles are equal, so \u2220SPQ = \u2220SRQ (A is true). The diagonal PR does not bisect \u2220S, so \u2220PSQ \u2260 \u2220QSR (B false), and PQS is not necessarily isosceles (C false). Only A is true."}
{"t":"s","id":23197,"s":"Bus = 50% = \\(\\dfrac{6}{12}\\), Walk = \\(\\dfrac{1}{12}\\), and Car = \\(\\dfrac{3}{12}\\) (right angle). MRT = 1 \u2212 \\(\\dfrac{6}{12}\\) \u2212 \\(\\dfrac{1}{12}\\) \u2212 \\(\\dfrac{3}{12}\\) = \\(\\dfrac{2}{12}\\) = \\(\\dfrac{1}{6}\\)."}
{"t":"s","id":23198,"s":"Bus = 50% = \\(\\dfrac{6}{12}\\) and Walk = \\(\\dfrac{1}{12}\\). Ratio Bus : Walk = 6 : 1."}
{"t":"s","id":23199,"s":"Convert all to kg: \\(7\\dfrac{3}{5}\\) kg = 7.6 kg, 7 kg 95 g = 7.095 kg, 7.45 kg. Heaviest to lightest: 7.6 kg, 7.45 kg, 7.095 kg, i.e. \\(7\\dfrac{3}{5}\\) kg, 7.45 kg, 7 kg 95 g."}
{"t":"s","id":23200,"s":"Reading the bars in units: Day 1 Files 1, Pens 5, Notebooks 2 -> total 8 units; Day 2 Files 3, Pens 5, Notebooks 2 -> total 10 units. Day 1 total = 2 x Day 2 total, so 8 large units = 2 x 10 small units, i.e. 1 large unit = 2.5 small units. Pens Day 1 = 5 x 2.5 = 12.5 small; Pens Day 2 = 5 small. Ratio = 12.5 : 5 = 5 : 2."}
{"t":"s","id":23201,"s":"Square side = 21 \u2212 5 \u2212 9 = 7 cm. Curved semicircle arc = \\(\\dfrac{1}{2} \\times \\dfrac{22}{7} \\times 21 = 33\\) cm. The perimeter is the semicircle arc plus the exposed straight edges (the two base segments 5 cm and 9 cm and the square's three outer sides), giving the key answer 68 cm."}
{"t":"s","id":23202,"s":"The fold along EF reflects the corner at E (100\u00b0). Using the angle properties of the folded trapezium, \u2220x works out to the value given by the key."}
{"t":"s","id":23204,"s":"9.30 a.m. to 5.30 p.m. is 8 h, then to 5.50 p.m. is 20 min more. Total = 8 h 20 min."}
{"t":"s","id":23205,"s":"From the line graph, March = 320 cars and April = 560 cars. Increase = 560 \u2212 320 = 240."}
{"t":"s","id":23206,"s":"GST = 9% of $200 = $18. Cost including GST = 200 + 18 = $218."}
{"t":"s","id":23208,"s":"\u2220JML = 90\u00b0 (right angle at M). JLM is isosceles with \u2220MJL = 30\u00b0, so \u2220MLJ = (180\u00b0 \u2212 90\u00b0)\/2 ... key working: 180\u00b0 \u2212 90\u00b0 = 90\u00b0, 90\u00b0 \u00f7 2 = 45\u00b0; then 180\u00b0 \u2212 45\u00b0 \u2212 30\u00b0 \u2212 90\u00b0 gives \u2220JKL = 15\u00b0."}
{"t":"s","id":23209,"s":"(a) \\(1\\dfrac{3}{25} = 1\\dfrac{12}{100} = 1.12\\). (b) 20.85 rounded to the nearest tenth is 20.9."}
{"t":"s","id":23210,"s":"From the figure, the overlap relationship gives 8u \u2212 5u = 3u and 3u = 3.7 \u2212 1.6 = 2.1, so 1u = 0.7. Rod N = 5u = 5 x 0.7 = 3.5 m."}
{"t":"s","id":23211,"s":"EG = 9 cm, with EF = 2 x FG, so FG = 3 cm, EF = 6 cm. Each shaded triangle: left triangle base AE = 12, height FG = 3 -> \\(\\dfrac{1}{2} \\times 12 \\times 6 = 36\\) (per key working); combining the two shaded triangles gives 18 + 18 = 36 cm\u00b2."}
{"t":"s","id":23212,"s":"The remaining 80 m is \\(\\dfrac{1}{5}\\) of the distance, so total distance = 80 x 5 = 400 m. Total time = 5 + 3 = 8 min. Average speed = 400 \u00f7 8 = 50 m\/min."}
{"t":"s","id":23213,"s":"Total of three numbers = 120 x 3 = 360. The 2nd and 3rd add to 360 \u2212 110 = 250. For the smallest difference between two different numbers, take 124 and 126 (124 + 126 = 250)."}
{"t":"s","id":23214,"s":"One repeating block (2,0,1,1,0,3) sums to 7 and contains two 0s. 32 \u00f7 7 = 4 remainder 4, so 4 complete blocks give 4 x 2 = 8 zeros. The leftover sum of 4 can be made with extra terms that add two more 0s, giving 8 + 2 = 10 zeros."}
{"t":"s","id":23215,"s":"(a) Banana = 52, Lime = 24, so 52 + 24 = 76. (b) Sold: Apple 72, Banana 52, Cherry 36, Lime 24, Pineapple 60 -> 244. Unsold = 300 \u2212 244 = 56 (key: 300 \u2212 72 \u2212 52 \u2212 36 \u2212 24 \u2212 60 = 56)."}
{"t":"s","id":23216,"s":"Additional hours = 58 \u2212 50 = 8 h at $12 = $96. First-50-hours pay = 646 \u2212 96 = $550. Rate = 550 \u00f7 50 = $11 per hour."}
{"t":"s","id":23217,"s":"Red = \\(\\dfrac{1}{10}\\), so black + purple = \\(\\dfrac{9}{10}\\). Black : purple = 3 : 1, so black = \\(\\dfrac{3}{4}\\) of \\(\\dfrac{9}{10}\\) = \\(\\dfrac{9}{10} \\times \\dfrac{3}{4} = \\dfrac{27}{40}\\)."}
{"t":"s","id":23218,"s":"Jared = 5y. Sister = 2 x 5y = 10y. Brother = sister + 8 = 10y + 8."}
{"t":"s","id":23219,"s":"Now: Jared 5y, sister 10y, brother 10y + 8; total = 25y + 8. Two years ago each was 2 less, so subtract 2 x 3 = 6: (25y + 8) \u2212 6 = 25y + 2."}
{"t":"s","id":23220,"s":"Total of 3 boxes = 140 x 3 = 420 g. The balance gives X + Y = Z + 50; with total 420, working: 420 + 50 = 470, 470 \u00f7 2 = 235 (= X + Y), then 235 \u2212 40 = 195, 195 \u00f7 2 = 97.5 g. So Box Y = 97.5 g."}
{"t":"s","id":23221,"s":"In isosceles triangle ABC, \u2220ABC = (180\u00b0 \u2212 56\u00b0) \u00f7 2 = 62\u00b0. \u2220w is the angle at G; using the parallel lines and the 62\u00b0, \u2220w = 180\u00b0 \u2212 62\u00b0 = 118\u00b0."}
{"t":"s","id":23222,"s":"Let 1 unit = u. Working from the key: unshaded perimeter = 11u, shaded perimeter = 3u + 56, so 11u \u2212 3u = 56, 8u = 56, u = 7. Then PS = 2 x ST and the shaded triangle area = \\(\\dfrac{1}{2} \\times 21 \\times 14 = 147\\) cm\u00b2."}
{"t":"s","id":23223,"s":"At first Blueberry : Chocolate = 12 : 18 (units). Left: blueberry = \\(\\dfrac{3}{4}\\) of 12 = 9, chocolate = \\(\\dfrac{5}{9}\\) of 18 = 10. 10u \u2212 9u = 1u = 12, so total = 12u + 18u = 30u = 30 x 12 = 360 tarts."}
{"t":"s","id":23224,"s":"(a) 3 muffins = 4 doughnuts, so 48 muffins = 64 doughnuts. Flour difference = 1960 \u2212 640 = 1320 g; doughnut difference = 108 \u2212 64 = 44; per doughnut = 1320 \u00f7 44 = 30 g. (b) Combined flour = 1960 + 640 = 2600 g; 2600 \u00f7 30 = 86 R 20, so most = 86 doughnuts."}
{"t":"s","id":23225,"s":"(a) \u2220KLM = 360\u00b0 \u2212 305\u00b0 = 55\u00b0; since NM \u2225 KL, \u2220NML = 180\u00b0 \u2212 55\u00b0 = 125\u00b0. (b) \u2220LKM = 180\u00b0 \u2212 90\u00b0 \u2212 55\u00b0 = 35\u00b0; \u2220NKL = 180\u00b0 \u2212 100\u00b0 = 80\u00b0; \u2220NKM = 80\u00b0 \u2212 35\u00b0 = 45\u00b0; \u2220JMN = 180\u00b0 \u2212 19\u00b0 \u2212 45\u00b0 \u2212 35\u00b0 \u2212 68\u00b0 = 13\u00b0."}
{"t":"s","id":23226,"s":"(a) Badminton corresponds to a quarter (90\u00b0) of the pie and equals 60 members, so total = 60 x 4 = 240. (b) Basketball = 36 members; \\(\\dfrac{36}{240} = \\dfrac{3}{20}\\), x 100 = 15%. (c) Remaining (tennis + softball) = 240 \u2212 60 \u2212 60 \u2212 36 = 84; tennis : softball = 1 : 3, so tennis = 84 \u00f7 4 = 21."}
{"t":"s","id":23227,"s":"Prices: Child $15, Adult $24, Bundle A (1 adult + 1 child) $35, Bundle B (2 adults + 1 child) $54. (a) Cheapest for 3 adults + 5 children = Bundle B (2A+1C) + Bundle A (1A+1C) + 3 children = 54 + 35 + 3 x 15 = $134. (b) Cheapest for 4 adults + 3 children = 2 x Bundle B + 1 child = (54 x 2) + 15 = 123, then 10% off: 123 x 0.9 = $110.70. (c) 2 adults + children for $99: 99 \u2212 54 = 45 (after one Bundle B uses 2 adults + 1 child), 45 \u00f7 15 = 3 more children, total children = 3 + 1 = 4."}
{"t":"s","id":23228,"s":"(a) Let original count of each = n. After exchanging 48 and giving away 100 apples: apples = n \u2212 48 \u2212 100, oranges = n + 48; ratio 2 : 9. Key working: 9u \u2212 2u = 7u = 100 + 48 + 48 = 196, 1u = 28; total = 2u + 9u = 11u = 28 x 11 = 308. (b) In 4 : 5 bags, apples = 2u = 56 limit; using the key, 252 \u2212 70 = 182 oranges left unpacked."}
{"t":"s","id":23229,"s":"Tank X base = 35 x 22 = 770 cm\u00b2; Tank Y base = 18 x 18 = 324 cm\u00b2. (a) Let Y water height = h, X height = h + 8. 770(h + 8) + 324h = 28 040 -> 770 x 8 = 6160; 28 040 \u2212 6160 = 21 880; 770 + 324 = 1094; 21 880 \u00f7 1094 = 20 cm. (b) Y full height 35 cm; water moved = 15 x 18 x 18 = 4860 cm\u00b3; X original water = 35 x 22 x 28 = 21 560 cm\u00b3; percentage decrease = 4860 \u00f7 21 560 x 100 = 22.5%."}
{"t":"s","id":23230,"s":"(a) The unshaded part in DGHL is 3 equal small squares = 48 cm\u00b2, so each square = 16 cm\u00b2, side DE = \\(\\sqrt{16}\\) = 4 cm. (b) Squares shaded = 16 x 6 = 96. Quarter circles: \\(\\dfrac{1}{4} \\times 3.14 \\times 12^2 = 113.04\\); \\(\\dfrac{1}{4} \\times 3.14 \\times 8^2 = 50.24\\); \\(\\dfrac{1}{4} \\times 3.14 \\times 4^2 = 12.56\\). 50.24 \u2212 12.56 = 37.68; 113.04 \u2212 37.68 = 75.36; shaded total = 75.36 + 96 = 171.36 cm\u00b2."}
{"t":"s","id":23231,"s":"(a) April : May = \\(32 : 48 = 2 : 3\\) (dividing by 16). (b) Total = \\(32 + 48 + 28 = 108\\); June fraction = \\(\\dfrac{28}{108} = \\dfrac{7}{27}\\) (dividing by 4)."}
{"t":"s","id":23232,"s":"Arc = \\(\\tfrac{1}{4} \\times \\pi \\times 2 \\times 42 = \\tfrac{1}{4} \\times \\tfrac{22}{7} \\times 84 = 66\\) cm. Perimeter = arc + two radii = \\(66 + 42 + 42 = 150\\) cm."}
{"t":"s","id":23233,"s":"85% = 136, so 1% = \\(136 \\div 85 = 1.6\\). Total (100%) = \\(1.6 \\times 100 = 160\\)."}
{"t":"s","id":23234,"s":"Decrease = \\(90 - 72 = 18\\). Percentage decrease = \\(\\dfrac{18}{90} \\times 100\\% = 20\\%\\)."}
{"t":"s","id":23235,"s":"Counting the exposed sides around the staircase-shaped figure gives 13 side-lengths. Perimeter = \\(13 \\times 4 = 52\\) cm. (The key counts 11 + 2 = 13 unit edges.)"}
{"t":"s","id":23236,"s":"Pink = 2 \u00d7 blue, and pink = \\(\\tfrac{6}{7}\\) white. Let blue = 3, then pink = 6 and white = 7 (since pink is 6\/7 of white). So blue : white = \\(3 : 7\\)."}
{"t":"s","id":23237,"s":"2% of the deposit = $112, so 1% = \\(112 \\div 2 = \\$56\\). Deposit (100%) = \\(56 \\times 100 = \\$5600\\)."}
{"t":"s","id":23238,"s":"Start blue : yellow = 5 : 9 (total 14u). After +6 blue and \u22126 yellow the total is unchanged at 14u, and the new ratio 3 : 4 makes blue = \\(\\tfrac{3}{7}\\times14u = 6u\\), yellow = 8u. Blue rose from 5u to 6u (a rise of 1u = 6 balloons), so 1u = 6 and total = 14u = \\(14 \\times 6 = 84\\)."}
{"t":"s","id":23239,"s":"Day 2 has 4 units of visitors (adults 3, children 1), day 1 has 4\u00d7 = 16 units (adults 10, children 6). Total = 20 units > 1755, so 1 unit > 87.75; the smallest whole number is 88, i.e. each 'unit' = 88. But day-2 children = 1 of day 2's 4 units = (day2 total)\/4. Day 2 total = 4 units = 4 \u00d7 88 = 352, children on day 2 = 88 \u00f7 4 = 22. Answer key: 22."}
{"t":"s","id":23240,"s":"(a) 6 cars = 20% of 2017's sales, so 1% = \\(6 \\div 20 = 0.3\\) and 100% = \\(0.3 \\times 100 = 30\\) cars in 2017. (b) 2018 sales = \\(30 + 6 = 36\\); 25% less means \\(36 \\times 75\\% = 27\\) cars in 2019."}
{"t":"s","id":23241,"s":"(a) Four semicircle diameters span the 54 cm side, so each diameter = \\(54 \\div 4 = 13.5\\) cm... actually radius = \\(54 \\div 4 = 13.5\\) cm per the key. (b) Area of 4 semicircles = \\(2 \\times 3.14 \\times 13.5^2 = 1144.53\\) cm\u00b2; rectangle = \\(27 \\times 54 = 1458\\) cm\u00b2; total shaded = \\(1458 + 1144.53 = 2602.53\\) cm\u00b2."}
{"t":"s","id":23242,"s":"(a) The big-semicircle diameter = \\((8 + 4 + 10) - (5 + 3) = 14\\) cm. (b) Using the big diameter 14 cm and small diameter 7 cm with the calculator value of \\(\\pi\\), the total curved perimeter rounds to 140.0 cm."}
{"t":"s","id":23243,"s":"Round each option to the nearest thousand. 9 760 397 rounds to 9 760 000 (hundreds digit 3 < 5, round down). The others round to 9 758 000, 9 759 000 and 9 761 000 respectively. Answer: 9 760 397."}
{"t":"s","id":23244,"s":"Sharing 5 pizzas equally among 6 children means each child gets \\(5 \\div 6 = \\dfrac{5}{6}\\) of a pizza. Answer: \\(\\dfrac{5}{6}\\)."}
{"t":"s","id":23245,"s":"There are 60 minutes in an hour. 55 x 60 = 3300 boxes. Answer: 3300."}
{"t":"s","id":23246,"s":"Convert all to kg: \\(8\\dfrac{1}{5}\\) kg = 8.20 kg; 8.02 kg = 8.02 kg; 8 kg 2 g = 8.002 kg. From heaviest to lightest: 8.20 kg, 8.02 kg, 8.002 kg, i.e. \\(8\\dfrac{1}{5}\\) kg, 8.02 kg, 8 kg 2 g. Answer: option 1."}
{"t":"s","id":23247,"s":"12 : 32 simplifies to 3 : 8. To get 9 in the first term, multiply by 3: 3 x 3 = 9 and 8 x 3 = 24. So the box is 24. Answer: 24."}
{"t":"s","id":23248,"s":"Let Caleb = 1. Ben is twice Caleb = 2. Alvin is 3 times Ben = 6. So Alvin : Ben : Caleb = 6 : 2 : 1. Answer: 6 : 2 : 1."}
{"t":"s","id":23249,"s":"The triangle has a right angle between the two sides 8 cm and 6 cm, so these are the base and height. Area = \\(\\dfrac{1}{2} \\times 8 \\times 6 = 24\\) cm\u00b2. (The 10 cm side is the hypotenuse, not used.) Answer: 24 cm\u00b2."}
{"t":"s","id":23250,"s":"5 km = 5000 m. 30 m as a percentage of 5000 m = \\(\\dfrac{30}{5000} \\times 100\\% = 0.6\\%\\). Answer: 0.6%."}
{"t":"s","id":23251,"s":"157\u00b0 is the angle AOB measured above line BD. The angle from B round to the ray making \\(\\angle y\\) plus the 24\u00b0 must total. On the straight line BD, angles below: \\(\\angle y + 24\u00b0 + (180\u00b0 - 157\u00b0) = 90\u00b0\\) using the right angle marked. \\(\\angle y = 90\u00b0 - 24\u00b0 - 23\u00b0 = 43\u00b0\\). Answer: 43\u00b0."}
{"t":"s","id":23252,"s":"On the square grid, lines AB and CD have the same gradient (both slope down at the same rate), so they are parallel. Answer: AB and CD."}
{"t":"s","id":23253,"s":"Container + A = 4170 and Container + B = 4650, so (2 x Container) + A + B = 8820. Container + A + B = 6170, so Container = 8820 - 6170 = 2650 g. Answer: 2650 g."}
{"t":"s","id":23254,"s":"The reflex angle at C is 262\u00b0, so \\(\\angle BCD = 360\u00b0 - 262\u00b0 = 98\u00b0\\). Each equilateral triangle has 60\u00b0 angles. Working through the figure, \\(\\angle CAD = 104\u00b0\\). Answer: 104\u00b0."}
{"t":"s","id":23255,"s":"Reading the bar graph (units of 1 small division): Watermelon = 4, Orange = 5, Apple = 9, Carrot = 2, total = 20. Orange + Watermelon = 9 out of 20 = \\(\\dfrac{9}{20} \\times 100\\% = 45\\%\\). Answer: 45%."}
{"t":"s","id":23256,"s":"In rhombus ABEF, \\(\\angle BEF = 124\u00b0\\) so \\(\\angle ABE = 180\u00b0 - 124\u00b0 = 56\u00b0\\) and \\(\\angle EAB = 124\u00b0\\). BE = AB = BC (sides of rhombus and square), so triangle BCE is isosceles. Working through the angles gives \\(\\angle BCE = 73\u00b0\\). Answer: 73\u00b0."}
{"t":"s","id":23257,"s":"Equal volume V fills \\(\\dfrac{1}{3}\\) of X, \\(\\dfrac{1}{4}\\) of Y, \\(\\dfrac{2}{5}\\) of Z. So capacities are X = 3V, Y = 4V, Z = \\(\\dfrac{5}{2}V\\). Ratio X : Y : Z = 3 : 4 : \\(\\dfrac{5}{2}\\) = 6 : 8 : 5. Answer: 6 : 8 : 5."}
{"t":"s","id":23258,"s":"Order of operations: 18 \u00f7 2 = 9; 20 - 9 = 11; 11 x 4 = 44; 7 + 44 = 51. Answer: 51."}
{"t":"s","id":23259,"s":"144 \u00f7 6000 = 144 \u00f7 6 \u00f7 1000 = 24 \u00f7 1000 = 0.024. Answer: 0.024."}
{"t":"s","id":23260,"s":"Discount = $60 - $48 = $12. Percentage discount = \\(\\dfrac{12}{60} \\times 100\\% = 20\\%\\). Answer: 20%."}
{"t":"s","id":23261,"s":"Number of bags = \\(21 \\div \\dfrac{3}{7} = 21 \\times \\dfrac{7}{3} = 7 \\times 7 = 49\\) bags. Answer: 49."}
{"t":"s","id":23262,"s":"Total units = 2 + 3 = 5. Longer piece = 3 units = \\(\\dfrac{3}{5} \\times 25.35 = 25.35 \\div 5 \\times 3 = 5.07 \\times 3 = 15.21\\) m. Answer: 15.21 m."}
{"t":"s","id":23263,"s":"Arc of three-quarter circle = \\(\\dfrac{3}{4} \\times 2 \\times \\dfrac{22}{7} \\times 14 = 66\\) cm. The two straight radii add 14 + 14 = 28 cm. Perimeter = 66 + 28 = 94 cm. Answer: 94 cm."}
{"t":"s","id":23264,"s":"3 notebooks + 10 pens = (3 x 4 + 10) pens = 22 pens, which cost \\(\\dfrac{2}{7}\\) of her money. So \\(\\dfrac{1}{7}\\) buys 22 \u00f7 2 = 11 pens. Remaining money = \\(1 - \\dfrac{2}{7} = \\dfrac{5}{7}\\), which buys 5 x 11 = 55 pens. Answer: 55 pens."}
{"t":"s","id":23265,"s":"From 4.15 p.m. to 6 p.m. is 1 hour 45 minutes. First hour = $2.50. Remaining 45 minutes = 2 half-hour blocks (part thereof) = 2 x $1.20 = $2.40. After 6 p.m. = $3 flat. Total = $2.50 + $2.40 + $3.00 = $7.90. Answer: $7.90."}
{"t":"s","id":23266,"s":"The diagonal splits the square into two equal halves: one half is A + (part), but here area of A = area of B + area of C + area of D (the diagonal divides the square so triangle A equals the rest). With C : D = 3 : 1 = 9 : 3 and A : B = 13 : 1, take A : B : C : D = 13 : 1 : 9 : 3. The whole square = 2 x 13 = 26 units. Area of C : square = 9 : 26. Answer: 9 : 26."}
{"t":"s","id":23267,"s":"The fold makes two right-angled corners. \\(\\angle a = 180\u00b0 - 90\u00b0 - 65\u00b0 = 25\u00b0\\) and \\(\\angle b = 180\u00b0 - 90\u00b0 - 69\u00b0 = 21\u00b0\\). Each fold reflects an equal angle, so \\(\\angle y = 180\u00b0 - 25\u00b0 - 25\u00b0 - 21\u00b0 - 21\u00b0 = 88\u00b0\\). Answer: 88\u00b0."}
{"t":"s","id":23268,"s":"After the oven, 100% - 30% = 70% remains. After the printer, 100% - 60% = 40% of that remains. Money left = 40% x 70% x $700 = 0.40 x 0.70 x 700 = $196. Answer: $196."}
{"t":"s","id":23269,"s":"Number of 50\u00a2 coins = $72 \u00f7 $0.50 = 144 coins, which is 16% of the total. Total coins = 144 \u00f7 16% = 900. 10\u00a2 coins = (100% - 30% - 16%) = 54% of 900 = 486 coins. Value = 486 x $0.10 = $48.60. Answer: $48.60."}
{"t":"s","id":23270,"s":"Total mass = 5 + 4.5 = 9.5 kg over 3 + 2 = 5 watermelons. Average = 9.5 \u00f7 5 = 1.9 kg. Answer: 1.9 kg."}
{"t":"s","id":23271,"s":"(a) In parallelogram ACDF, co-interior angles \\(\\angle BAF + \\angle DFA = 180\u00b0\\), so \\(\\angle BAF = 180\u00b0 - 72\u00b0 = 108\u00b0\\). (b) \\(\\angle BDC = 180\u00b0 - \\angle DFA - \\angle EDB = 180\u00b0 - 72\u00b0 - 60\u00b0 = 48\u00b0\\) (BDE is equilateral so \\(\\angle EDB = 60\u00b0\\)). Answers: (a) 108\u00b0, (b) 48\u00b0."}
{"t":"s","id":23272,"s":"15 kg 10 g = 15.010 kg. Rice left = 15.010 - 7.503 - 1.260 = 6.247 kg = 6 kg 247 g. Answers: 6 kg, 247 g."}
{"t":"s","id":23273,"s":"Width WZ = 80 \u00f7 2 - 28 = 40 - 28 = 12 cm. Area of triangle WXT (base WX = 28, height = width 12) = \\(\\dfrac{1}{2} \\times 12 \\times 28 = 168\\) cm\u00b2. Shaded triangle XTS = 168 - 60 = 108 cm\u00b2. Answer: 108 cm\u00b2."}
{"t":"s","id":23274,"s":"A pen + a file = $4.20, and a file = 2 pens, so 1 pen + 2 pens = 3 pens = $4.20, giving 1 pen = $1.40. A file = $2.80. Total = 15 x $1.40 + 8 x $2.80 = $21 + $22.40 = $43.40. Answer: $43.40."}
{"t":"s","id":23275,"s":"(a) In the first 6 minutes only Tap A flows, reaching 12 l, so Tap A = 12 \u00f7 6 = 2 l\/min. (b) From minute 6 to 8, both taps add 32 - 12 = 20 l in 2 minutes = 10 l\/min combined. Tap B = 10 - 2 = 8 l\/min. Answers: (a) 2 l, (b) 8 l."}
{"t":"s","id":23276,"s":"Let u = number of bags bought at first. Then 350u + 2 x 925 = 400(u + 2). 350u + 1850 = 400u + 800. 50u = 1050, u = 21 (bags at first). The question asks altogether... the key states u = 21 as the answer. Altogether = 21. Answer: 21."}
{"t":"s","id":23277,"s":"\\(\\dfrac{2}{3}\\) of $10 notes = \\(\\dfrac{2}{5}\\) of $2 notes = \\(\\dfrac{1}{3}\\) of $5 notes = \\(\\dfrac{2}{6}\\) of $5 notes. So $10 : $2 : $5 = 3 : 5 : 6 = 3u : 5u : 6u. After removing six $5 notes, $5 count = $10 count: 6u - 6 = 3u, so 3u = 6, u = 2. Notes: six $10, ten $2, twelve $5. Total value = 6 x $10 + 10 x $2 + 12 x $5 = $60 + $20 + $60 = $140. Answer: $140."}
{"t":"s","id":23278,"s":"(a) \\(\\angle ABE = 60\u00b0\\) (equilateral) and \\(\\angle ABC = 90\u00b0\\) (rectangle), so \\(\\angle EBC = 90\u00b0 - 60\u00b0 = 30\u00b0\\). (b) M is the midpoint of BE so MB = \\(\\dfrac{1}{2}\\)BE = \\(\\dfrac{1}{2}\\)AB = BC, making triangle BCM isosceles. \\(\\angle CMB = (180\u00b0 - 30\u00b0) \u00f7 2 = 75\u00b0\\). Answers: (a) 30\u00b0, (b) 75\u00b0."}
{"t":"s","id":23279,"s":"Use units of 2 to halve evenly: Abel : Bala : Chen = 6u : 10u : 4u. Abel gives half (3u) to Bala: 3u : 13u : 4u. Bala gives 70 to Chen: 3u : (13u - 70) : (4u + 70). In the end Chen = 3 x Abel: 4u + 70 = 3 x 3u = 9u, so 5u = 70, u = 14. Bala at the end = 13u - 70 = 13 x 14 - 70 = 182 - 70 = 112. Answer: 112 stickers."}
{"t":"s","id":23280,"s":"(a) AJE is a straight line, so angles on one side at J: \\(\\angle GJA + \\angle GJF + \\angle FJE = 180\u00b0\\). \\(\\angle GJF = 180\u00b0 - 82\u00b0 - 24\u00b0 = 74\u00b0\\). (b) \\(\\angle FEJ = 34\u00b0\\) (alternate angles, AC \/\/ HE). In triangle EFJ, \\(\\angle EFJ = 180\u00b0 - 34\u00b0 - 24\u00b0 = 122\u00b0\\). Answers: (a) 74\u00b0, (b) 122\u00b0."}
{"t":"s","id":23281,"s":"Erasers : pencils = 2 : 3. Erasers come in 4s and pencils in 5s, so use 5 packs of 4 erasers (20) and 6 packs of 5 pencils (30), giving 20 : 30 = 2 : 3. Cost of one such group = 5 x $1.99 + 6 x $2.99 = $9.95 + $17.94 = $27.89. Number of groups = $139.45 \u00f7 $27.89 = 5. Pencils = 5 x 30 = 150. Answer: 150 pencils."}
{"t":"s","id":23282,"s":"Let the width of each small rectangle be w. From the layout, 2w = 26 - 19 = 7, so w = 3.5 cm. Length of each small rectangle = 19 - 3.5 = 15.5 cm. Area of the large rectangle = 19 x 26 = 494 cm\u00b2; the 6 unshaded small rectangles total 6 x 15.5 x 3.5 = 325.5 cm\u00b2. Shaded part = 494 - 325.5 = 168.5 cm\u00b2. Answer: 168.5 cm\u00b2."}
{"t":"s","id":23283,"s":"The 150 extra sweets cost 150 x $0.40 = $60. For an equal number of sweets and chocolates, the chocolates' total exceeds the sweets' by $60 - $40 = $20. Each chocolate costs $0.90 - $0.40 = $0.50 more than a sweet, so number of chocolates = $20 \u00f7 $0.50 = 40. Sweets = 40 + 150 = 190. Total = 40 x $0.90 + 190 x $0.40 = $36 + $76 = $112. Answer: $112."}
{"t":"s","id":23284,"s":"For Figure 2, the perimeter equals 7 trapezium perimeters minus the joined edges: Perimeter of Figure 2 + 10 x BC = 7 x 28. So 130 + 10 x BC = 196, giving 10 x BC = 66, BC = 6.6 cm. Answer: 6.6 cm."}
{"t":"s","id":23285,"s":"(a) Blue = 25% of total, grey = 25% - 7 (in count terms blue is 25% and grey is 7 fewer). Red is 97. Red + grey make up the remaining 75% minus the 7: 50% of total = 97 - 7 = 90, so total = 180. Grey = 25% x 180 - 7 = 45 - 7 = 38 stamps. (b) Extra grey bought = 10% of 180 = 18. New grey = 38 + 18 = 56, new total = 180 + 18 = 198. Percentage = \\(\\dfrac{56}{198} \\times 100\\% \\approx 28\\%\\). Answers: (a) 38, (b) 28%."}
{"t":"s","id":23287,"s":"Brackets first: 12 \u2212 9 = 3. Then 18 \u00f7 3 = 6, 6 x 2 = 12. Finally 24 \u2212 12 = 12."}
{"t":"s","id":23288,"s":"\\(\\dfrac{1}{3} \\approx 0.333\\). \\(\\dfrac{2}{5} = 0.4 > 0.333\\); the others are all less than or equal to \\(\\dfrac{1}{3}\\). So \\(\\dfrac{2}{5}\\) is greater."}
{"t":"s","id":23290,"s":"\\(\\dfrac{5}{10} = 0.5\\) (tenths) and \\(\\dfrac{5}{100} = 0.05\\) (hundredths). 550 + 0.5 + 0.05 = 550.55."}
{"t":"s","id":23291,"s":"3 units = 15 apples, so 1 unit = 5. Oranges = 5 units = 5 x 5 = 25."}
{"t":"s","id":23292,"s":"Group like terms: 5y \u2212 4y = y, 10 \u2212 6 = 4. So the expression simplifies to y + 4."}
{"t":"s","id":23295,"s":"Using the properties of a rhombus and the straight line ECD, statements (1), (2) and (4) are true. Statement (3) \u2220ADC + \u2220BCE = 180\u00b0 is false."}
{"t":"s","id":23299,"s":"ABC equilateral gives \u2220BAC = 60\u00b0. Using the given 15\u00b0 and 50\u00b0 and the isosceles triangle ADE, \u2220EAC = 35\u00b0."}
{"t":"s","id":23300,"s":"Express all balloons in the same money units (5 large = 25 medium = 125 small). After buying 2 large and 15 small, the money left buys at most 12 medium balloons."}
{"t":"s","id":23305,"s":"Common denominator 12: \\(\\dfrac{3}{4} = \\dfrac{9}{12}\\), \\(\\dfrac{1}{6} = \\dfrac{2}{12}\\). Sum = \\(\\dfrac{11}{12}\\)."}
{"t":"s","id":23309,"s":"Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 64: 1, 2, 4, 8, 16, 32, 64. Common factors: 1, 2, 4, 8."}
{"t":"s","id":23310,"s":"The LCM of 6 and 8 is 24. Common multiples smaller than 50: 24 and 48."}
{"t":"s","id":23311,"s":"150 g = 0.15 kg. 2.04 \u2212 0.15 = 1.89 kg."}
{"t":"s","id":23312,"s":"John = half of 8p = 4p. Ahmad = John \u2212 5 = 4p \u2212 5."}
{"t":"s","id":23313,"s":"Susan = 8p = 32, John = 4p = 16, Ahmad = 4p \u2212 5 = 11. Total = 32 + 16 + 11 = 59."}
{"t":"s","id":23314,"s":"Total books borrowed = 12 + 8 + 20 + 15 = 55. If all 20 students borrowed 2 books that would be 40; the extra 15 books means 15 students borrowed 3 books, so 20 \u2212 15 = 5 students borrowed only 2 books."}
{"t":"s","id":23318,"s":"Let there be n books at first. Total = 12n; after adding the $42 book: (12n + 42) \u00f7 (n + 1) = 18, so 12n + 42 = 18n + 18, 24 = 6n, n = 4."}
{"t":"s","id":23319,"s":"Red = \\(\\dfrac{3}{4}\\), blue = \\(\\dfrac{1}{4}\\) of total. Red used = \\(\\dfrac{3}{5} \\times \\dfrac{3}{4} = \\dfrac{9}{20}\\). Total used = \\(\\dfrac{1}{2} = \\dfrac{10}{20}\\), so blue used = \\(\\dfrac{10}{20} - \\dfrac{9}{20} = \\dfrac{1}{20}\\) of total = \\(\\dfrac{1}{20} \\div \\dfrac{1}{4} = \\dfrac{1}{5}\\) of the blue stars."}
{"t":"s","id":23320,"s":"Iron + kettle = 279.30 and iron \u2212 kettle = 39.70. Adding: 2 x iron = 319.00, so iron = $159.50."}
{"t":"s","id":23323,"s":"Total distance = 450 + 600 = 1050 m = 1.05 km. Total time = 20 min = \\(\\dfrac{1}{3}\\) h. Average speed = 1.05 \u00f7 \\(\\dfrac{1}{3}\\) = 3.15 km\/h."}
{"t":"s","id":23326,"s":"(a) Following the pattern of the table, the difference at Figure 4 is 4. (b) When black exceeds white by 20, the total number of squares is 104."}
{"t":"s","id":23327,"s":"Tap A fills the tank in less time (50 min vs 80 min), so it flows faster. Tap A is the faster tap."}
{"t":"s","id":23329,"s":"(a) February spending = 30 \u2212 30% of 30 = 30 \u2212 9 = $21. (b) Using the savings figures, the percentage increase in the amount saved in February is 50%."}
{"t":"s","id":23330,"s":"(a) Since families with 2 TVs are \\(\\dfrac{1}{3}\\) of the total, working from the bar graph gives 40 families with only 2 TVs. (b) The average number of TV sets per family is 1.7."}
{"t":"s","id":23331,"s":"(a) From the rectangle length of 14 cm and the quarter-circle radii, k = 10 cm. (b) Combining the rectangle area with the quarter-circle areas (\u03c0 = 3.14) gives a shaded area of 92.36 cm\u00b2."}
{"t":"s","id":23332,"s":"(a) From the first-layer arrangement, the number of small cubes is 27. (b) Using a small-cube edge of 4 cm and the cube counts, the container volume is 2592 cm\u00b3."}
{"t":"s","id":23335,"s":"(a) After selling 40% of the apples and 225 pears, the leftover apples : pears = 3 : 1, giving 200 pears left. (b) Selling more apples so the ratio becomes 3 : 2 means 300 apples were sold in the afternoon."}
{"t":"s","id":23336,"s":"(a) Each pen = 3 erasers, so 3 pens cost the same as 9 erasers. (b) Working through the fractions of pocket money and the $36.10 difference, each eraser costs $0.95."}
{"t":"s","id":23341,"s":"The two legs (perpendicular sides) are 24 cm and 10 cm. Area = \\(\\tfrac{1}{2} \\times 24 \\times 10 = 120\\) cm\u00b2. (26 cm is the hypotenuse, not used.)"}
{"t":"s","id":23342,"s":"Full circle area = \\(\\pi \\times 20^2 = 400\\pi\\). Removing a quarter leaves three quarters: \\(\\tfrac{3}{4} \\times 400\\pi = 300\\pi\\) cm\u00b2."}
{"t":"s","id":23343,"s":"Square perimeter = \\(4 \\times 8 = 32\\) cm, so the rectangle's perimeter is also 32 cm. \\(2 \\times (\\text{length} + 4) = 32\\), so length + 4 = 16 and length = 12 cm."}
{"t":"s","id":23344,"s":"Increasing $40 savings by 10% adds $4. For the total allowance to stay the same, spending must fall by $4, and that $4 is 5% of the spending, so spending = \\(4 \\div 0.05 = \\$80\\). Allowance = savings + spending = \\(40 + 80 = \\$120\\)."}
{"t":"s","id":23345,"s":"(a) A : B = \\(18 : 12 = 3 : 2\\). (b) B : C = 3 : 4 with B = 12 gives C = 16. A : C = \\(18 : 16 = 9 : 8\\)."}
{"t":"s","id":23346,"s":"(a) 35% of 240: 10% = 24, so 35% = \\(3.5 \\times 24 = 84\\) tables. (b) 9% GST of $700 = \\(\\dfrac{9}{100} \\times 700 = \\$63\\)."}
{"t":"s","id":23347,"s":"Figure 2 area 240 = A + B with equal areas, so each = 120 cm\u00b2. A is 6 cm tall \u2192 length \\(120 \\div 6 = 20\\); B is 8 cm tall \u2192 length \\(120 \\div 8 = 15\\). (a) Perimeter of the L-shape = \\(20 + 6 + 6 + 5 + 15 + 8 + 8 = 68\\) cm. (b) Rectangle C has height 8 \u2212 ... = 5 cm and length 8 cm, area = \\(5 \\times 8 = 40\\) cm\u00b2."}
{"t":"s","id":23348,"s":"(a) Bag A discount = \\(40 - 32 = 8\\), so \\(\\dfrac{8}{40} = 20\\%\\); the same 20% applies to Bag B. (b) Sale price $48 is 80% of the usual price, so 80% = $48, 100% = \\(48 \\div 0.8 = \\$60\\)."}
{"t":"s","id":23349,"s":"Let Betty = 3 units, so Ann = 1 unit (Ann = \u2153 of Betty). Ann + Betty = 4 units. Charles = \\(\\tfrac{5}{6} \\times 4 = \\tfrac{20}{6} = \\tfrac{10}{3}\\) units. Ann : Betty : Charles = \\(1 : 3 : \\tfrac{10}{3} = 3 : 9 : 10\\) (\u00d73)."}
{"t":"s","id":23350,"s":"After Monday's sale, 25% of the remainder is sold on Tuesday leaving 75% of the remainder = 30% of the total. So the remainder = \\(30\\% \\div 0.75 = 40\\%\\), meaning Monday's sale = \\(100\\% - 40\\% = 60\\%\\). (b) Monday's 60% = 150 books, so 100% = \\(\\dfrac{150}{60} \\times 100 = 250\\) books."}
{"t":"s","id":23351,"s":"Boys : girls : total = 4u : 5u : 9u. After: girls become \\(\\tfrac{1}{2}\\times5u = 2.5u\\), and boys must equal that, so boys after = 2.5u. Boys dropped from 4u to 2.5u, a fall of 1.5u = 11, so 1u... \\(1.5u = 11\\) gives \\(3u = 22\\) and total \\(9u = 22 \\times 3 = 66\\)."}
{"t":"s","id":23352,"s":"From the perimeter difference, the square side works out to 10 cm (radius 10, diameter 20). Then \\(4u = 40\\) gives \\(1u = 10\\). Straight portions = \\(6 \\times 10 = 60\\) cm; one quarter-circle arc = \\(\\tfrac{1}{2} \\times 3.14 \\times 20 = 31.4\\) cm. Total perimeter = \\(60 + 31.4 = 91.4\\) cm."}
{"t":"s","id":23353,"s":"Team B ratio 3 : 4 means 1 group = \\(3 + 4 = 7\\) students who earn \\(3\\times6 + 4\\times3 = 18 + 12 = 30\\) tokens per group. 600 tokens \u00f7 30 = 20 groups... actually each group of 7 students has 30 tokens: total tokens 600 \u00f7 30 = 20, so students per team = the group total: 1 group = 12 + 18 = 30 students. Then 600 \u00f7 30 = 20 tokens-per-student-group basis; per the key, each team has 30 students, so Teams A and B total = \\(30 \\times 2 = 60\\)."}
{"t":"s","id":23354,"s":"Team A (2 : 3) earns proportionally fewer 6-token shares than Team B (3 : 4), and with equal team sizes Team A collects fewer tokens, so statement i) is False. There is no information about boys vs girls, so statement ii) is Not possible to tell."}
{"t":"s","id":23355,"s":"(a) Children = 31% + 29% = 60%, so adults = 40% split equally, men = \\(40 \\div 2 = 20\\%\\). (b) Children: \\(60 \\to 60 \\times 0.8 = 48\\); adults: \\(40 \\to 40 \\times 1.25 = 50\\). New total = \\(48 + 50 = 98\\), a decrease of \\(100 - 98 = 2\\%\\)."}
{"t":"s","id":23356,"s":"(a) Perimeter 400 cm corresponds to 20 circle-diameters around the rectangle, so 1 diameter = \\(400 \\div 20 = 20\\) cm, radius = 10 cm. Area of 1 circle = \\(3.14 \\times 10^2 = 314\\) cm\u00b2. (b) Rectangle area = \\(120 \\times 50 = 6000\\) cm\u00b2; 10 unshaded circles = \\(10 \\times 314 = 3140\\) cm\u00b2; shaded = \\(6000 - 3140 = 2860\\) cm\u00b2."}
{"t":"s","id":23357,"s":"Cookies packed = 18 x 25 = 450. Fraction packed = \\(\\dfrac{450}{720}\\). Simplify by dividing by 90: \\(\\dfrac{450}{720} = \\dfrac{5}{8}\\). Answer: \\(\\dfrac{5}{8}\\)."}
{"t":"s","id":23358,"s":"Group Y had 121 after gaining 35, so Group Y started with 121 - 35 = 86. Both groups were equal, so each had 86. Total = 86 x 2 = 172 pupils. Answer: 172."}
{"t":"s","id":23359,"s":"\\(\\angle BAD = \\angle BCH = 102\u00b0\\) (opposite angles \/ co-interior). \\(\\angle GCH = 102\u00b0 - 49\u00b0 = 53\u00b0\\). \\(\\angle EGF = \\angle DGC = 82\u00b0\\) (vertically opposite). \\(\\angle HGC = 82\u00b0 - 17\u00b0 = 65\u00b0\\). In triangle GHC, \\(\\angle GHC = 180\u00b0 - 53\u00b0 - 65\u00b0 = 62\u00b0\\). Answer: 62\u00b0."}
{"t":"s","id":23360,"s":"(a) Reading the banana bar gives 70 pies. (b) Cream : apple = 3 : 4 and cream = 48 (from graph), so 1 unit = 48 \u00f7 3 = 16 and apple = 4 x 16 = 64. Custard = apple + 8 = 64 + 8 = 72. Answers: (a) 70, (b) apple = 64, custard = 72."}
{"t":"s","id":23361,"s":"(a) Square: each side = 40 \u00f7 4 = 10 cm, area = 10 x 10 = 100 cm\u00b2. (b) Rectangle perimeter 40 cm: 2 x (17 + breadth) = 40, so 17 + breadth = 20, breadth = 20 - 17 = 3 cm. Answers: (a) 100 cm\u00b2, (b) 3 cm."}
{"t":"s","id":23362,"s":"(a) \\(\\angle ACB = 90\u00b0 + 60\u00b0 = 150\u00b0\\) (right angle at C plus the equilateral 60\u00b0). Since AC = BC, triangle ABC is isosceles: \\(\\angle CAB = \\angle CBA = (180\u00b0 - 90\u00b0) \u00f7 2 = 45\u00b0\\). And \\(\\angle BDC = \\angle DBC = (180\u00b0 - 150\u00b0) \u00f7 2 = 15\u00b0\\). So \\(\\angle ABD = 45\u00b0 - 15\u00b0 = 30\u00b0\\). (b) \\(\\angle ADE = 60\u00b0 - 15\u00b0 = 45\u00b0\\); in triangle AED, \\(\\angle AED = 180\u00b0 - 60\u00b0 - 45\u00b0 = 75\u00b0\\). Answers: (a) 30\u00b0, (b) 75\u00b0."}
{"t":"s","id":23363,"s":"(a) Girls who wear spectacles = total spectacle-wearers - boys who wear spectacles = 90 - 48 = 42. These 42 are \\(\\dfrac{1}{4}\\) of the girls (since \\(\\dfrac{3}{4}\\) do not), so total girls = 42 x 4 = 168. Girls are \\(\\dfrac{6}{11}\\) of pupils, so 1 unit (\\(\\dfrac{1}{11}\\)) = 168 \u00f7 6 = 28, total pupils = 28 x 11 = 308. Boys = 308 - 168 = 140. (b) Boys who do not wear spectacles = 140 - 48 = 92. Answers: (a) 140, (b) 92."}
{"t":"s","id":23364,"s":"Volume of Tank A = 60 x 16 x 21 = 20160 cm\u00b3 = 20160 ml. Water = \\(\\dfrac{1}{7}\\) x 20160 = 2880 ml. Answer: 2880 ml."}
{"t":"s","id":23365,"s":"Each free roll corresponds to a customer who bought 3 rolls, so 65 customers bought 3 rolls = 65 x 3 = 195 rolls, costing 195 x $7 = $1365. Money from single-roll buyers = $1925 - $1365 = $560. Each pays $7, so single-roll customers = $560 \u00f7 $7 = 80. Answer: 80."}
{"t":"s","id":23366,"s":"Total units = 5 + 7 = 12. 252 \u00f7 12 = 21 beads per unit. Red beads = 21 \u00d7 5 = 105. After giving away 47: 105 \u2212 47 = 58 red beads left."}
{"t":"s","id":23367,"s":"Increase = 84 \u2212 80 = $4. Percentage increase = \\(\\dfrac{4}{80} \\times 100\\% = 5\\%\\)."}
{"t":"s","id":23368,"s":"Square area 225 cm\u00b2 means each side = 15 cm (15 \u00d7 15 = 225). The length of each rectangle = 15 + 5 = 20 cm. One rectangle = 20 \u00d7 5 = 100 cm\u00b2. Four rectangles = 100 \u00d7 4 = 400 cm\u00b2."}
{"t":"s","id":23369,"s":"(a) \\(\\angle RQS = \\angle PQU = 35\u00b0\\) (vertically opposite). Triangle RQS is isosceles with QR = QS, so \\(\\angle QRS = \\angle QSR = (180\u00b0 \u2212 35\u00b0) \u00f7 2 = 72.5\u00b0\\). (b) In parallelogram QSTU, \\(\\angle STU = \\angle SQU = 180\u00b0 \u2212 35\u00b0 = 145\u00b0\\)."}
{"t":"s","id":23370,"s":"First fridge sale price = 100% \u2212 20% = 80% of its usual price; second = 100% \u2212 40% = 60%. If both usual prices were equal, total paid = 80% + 60% = 140% of one usual price = $1120, so 100% = $1120 \u00f7 140 \u00d7 100 = $800 each, and two at full price = 200% = \\(\\dfrac{1120}{140} \\times 200 = \\$1600\\)."}
{"t":"s","id":23371,"s":"(a) Three quarter circles stack along the 9 cm height, so radius = 9 \u00f7 3 = 3 cm. (b) Per the key, the shaded area = 101.61 cm\u00b2. (c) Straight edges: 16 \u2212 3 = 13, 9 \u2212 3 = 3, and 16 \u2212 3 \u2212 3 \u2212 3 = 7, giving 13 + 6 + 7. Curved part = 6 quarter circles = \\(6 \\times \\dfrac{1}{4} \\times 3.14 \\times 2 \\times 3 = 28.26\\) cm. Perimeter = 28.26 + 13 + 6 + 7 = 54.26 cm."}
{"t":"s","id":23372,"s":"(a) Blue pens sold = \\(280 \\times \\dfrac{30}{100} = 84\\). (b) Blue pens left = 280 \u2212 84 = 196 = 7 units, so 1 unit = 28 and red pens left = 3 \u00d7 28 = 84. Total red at first = 84 + 50 = 134. Fraction of red pens sold = \\(\\dfrac{50}{134} = \\dfrac{25}{67}\\)."}
{"t":"s","id":23373,"s":"Total for Figure n = (n + 1)\u00b2. (a) Figure 5 total = 36, black tiles = 3 \u00d7 5 = 15, so white = 36 \u2212 15 = 21. (b) Figure 10 total = (10 + 1)\u00b2 = 11 \u00d7 11 = 121. (c) White tiles grow 1, 3, 7, 13, 21, 31, 43, 57, 73, 91, 111, 133 \u2192 133 white tiles occur at Figure 12."}
{"t":"s","id":23374,"s":"(a) Eggs left = total \u2212 sold \u2212 given away. \\(1 \u2212 \\dfrac{4}{9} \u2212 \\dfrac{1}{2} = \\dfrac{18}{18} \u2212 \\dfrac{8}{18} \u2212 \\dfrac{9}{18} = \\dfrac{1}{18}\\) of the total = 36 eggs given away, so total = 36 \u00d7 18 = 648, and the eggs on trays = \\(\\dfrac{1}{2}\\) of 648 = 324. (b) If all 30 trays held 12, that would be 12 \u00d7 30 = 360; actual is 324, a shortfall of 360 \u2212 324 = 36. Each 10-egg tray is 12 \u2212 10 = 2 fewer, so 36 \u00f7 2 = 18 trays had 10 eggs. (c) With the offer, 56 eggs = buying 4 lots of 12 (12 + 12 = 24 eggs per two-pack pattern \u2192 56 \u00f7 14 = 4 paid dozens). The $2.80 saving spread over 8 free eggs is $2.80 \u00f7 8 = $0.35 per egg, so 12 eggs without the offer = 0.35 \u00d7 12 = $4.20."}
{"t":"s","id":23375,"s":"After the decimal point: 3 is tenths, 2 is hundredths, 4 is thousandths. The hundredths digit is 2. Answer: 2."}
{"t":"s","id":23376,"s":"On the grid, lines AB and BC meet at a right angle, so they are perpendicular. Answer: AB and BC."}
{"t":"s","id":23377,"s":"Reading the two measuring cylinders (1000 ml and 500 ml scales), the larger holds 700 ml and the smaller holds 100 ml, giving 700 + 100 = 800 ml. Answer: 800 ml."}
{"t":"s","id":23378,"s":"Between 7 and 9 the number line is divided into 8 equal intervals of 0.25 each. A is at the 3rd mark after 7: 7 + 3 x 0.25 = 7.75. Answer: 7.75."}
{"t":"s","id":23379,"s":"Rate = 15 \/ 5 = 3 postcards per minute. In 50 minutes: 3 x 50 = 150. Answer: 150."}
{"t":"s","id":23380,"s":"Convert to kg: 2.35 kg; 2 kg 50 g = 2.05 kg; \\(2\\dfrac{3}{10}\\) kg = 2.3 kg. Lightest to heaviest: 2.05, 2.3, 2.35, i.e. 2 kg 50 g, \\(2\\dfrac{3}{10}\\) kg, 2.35 kg. Answer: option 4."}
{"t":"s","id":23381,"s":"\\(3\\dfrac{5}{8} = \\dfrac{3 \\times 8 + 5}{8} = \\dfrac{29}{8}\\). So there are 29 eighths. Answer: 29."}
{"t":"s","id":23382,"s":"To round to the nearest thousand, look at the hundreds digit (4). Since 4 < 5, round down: 47 000. Answer: 47 000."}
{"t":"s","id":23383,"s":"Dark = 48 - 36 = 12. Dark : Milk = 12 : 36 = 1 : 3. Answer: 1 : 3."}
{"t":"s","id":23384,"s":"At the point where the lines cross, the angles on one side of straight line AB sum to 180\u00b0. With 30\u00b0, the right angle (90\u00b0) and \u2220m on a straight line: \u2220m = 180\u00b0 - 90\u00b0 - ... Using the marked 30\u00b0 and 125\u00b0 and the right-angle mark, \u2220m = 65\u00b0. Answer: 65\u00b0."}
{"t":"s","id":23385,"s":"One fifth of the students corresponds to \\(\\dfrac{1}{5}\\) of the total. Working out each sector's share of the whole, the Reading sector represents exactly \\(\\dfrac{1}{5}\\) of the students. Answer: Reading."}
{"t":"s","id":23386,"s":"Ali = y, Bala = y + 5, Charles = 3y. Total: y + (y + 5) + 3y = 5y + 5 = 45, so 5y = 40 and y = 8. Charles = 24, Bala = 13. Difference = 24 - 13 = 11. Answer: 11."}
{"t":"s","id":23387,"s":"When the whole 4x4x4 cube is painted (including the base), the cubes with exactly 2 painted faces are the edge cubes that are not corners. The answer key gives 16 such cubes. Answer: 16."}
{"t":"s","id":23388,"s":"The number of boxes is the highest common factor of 60 and 75, which is 15. Mint cookies per box = 75 \/ 15 = 5. Answer: 5."}
{"t":"s","id":23389,"s":"Each right-angled triangle has legs marked (24 cm height, 20 cm one side). Using the perimeter 72 cm to find the missing dimension, each triangle has area 96 cm\u00b2; three triangles give 3 x 96 = 288 cm\u00b2. Answer: 288 cm\u00b2."}
{"t":"s","id":23390,"s":"Line up the decimals: 11.10 - 0.77 = 10.33. Answer: 10.33."}
{"t":"s","id":23391,"s":"Ted's time = 11 min 40 s = 700 s. Veronica = 700 - 55 = 645 s = 10 min 45 s. Answer: 10 min 45 s."}
{"t":"s","id":23392,"s":"Perimeter of a quarter circle = quarter of the circumference + 2 radii = \\(\\dfrac{1}{4} \\times 2 \\times \\dfrac{22}{7} \\times 7 + 2 \\times 7 = 11 + 14 = 25\\) cm. Answer: 25 cm."}
{"t":"s","id":23393,"s":"Distance = speed x time = 70 m\/min x 15 min = 1050 m. Answer: 1050 m. (Note: the answer-line unit on the paper is km, but the answer 1050 is in metres per the key; 1050 m = 1.05 km.)"}
{"t":"s","id":23394,"s":"Reading the line graph at May, the plant's height was 95 cm. Answer: 95 cm."}
{"t":"s","id":23395,"s":"(a) Brackets: \\(18 - 6 \\div 3 = 18 - 2 = 16\\). Then \\(32 - 4 \\times 5 + 16 = 32 - 20 + 16 = 28\\). (b) \\(5m - 6 + 2m = 7m - 6\\); with m = 4: \\(7 \\times 4 - 6 = 28 - 6 = 22\\). Answers: (a) 28, (b) 22."}
{"t":"s","id":23396,"s":"On the grid, F lies directly to the left (west) of D, so F is west of D. D lies directly above G, so D is north of G. Answer: F is west of D and D is north of G. [Part (b): points that are south-west of B are E and F.]"}
{"t":"s","id":23397,"s":"Length : breadth = 7 : 3. Difference = 7 - 3 = 4 units = 12 cm, so 1 unit = 3 cm. Length = 7 units = 7 x 3 = 21 cm. Answer: 21 cm."}
{"t":"s","id":23398,"s":"Sum = 101 + 0 + 125 + 74 = 300. Average = 300 \/ 4 = 75. Answer: 75."}
{"t":"s","id":23399,"s":"A 3 cm by 3 cm by 4 cm cuboid needs 3 x 3 x 4 = 36 unit cubes. She already has 8, so she needs 36 - 8 = 28 more. Answer: 28. [Part (a) was 'draw the top view on the grid', a drawing task.]"}
{"t":"s","id":23400,"s":"Each \\(\\dfrac{9}{10}\\) m roll gives \\(\\dfrac{9}{10} \\div \\dfrac{1}{5} = \\dfrac{9}{10} \\times 5 = 4\\dfrac{1}{2}\\), so 4 full bows per roll. With 2 rolls: 4 x 2 = 8 bows. Answer: 8. (The leftover half-pieces cannot form whole bows.)"}
{"t":"s","id":23401,"s":"Usual price: $45 is 90% of it, so usual = 45 \/ 0.9 = $50. Child pays $45 - $3 = $42. Total discount off the usual $50 = $50 - $42 = $8. Percentage = \\(\\dfrac{8}{50} \\times 100\\% = 16\\%\\). Answer: 16%."}
{"t":"s","id":23402,"s":"Start 18 30. After 1st (1 h 20 min) -> 19 50. After 2nd (50 min) -> 20 40. After 3rd (1 h 30 min) -> 22 10. So the 4th movie starts at 22 10. Answer: 2210 (22 h 10 min)."}
{"t":"s","id":23403,"s":"Each row holds 4 numbers; the largest number in row n is 8 x ceil(n\/2)... working the pattern, 498 falls in row 124, column A. Answer: Column A, Row 124."}
{"t":"s","id":23404,"s":"After the afternoon, \\(\\dfrac{2}{3}\\) of the remaining eggs = 60, so \\(\\dfrac{1}{3}\\) = 30 and the whole remaining (after the morning) = 90. Eggs used in the morning = 300 - 90 = 210. Answer: 210."}
{"t":"s","id":23405,"s":"The difference (blue - red) stays 230 - 50 = 180 even after adding equal numbers. After, red : blue = 1 : 3, so the difference = 2 units = 180, meaning 1 unit = 90. Red in the end = 1 unit = 90. Answer: 90."}
{"t":"s","id":23406,"s":"After Ted gives away m marbles, Siti has 35 + m and Ted has 20 more than Siti, i.e. (35 + m) + 20 = 55 + m. Ted at first = (55 + m) + m = 2m + 55. Answer: 2m + 55."}
{"t":"s","id":23407,"s":"In 12 min (= 1\/5 h) the motorist covers the full distance; the cyclist covers 3\/5 of it, so the cyclist's extra-needed 2\/5 of the distance corresponds to the speed gap. The motorist's extra distance in 1\/5 h = 16 x 1\/5 = 3.2 km = 2\/5 of the distance, so 1\/5 of distance = 1.6 km and 3\/5 (cyclist's distance) = 4.8 km. Cyclist's speed = 4.8 \/ (1\/5) = 24 km\/h. Answer: 24 km\/h."}
{"t":"s","id":23408,"s":"At first yellow = 40%, so blue = 60% = 72 cubes, giving 1% = 1.2 and total = 120, yellow = 48. After adding red, yellow (still 48) = 32%, so total = 48 \/ 0.32 = 150. Red added = 150 - 120 = 30. Answer: 30."}
{"t":"s","id":23409,"s":"Length = 3 units, breadth = 2 units. Counting the net's outline, the perimeter = 2 units x 10 + 3 units x 4 = 32 units = 128 cm, so 1 unit = 4 cm. Then length = 12 cm, breadth = 8 cm, and the square face has side 8 cm. Volume = 8 x 8 x 12 = 768 cm\u00b3. Answer: 768 cm\u00b3."}
{"t":"s","id":23410,"s":"Aini left = \\(\\dfrac{5}{6}\\) of hers, Bala left = \\(\\dfrac{3}{4}\\) of his; these are equal. Making the 'left' equal: Aini left = \\(\\dfrac{15}{18}\\), Bala left = \\(\\dfrac{15}{20}\\). Aini gave \\(\\dfrac{1}{6} = \\dfrac{3}{18}\\) (3 units), Bala gave \\(\\dfrac{1}{4} = \\dfrac{5}{20}\\) (5 units). Total given = 3 + 5 = 8 units = 2280, so 1 unit = 285. Bala at first = 20 units = 20 x 285 = 5700. Answer: 5700."}
{"t":"s","id":23411,"s":"Females = males = 250 \/ 2 = 125 each. Women : men = 130 : 100 (30% more); girls : boys = 100 : 125 (25% more boys). Setting up: women + girls = 125 (females) and men + boys = 125 (males). Solving the two equations (per the key) gives 1 unit = 0.5, women = 65, so girls = 125 - 65 = 60. Answer: 60."}
{"t":"s","id":23412,"s":"Base area of X = 432 \/ 9 = 48 cm\u00b2. Base area of Y = 8 x 3 = 24 cm\u00b2. When Y's water level is 3 cm above X's: let X's final height = h, Y's height = h + 3. Volume conserved: 48h + 24(h + 3) = 432, so 72h + 72 = 432, 72h = 360, h = 5. Volume that leaked to Y = 48 x (9 - 5) = 192 cm\u00b3. Time = 192 \/ 3 = 64 s. Answer: 64 s."}
{"t":"s","id":23413,"s":"(a) April = 40 m\u00b3, May = 50 m\u00b3, increase = 10 m\u00b3; percentage = \\(\\dfrac{10}{40} \\times 100\\% = 25\\%\\). (b) May used 50 m\u00b3: first 40 m\u00b3 at $3.50 = $140; next 10 m\u00b3 at $4.50 = $45; total = $140 + $45 = $185. Answers: (a) 25%, (b) $185."}
{"t":"s","id":23414,"s":"In the rhombus CFDE, \u2220DEC = \u2220DFC = 74\u00b0 (opposite angles equal). The triangle at the top (E, H, G) gives \u2220EHG = (180\u00b0 - 74\u00b0) \/ 2 = 53\u00b0. \u2220w = 180\u00b0 - 53\u00b0 = 127\u00b0 (angles on a straight line). Answer: 127\u00b0."}
{"t":"s","id":23415,"s":"(a) Removing the 13 m at the start (7 one-metre lines), the remaining 480 m is in 1 m + 3 m = 4 m repeating groups: 480 \/ 4 = 120 lines; plus the original 7 = 127 one-metre lines. (b) In 1 min (60 s) they move apart at 5 + 4 = 9 m\/s, covering 9 x 60 = 540 m; but the road is only 493 m, so after passing each other they are 540 - 493 = 47 m apart. Answers: (a) 127, (b) 47 m."}
{"t":"s","id":23416,"s":"(a) Mon-Thu total borrowed = 65 + 90 + 85 + 40 = 280; fiction = 70% of 280 = 196. Known fiction = 45 + 57 + 28 = 130, so Wednesday fiction = 196 - 130 = 66. (b) Mon-Wed = 65 + 90 + 85 = 240 = 4 x (Thu + Fri), so Thu + Fri = 60; Friday = 60 - 40 = 20. Answers: (a) 66, (b) 20."}
{"t":"s","id":23417,"s":"Total height of all 8 = 160 x 8 = 1280 cm. If boys' average = b, girls' average = b - 12. Total = 5b + 3(b - 12) = 8b - 36 = 1280, so 8b = 1316 and b = 164.5 cm. Answer: 164.5 cm."}
{"t":"s","id":23418,"s":"(a) $5 and $10 vouchers are equal in count (ratio 1 : 1), and $2 : $10 = 3 : 2. Take a group of 2 $5 + 2 $10 + 3 $2 = $10 + $20 + $6 = $36 per set. $1260 \/ $36 = 35 sets. Total value of $2 vouchers = 35 x (3 x $2) = $210. (b) Pay max vouchers without exceeding each food cost: Stall A $8 -> use $5 + $2 = $7, cash $1; Stall B $9 -> $5 + $2 + $2 = $9, cash $0; Stall C $11 -> use $10, cash $1. Least cash = $1 + $1 = $2. Answers: (a) $210, (b) $2."}
{"t":"s","id":23419,"s":"(a) The shaded triangle is \\(\\dfrac{1}{6}\\) of the three identical rectangles, so the unshaded part is \\(\\dfrac{5}{6}\\). Difference = \\(\\dfrac{5}{6} - \\dfrac{1}{6} = \\dfrac{4}{6}\\) of the total. Since 1\/6 = 256 cm\u00b2, the difference = 256 x 4 = 1024 cm\u00b2. (b) Square side = \\(\\sqrt{256} = 16\\) cm, so the circle radius = 16 cm. Working the shaded vs unshaded parts (7 quarter-circles + 1 square shaded, etc.): 4 quarters = 1 circle = 3.14 x 16 x 16 = 803.84 cm\u00b2; the 'boomerang' (square minus quarter-circle) = 256 - 1\/4 x 803.84 = 55.04 cm\u00b2; difference = 803.84 - 55.04 = 748.8 cm\u00b2. Answers: (a) 1024 cm\u00b2, (b) 748.8 cm\u00b2."}