{
"paper": {
"school": "Methodist Girls' School (Primary)",
"year": 2023,
"level": "P6",
"label": "Prelim",
"source_prefix": "MGS 2023 P6 Prelim",
"has_answer_key": true
},
"questions": [
{
"n": 1,
"type_id": 1,
"question": "What is the value of the digit 5 in 45 678?",
"answer0": "50",
"answer1": "500",
"answer2": "5000",
"answer3": "50 000",
"correct_answer": 2,
"skill_id": 105,
"difficulty_id": 1,
"explanation": "In 45 678 the digit 5 is in the thousands place, so its value is 5000.",
"hints": ["Identify which place the digit 5 sits in.", "45 678: the 5 is in the thousands column."],
"source": "MGS 2023 P6 Prelim P1 Q1",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 3 (5000)."
},
{
"n": 2,
"type_id": 1,
"question": "Round 4.567 to 2 decimal places.",
"answer0": "4.50",
"answer1": "4.56",
"answer2": "4.57",
"answer3": "4.60",
"correct_answer": 2,
"skill_id": 128,
"difficulty_id": 1,
"explanation": "To round 4.567 to 2 decimal places, look at the 3rd decimal (7). Since 7 ≥ 5, round up the hundredths: 4.567 ≈ 4.57.",
"hints": ["Look at the digit in the third decimal place.", "7 rounds the hundredths digit up."],
"source": "MGS 2023 P6 Prelim P1 Q2",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 3 (4.57)."
},
{
"n": 3,
"type_id": 1,
"question": "In the number line, what is the number represented by A?",
"answer0": "6.5",
"answer1": "6.75",
"answer2": "7.2",
"answer3": "7.25",
"correct_answer": 3,
"skill_id": 124,
"difficulty_id": 2,
"explanation": "The interval from 6 to 8 is divided into 8 equal parts, so each part is \\(\\dfrac{2}{8}=0.25\\). A is at the 5th mark from 6: \\(6+5\\times0.25=7.25\\).",
"hints": ["Count how many equal divisions lie between 6 and 8.", "Each small division is 0.25."],
"source": "MGS 2023 P6 Prelim P1 Q3",
"image_needed": true,
"image_options": false,
"image_file": "q3.png",
"image_page": 3,
"image_bbox": [0.24, 0.62, 0.58, 0.73],
"image_loc": "number line from 6 to 8 with arrow A, middle of page",
"notes": "Key: option 4 (7.25)."
},
{
"n": 4,
"type_id": 1,
"question": "GH, KL and MN are straight lines. Find \\(\\angle p\\).",
"answer0": "27°",
"answer1": "36°",
"answer2": "54°",
"answer3": "73°",
"correct_answer": 1,
"skill_id": 194,
"difficulty_id": 2,
"explanation": "There is a right angle (90°) marked at the point. The angles 54°, 90° and ∠p lie on straight line GH, so ∠p = 180° − 90° − 54° = 36°.",
"hints": ["A right-angle (90°) is marked at the intersection.", "Angles on a straight line add up to 180°."],
"source": "MGS 2023 P6 Prelim P1 Q4",
"image_needed": true,
"image_options": false,
"image_file": "q4.png",
"image_page": 4,
"image_bbox": [0.42, 0.08, 0.86, 0.30],
"image_loc": "intersecting straight lines GH, KL, MN with 54° and p marked, top right",
"notes": "Key: option 2 (36°)."
},
{
"n": 5,
"type_id": 1,
"question": "Five landmarks A, B, C, D and E on a map are shown in the square grid. Neha is at landmark B. She faces east and turns 135° anti-clockwise. Which landmark is Neha facing now?",
"answer0": "A",
"answer1": "C",
"answer2": "D",
"answer3": "E",
"correct_answer": 0,
"skill_id": 142,
"difficulty_id": 2,
"explanation": "Facing east and turning 135° anti-clockwise points her towards the north-west (45° above due west). From B that direction passes through landmark A.",
"hints": ["East turned 135° anti-clockwise is north-west.", "Trace the north-west direction from B on the grid."],
"source": "MGS 2023 P6 Prelim P1 Q5",
"image_needed": true,
"image_options": false,
"image_file": "q5.png",
"image_page": 4,
"image_bbox": [0.33, 0.46, 0.78, 0.70],
"image_loc": "square grid with landmarks A,B,C,D,E and a North arrow, middle of page",
"notes": "Key: option 1 (A)."
},
{
"n": 6,
"type_id": 1,
"question": "ABCD is a trapezium. AF and EC are straight lines. Peishan wrote four statements to describe the figure.
Statement A: \\(\\angle AED = \\angle ABC\\)
Statement B: \\(\\angle EDA = \\angle FDC\\)
Statement C: \\(\\angle ABC + \\angle ECB = 180°\\)
Statement D: \\(\\angle DAB + \\angle ABC = 180°\\)
Which of the following statements are true?",
"answer0": "A and C only",
"answer1": "A and D only",
"answer2": "B and C only",
"answer3": "B and D only",
"correct_answer": 2,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "With AB parallel to EC: ∠EDA = ∠FDC are vertically opposite angles (B true). ∠ABC and ∠ECB are interior angles on the same side of the parallel lines AB and EC, so they sum to 180° (C true). Hence B and C only.",
"hints": ["Vertically opposite angles are equal.", "Co-interior (same-side) angles between parallel lines sum to 180°."],
"source": "MGS 2023 P6 Prelim P1 Q6",
"image_needed": true,
"image_options": false,
"image_file": "q6.png",
"image_page": 5,
"image_bbox": [0.52, 0.13, 0.90, 0.30],
"image_loc": "trapezium ABCD with lines AF and EC, top right of question",
"notes": "Key: option 3 (B and C only)."
},
{
"n": 7,
"type_id": 1,
"question": "Arrange the following fractions from the smallest to the largest.
\\(\\dfrac{3}{2}\\), \\(1\\dfrac{5}{9}\\), \\(\\dfrac{6}{5}\\)",
"answer0": "\\(\\dfrac{6}{5}\\), \\(\\dfrac{3}{2}\\), \\(1\\dfrac{5}{9}\\)",
"answer1": "\\(1\\dfrac{5}{9}\\), \\(\\dfrac{3}{2}\\), \\(\\dfrac{6}{5}\\)",
"answer2": "\\(\\dfrac{3}{2}\\), \\(\\dfrac{6}{5}\\), \\(1\\dfrac{5}{9}\\)",
"answer3": "\\(\\dfrac{6}{5}\\), \\(1\\dfrac{5}{9}\\), \\(\\dfrac{3}{2}\\)",
"correct_answer": 0,
"skill_id": 158,
"difficulty_id": 2,
"explanation": "As decimals: \\(\\dfrac{6}{5}=1.2\\), \\(\\dfrac{3}{2}=1.5\\), \\(1\\dfrac{5}{9}\\approx1.56\\). Smallest to largest: \\(\\dfrac{6}{5}\\), \\(\\dfrac{3}{2}\\), \\(1\\dfrac{5}{9}\\).",
"hints": ["Convert each fraction to a decimal.", "1.2 < 1.5 < 1.56."],
"source": "MGS 2023 P6 Prelim P1 Q7",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 1. Fraction answers -> MCQ."
},
{
"n": 8,
"type_id": 1,
"question": "The figure shows an isosceles triangle XYZ, where XY = YZ. WY = 12 cm, YZ = 15 cm and XZ = 18 cm. Find the area of triangle WXY.",
"answer0": "216 cm²",
"answer1": "108 cm²",
"answer2": "90 cm²",
"answer3": "54 cm²",
"correct_answer": 3,
"skill_id": 186,
"difficulty_id": 2,
"explanation": "Since XYZ is isosceles with XY = YZ, the height YW bisects XZ, so XW = 18 ÷ 2 = 9 cm. Area of triangle WXY = \\(\\dfrac{1}{2}\\times9\\times12=54\\) cm².",
"hints": ["The height YW splits the base XZ into two equal halves.", "Area = \\(\\dfrac{1}{2}\\times\\text{base}\\times\\text{height}\\)."],
"source": "MGS 2023 P6 Prelim P1 Q8",
"image_needed": true,
"image_options": false,
"image_file": "q8.png",
"image_page": 6,
"image_bbox": [0.30, 0.15, 0.72, 0.36],
"image_loc": "isosceles triangle XYZ with shaded WXY, 12cm, 15cm, 18cm marked, top of page",
"notes": "Key: option 4 (54 cm²)."
},
{
"n": 9,
"type_id": 1,
"question": "There are 36 pens in a box. \\(\\dfrac{1}{3}\\) of them are red, 50% are blue and the rest are green. Express the number of green pens as a fraction of the number of blue pens.",
"answer0": "\\(\\dfrac{1}{2}\\)",
"answer1": "\\(\\dfrac{1}{3}\\)",
"answer2": "\\(\\dfrac{1}{4}\\)",
"answer3": "\\(\\dfrac{1}{6}\\)",
"correct_answer": 1,
"skill_id": 209,
"difficulty_id": 2,
"explanation": "Red = \\(\\dfrac{1}{3}\\times36=12\\). Blue = 50% of 36 = 18. Green = 36 − 12 − 18 = 6. Green as a fraction of blue = \\(\\dfrac{6}{18}=\\dfrac{1}{3}\\).",
"hints": ["Find the number of red, blue and green pens separately.", "Green ÷ Blue, then simplify."],
"source": "MGS 2023 P6 Prelim P1 Q9",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 2 (1/3). Fraction answers -> MCQ."
},
{
"n": 10,
"type_id": 1,
"question": "The pie chart shows the number of boys, girls, men and women who were in a cinema. There were 180 girls in the cinema. How many boys were there?",
"answer0": "25",
"answer1": "60",
"answer2": "300",
"answer3": "360",
"correct_answer": 2,
"skill_id": 236,
"difficulty_id": 2,
"explanation": "Girls are 15%, representing 180 people, so 1% = 180 ÷ 15 = 12 people. The Boys sector is a right angle (90°) = 25% of the chart, so Boys = 25 × 12 = 300.",
"hints": ["Girls 15% = 180, so find what 1% represents.", "The Boys sector is marked as a right angle (25%)."],
"source": "MGS 2023 P6 Prelim P1 Q10",
"image_needed": true,
"image_options": false,
"image_file": "q10.png",
"image_page": 7,
"image_bbox": [0.36, 0.13, 0.66, 0.31],
"image_loc": "pie chart with sectors Boys, Men, Girls 15%, Women, top of page",
"notes": "Key: option 3 (300)."
},
{
"n": 11,
"type_id": 1,
"question": "Sandy is given a total of $30 to spend from Monday to Friday. Every day, she spends $4 on food, $q on transport and saves the rest. How much does she save each week?",
"answer0": "$ (130 − 5q)",
"answer1": "$ (30 − 4q)",
"answer2": "$ (26 − q)",
"answer3": "$ (10 − 5q)",
"correct_answer": 3,
"skill_id": 241,
"difficulty_id": 2,
"explanation": "Each day she spends $(4 + q), over 5 days that is $(20 + 5q). Savings = 30 − (20 + 5q) = $(10 − 5q).",
"hints": ["Total spent in 5 days = 5 × (4 + q).", "Savings = 30 − total spent."],
"source": "MGS 2023 P6 Prelim P1 Q11",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 4 ($(10−5q)). Algebraic answer -> MCQ."
},
{
"n": 12,
"type_id": 1,
"question": "Lisa paid $18.90 for 3 identical files and 3 identical pencils. Howard paid $10.50 for 2 such files and 1 such pencil. How much did each file cost?",
"answer0": "$3.15",
"answer1": "$3.50",
"answer2": "$4.20",
"answer3": "$7.00",
"correct_answer": 2,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Lisa: 3 files + 3 pencils = $18.90, so 1 file + 1 pencil = $6.30. Howard: 2 files + 1 pencil = $10.50. Subtracting: 1 file = $10.50 − $6.30 = $4.20.",
"hints": ["Divide Lisa's total by 3 to get 1 file + 1 pencil.", "Subtract that from Howard's amount."],
"source": "MGS 2023 P6 Prelim P1 Q12",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 3 ($4.20)."
},
{
"n": 13,
"type_id": 1,
"question": "The ratio of Tianwei's height to Bala's height is 6 : 5. Bala is \\(\\dfrac{10}{11}\\) as tall as Chelsea. What is the ratio of Tianwei's height to Chelsea's height?",
"answer0": "5 : 11",
"answer1": "6 : 11",
"answer2": "10 : 11",
"answer3": "12 : 11",
"correct_answer": 3,
"skill_id": 178,
"difficulty_id": 3,
"explanation": "Bala : Chelsea = 10 : 11. Tianwei : Bala = 6 : 5 = 12 : 10. Making Bala common (10): Tianwei : Bala : Chelsea = 12 : 10 : 11, so Tianwei : Chelsea = 12 : 11.",
"hints": ["Write Bala : Chelsea as 10 : 11.", "Scale Tianwei : Bala so Bala's share matches 10."],
"source": "MGS 2023 P6 Prelim P1 Q13",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 4 (12 : 11). Ratio answer -> MCQ."
},
{
"n": 14,
"type_id": 1,
"question": "A rectangular piece of paper was folded as shown. Given that \\(\\angle GHF\\) is 48°, find \\(\\angle FKH\\).",
"answer0": "21°",
"answer1": "42°",
"answer2": "48°",
"answer3": "69°",
"correct_answer": 0,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "When folded, the part below the fold mirrors the part above. ∠GHF = 48°; the fold creates equal angles so ∠FKH = (90° − 48°) ÷ 2 = 21°.",
"hints": ["A fold produces equal (mirror) angles.", "Use the right angle of the rectangle's corner."],
"source": "MGS 2023 P6 Prelim P1 Q14",
"image_needed": true,
"image_options": false,
"image_file": "q14.png",
"image_page": 8,
"image_bbox": [0.22, 0.34, 0.70, 0.52],
"image_loc": "folded rectangular paper with points F,G,H,J,K and 48° marked, middle of page",
"notes": "Key: option 1 (21°)."
},
{
"n": 15,
"type_id": 1,
"question": "Dalia has 30 more stickers than Huda at first. Dalia gave 40% of her stickers to Huda. Then, Huda gave 50% of her stickers to Dalia. In the end, Dalia has 48 more stickers than Huda. How many stickers did Dalia have at first?",
"answer0": "24",
"answer1": "48",
"answer2": "50",
"answer3": "80",
"correct_answer": 3,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "Let Dalia = D at first, Huda = D − 30. Dalia gives 40%: Dalia keeps 0.6D, Huda has D−30+0.4D=1.4D−30. Huda gives 50% to Dalia: Dalia = 0.6D+0.5(1.4D−30)=1.3D−15, Huda = 0.7D−15. Difference = (1.3D−15)−(0.7D−15)=0.6D=48, so D=80.",
"hints": ["Let Dalia's start = D, Huda = D − 30.", "Track each person's amount after both transfers; difference = 48."],
"source": "MGS 2023 P6 Prelim P1 Q15",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: option 4 (80)."
},
{
"n": 16,
"type_id": 2,
"question": "Express \\(6\\dfrac{7}{100}\\) as a decimal. [?]",
"answer0": "6.07",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 158,
"difficulty_id": 1,
"explanation": "\\(\\dfrac{7}{100}=0.07\\), so \\(6\\dfrac{7}{100}=6.07\\).",
"hints": ["7 hundredths = 0.07.", "Add it to the whole number 6."],
"source": "MGS 2023 P6 Prelim P1 Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 6.07."
},
{
"n": 17,
"type_id": 2,
"question": "Write down all the common multiples of 3 and 5 that are smaller than 40. [?] [?]",
"answer0": "15",
"answer1": "30",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 115,
"difficulty_id": 1,
"explanation": "Common multiples of 3 and 5 are multiples of 15: 15, 30, 45, ... Those smaller than 40 are 15 and 30.",
"hints": ["Common multiples of 3 and 5 are multiples of 15.", "List the multiples of 15 below 40."],
"source": "MGS 2023 P6 Prelim P1 Q17",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 15, 30 (two integer answers)."
},
{
"n": 18,
"type_id": 1,
"question": "Find the value of \\(\\dfrac{2}{5}\\div 12\\).",
"answer0": "\\(\\dfrac{1}{30}\\)",
"answer1": "\\(\\dfrac{1}{24}\\)",
"answer2": "\\(\\dfrac{2}{60}\\)",
"answer3": "\\(\\dfrac{5}{24}\\)",
"correct_answer": 0,
"skill_id": 164,
"difficulty_id": 1,
"explanation": "\\(\\dfrac{2}{5}\\div12=\\dfrac{2}{5}\\times\\dfrac{1}{12}=\\dfrac{2}{60}=\\dfrac{1}{30}\\).",
"hints": ["Dividing by 12 = multiplying by \\(\\dfrac{1}{12}\\).", "Simplify the result."],
"source": "MGS 2023 P6 Prelim P1 Q18",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 1/30 (equivalent fractions accepted). Fraction answer -> converted from FIB to MCQ."
},
{
"n": 19,
"type_id": 0,
"question": "Simplify 11 + 5y − 2y + 4y.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 239,
"difficulty_id": 1,
"explanation": "Combine like terms: 5y − 2y + 4y = 7y, so the expression simplifies to 11 + 7y.",
"hints": ["Group the y terms together.", "5y − 2y + 4y = 7y."],
"source": "MGS 2023 P6 Prelim P1 Q19",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 11 + 7y. Algebraic-expression answer cannot be a numeric FIB nor a clean MCQ; set type_id 0 (skipped on insert). Answer = 11 + 7y."
},
{
"n": 20,
"type_id": 2,
"question": "PQRS is a parallelogram. Find \\(\\angle z\\). [?]",
"answer0": "108",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 200,
"difficulty_id": 2,
"explanation": "The reflex angle at S is 288°, so ∠PSR = 360° − 288° = 72°. In a parallelogram, co-interior angles are supplementary, so ∠z = ∠SRQ = 180° − 72° = 108°.",
"hints": ["Find the inner angle at S: 360° − 288°.", "Adjacent angles of a parallelogram sum to 180°."],
"source": "MGS 2023 P6 Prelim P1 Q20",
"image_needed": true,
"image_options": false,
"image_file": "q20.png",
"image_page": 13,
"image_bbox": [0.30, 0.13, 0.70, 0.27],
"image_loc": "parallelogram PQRS with 288° at S and z at R, top of page",
"notes": "Key: 108 (degrees). Unit is degrees."
},
{
"n": 21,
"type_id": 2,
"question": "The figure, not drawn to scale, shows the net of a cuboid. The cuboid has a square base. Find the volume of the cuboid. [?]",
"answer0": "686",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 190,
"difficulty_id": 3,
"explanation": "From the net, the square base side = 21 ÷ 3 = 7 cm. The length = (35 − 7) ÷ 2 = 14 cm. Volume = 14 × 7 × 7 = 686 cm³.",
"hints": ["The height 21 cm spans 3 base edges, so one side = 21 ÷ 3.", "Volume = length × base × base."],
"source": "MGS 2023 P6 Prelim P1 Q21",
"image_needed": true,
"image_options": false,
"image_file": "q21.png",
"image_page": 13,
"image_bbox": [0.25, 0.59, 0.62, 0.76],
"image_loc": "net of a cuboid with 35 cm and 21 cm marked, middle of page",
"notes": "Key: 686 cm³. Answer in cm³."
},
{
"n": 22,
"type_id": 2,
"question": "Mrs Pandi wants to send letters overseas by airmail. The airmail rates to two countries are shown in the table. Mrs Pandi wants to send a letter weighing 33 g to Thailand and a letter weighing 42 g to Australia. How much will she need to pay in total? $[?]",
"answer0": "3.20",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 2,
"explanation": "Thailand 33 g: first 25 g = $0.90, extra 8 g needs 1 unit of 10 g = $0.20, total $1.10. Australia 42 g: first 25 g = $1.50, extra 17 g needs 2 units = $0.30 × 2 = $0.60, total $2.10. Overall = $1.10 + $2.10 = $3.20.",
"hints": ["Charge the first 25 g, then round each additional 10 g up.", "Add the two countries' postage."],
"source": "MGS 2023 P6 Prelim P1 Q22",
"image_needed": true,
"image_options": false,
"image_file": "q22.png",
"image_page": 14,
"image_bbox": [0.20, 0.15, 0.73, 0.28],
"image_loc": "Airmail Rates table (Thailand/Australia) near top of question",
"notes": "Key: $3.20. Dollar amount."
},
{
"n": 23,
"type_id": 2,
"question": "ABCD is a square. EFG is an isosceles triangle where EF = EG. DGBE and GCF are straight lines, BC is parallel to EF. Find \\(\\angle EGF\\). [?]",
"answer0": "67.5",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "DGBE is a diagonal of the square, so ∠DBC = 45°; ∠DBC = ∠FEG = 45° (BC parallel to EF). Since EF = EG, the base angles are equal: ∠EGF = (180° − 45°) ÷ 2 = 67.5°.",
"hints": ["A square's diagonal makes a 45° angle with its side.", "Base angles of an isosceles triangle are equal."],
"source": "MGS 2023 P6 Prelim P1 Q23",
"image_needed": true,
"image_options": false,
"image_file": "q23.png",
"image_page": 14,
"image_bbox": [0.55, 0.55, 0.80, 0.76],
"image_loc": "square ABCD with isosceles triangle EFG attached, lower-right of question",
"notes": "Key: 67.5 (degrees). Decimal answer, FIB ok."
},
{
"n": 24,
"type_id": 1,
"question": "The figure is formed by 3 identical quarter circles and a triangle. The radius of each quarter circle is 8 cm. Find the area of the figure. (Leave your answer in terms of \\(\\pi\\))",
"answer0": "\\((48\\pi + 32)\\) cm²",
"answer1": "\\((48\\pi + 64)\\) cm²",
"answer2": "\\((24\\pi + 32)\\) cm²",
"answer3": "\\((16\\pi + 32)\\) cm²",
"correct_answer": 0,
"skill_id": 221,
"difficulty_id": 3,
"explanation": "Area of 3 quarter circles = \\(\\dfrac{3}{4}\\times\\pi\\times8\\times8=48\\pi\\) cm². Area of the triangle = \\(\\dfrac{1}{2}\\times8\\times8=32\\) cm². Total = \\((48\\pi+32)\\) cm².",
"hints": ["Three quarter circles = \\(\\dfrac{3}{4}\\) of a full circle.", "Add the triangle's area."],
"source": "MGS 2023 P6 Prelim P1 Q24",
"image_needed": true,
"image_options": false,
"image_file": "q24.png",
"image_page": 15,
"image_bbox": [0.24, 0.13, 0.45, 0.27],
"image_loc": "figure of 3 quarter circles and a triangle, upper-left of question",
"notes": "Key: (48π + 32) cm². Answer in terms of pi -> MCQ (not a plain decimal)."
},
{
"n": 25,
"type_id": 0,
"question": "Figure ABCD is drawn on a square grid. By joining the dots on the grid with straight lines, (a) draw and label triangle PQR, such that it has the same area as ABCD and without overlapping. (b) draw and label a parallelogram ADEF such that DE is shorter than AD.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 201,
"difficulty_id": 2,
"explanation": "On the grid, draw a triangle PQR (base PQ given) with area equal to kite ABCD, and a parallelogram ADEF where side DE is shorter than AD. These are construction (draw-on-grid) tasks; see the answer key diagram on the solutions page.",
"hints": ["Match the area of ABCD when drawing triangle PQR.", "For the parallelogram, keep DE shorter than AD."],
"source": "MGS 2023 P6 Prelim P1 Q25",
"image_needed": true,
"image_options": false,
"image_file": "q25.png",
"image_page": 15,
"image_bbox": [0.20, 0.46, 0.78, 0.62],
"image_loc": "dot grid with figure ABCD and points P, Q, middle of page",
"notes": "Draw-on-grid construction task; no value answer. type_id 0 (skipped on insert). Key: refer to diagram."
},
{
"n": 26,
"type_id": 2,
"question": "The figure shows a cuboid with a square base of area 64 cm². The area of the shaded face is 72 cm². Find the height of the cuboid. [?]",
"answer0": "9",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 226,
"difficulty_id": 2,
"explanation": "Square base area 64 cm² means base side = \\(\\sqrt{64}=8\\) cm. The shaded (side) face = base side × height = 72, so height = 72 ÷ 8 = 9 cm.",
"hints": ["Base is square: side = \\(\\sqrt{64}\\).", "Shaded face area = side × height."],
"source": "MGS 2023 P6 Prelim P1 Q26",
"image_needed": true,
"image_options": false,
"image_file": "q26.png",
"image_page": 16,
"image_bbox": [0.22, 0.18, 0.42, 0.34],
"image_loc": "cuboid with square base 64 cm² and shaded face, upper-left of question",
"notes": "Key: 9 cm. Answer in cm."
},
{
"n": 27,
"type_id": 2,
"question": "Lishi pressed a calculator to multiply a 3-digit number by a 1-digit number. For the 1-digit number, she made a mistake by pressing a wrong number. She obtained an incorrect product of 624 which is \\(\\dfrac{3}{4}\\) of the correct product. What is the smallest possible value of the 3-digit number? [?]",
"answer0": "104",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Correct product = 624 ÷ \\(\\dfrac{3}{4}\\) = 832. The 3-digit number must divide both 624 and 832; the largest 1-digit factors give the smallest 3-digit number. 624 ÷ 6 = 104 and 832 ÷ 8 = 104, so the smallest 3-digit number is 104.",
"hints": ["Find the correct product: 624 ÷ (3/4).", "The 3-digit number divides both 624 and 832; use the largest 1-digit multipliers."],
"source": "MGS 2023 P6 Prelim P1 Q27",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 104."
},
{
"n": 28,
"type_id": 0,
"question": "There are 5 shaded squares in the figure. Shade 3 more squares to form a symmetric figure with ST as the line of symmetry.",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 145,
"difficulty_id": 2,
"explanation": "Reflect the existing shaded squares across the diagonal line ST. Shade the 3 squares that are the mirror images of the unmatched shaded squares so the figure becomes symmetric about ST. See the answer key diagram.",
"hints": ["Reflect each shaded square across line ST.", "Shade the mirror positions that are not yet shaded."],
"source": "MGS 2023 P6 Prelim P1 Q28",
"image_needed": true,
"image_options": false,
"image_file": "q28.png",
"image_page": 17,
"image_bbox": [0.35, 0.14, 0.64, 0.36],
"image_loc": "5x5 grid with 5 shaded squares and diagonal line ST, top of question",
"notes": "Shade-the-grid symmetry task; no value answer. type_id 0 (skipped on insert). Key: refer to diagram (3rd square can be any of 4 labelled positions)."
},
{
"n": 29,
"type_id": 1,
"question": "ABDG is a square. Given that BC = DE = EF = FG = AH, what fraction of the figure is shaded?",
"answer0": "\\(\\dfrac{7}{18}\\)",
"answer1": "\\(\\dfrac{1}{2}\\)",
"answer2": "\\(\\dfrac{5}{18}\\)",
"answer3": "\\(\\dfrac{2}{9}\\)",
"correct_answer": 0,
"skill_id": 165,
"difficulty_id": 3,
"explanation": "Top shaded triangle (apex at midpoint of HC) = \\(\\dfrac{1}{2}\\times\\dfrac{1}{3}=\\dfrac{1}{6}\\) of the square. The two lower shaded triangles together = \\(\\dfrac{1}{3}\\times\\dfrac{2}{3}=\\dfrac{2}{9}\\). Total shaded = \\(\\dfrac{1}{6}+\\dfrac{2}{9}=\\dfrac{3}{18}+\\dfrac{4}{18}=\\dfrac{7}{18}\\).",
"hints": ["Split the figure into the upper triangle and the lower shaded region.", "Add \\(\\dfrac{1}{6}+\\dfrac{2}{9}\\)."],
"source": "MGS 2023 P6 Prelim P1 Q29",
"image_needed": true,
"image_options": false,
"image_file": "q29.png",
"image_page": 17,
"image_bbox": [0.20, 0.50, 0.47, 0.73],
"image_loc": "square ABDG with shaded triangular regions, lower-left of question",
"notes": "Key: 7/18. Fraction answer -> MCQ."
},
{
"n": 30,
"type_id": 2,
"question": "A player has to score an average of 18 points and above over 5 rounds of a game to qualify for the next level. The scores for rounds One to Four are 20, 15, 25 and 15. What is the lowest score Mathew can get in the fifth round in order to qualify for the next level? [?]",
"answer0": "15",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 204,
"difficulty_id": 2,
"explanation": "Total of first 4 rounds = 20 + 15 + 25 + 15 = 75. To average 18 over 5 rounds, total needed = 18 × 5 = 90. Lowest fifth-round score = 90 − 75 = 15.",
"hints": ["Required total = average × number of rounds.", "Subtract the four known scores."],
"source": "MGS 2023 P6 Prelim P1 Q30",
"image_needed": true,
"image_options": false,
"image_file": "q30.png",
"image_page": 18,
"image_bbox": [0.32, 0.18, 0.71, 0.30],
"image_loc": "Round/Score table (One to Five) near top of question",
"notes": "Key: 15. Table values transcribed into stem. Answer is an integer."
},
{
"n": 31,
"type_id": 0,
"question": "Measure and write down (a) the length of BC (b) the size of \\(\\angle ACB\\).",
"answer0": null,
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 140,
"difficulty_id": 1,
"explanation": "Using a ruler, BC measures about 4.1 cm (accepted 4 cm – 4.2 cm). Using a protractor, ∠ACB is about 94° (accepted 92° – 95°).",
"hints": ["Use a ruler for the length and a protractor for the angle.", "BC ≈ 4.1 cm; ∠ACB ≈ 94°."],
"source": "MGS 2023 P6 Prelim P2 Q1",
"image_needed": true,
"image_options": false,
"image_file": "q31.png",
"image_page": 20,
"image_bbox": [0.18, 0.20, 0.70, 0.42],
"image_loc": "triangle ABC drawn to scale, top of question",
"notes": "Measure-from-the-figure task: answer depends on the printed scale drawing, not derivable from text. type_id 0 (skipped on insert). Key: (a) 4.1 cm (4–4.2), (b) 94° (92–95)."
},
{
"n": 32,
"type_id": 2,
"question": "The figure is made up of 2 identical 4-sided figures. Find the sum of \\(\\angle a + \\angle b + \\angle c\\). [?]",
"answer0": "298",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 2,
"explanation": "Each 4-sided figure has angles summing to 360°. The angles a, b, c are the angles of one quadrilateral other than the 62° angle, so ∠a + ∠b + ∠c = 360° − 62° = 298°.",
"hints": ["Angles in a 4-sided figure sum to 360°.", "Subtract the known 62° angle."],
"source": "MGS 2023 P6 Prelim P2 Q2",
"image_needed": true,
"image_options": false,
"image_file": "q32.png",
"image_page": 20,
"image_bbox": [0.16, 0.55, 0.52, 0.80],
"image_loc": "two identical 4-sided figures with a, b, c and 62° marked, lower part of page",
"notes": "Key: 298 (degrees)."
},
{
"n": 33,
"type_id": 2,
"question": "Kenny took 3 hours to paint 3 bedrooms. He took the same amount of time to paint the first 2 bedrooms. He took 15 minutes longer to paint the third bedroom than the first. How many minutes did he take to paint the third bedroom? [?]",
"answer0": "70",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "3 hours = 180 min. First 2 bedrooms take equal time, and the third = first + 15 min. So 180 − 15 = 165 min split equally over 3 equal portions → 165 ÷ 3 = 55 min (the first/each base portion). Third bedroom = 55 + 15 = 70 min.",
"hints": ["Convert 3 hours to minutes.", "Remove the extra 15 min, divide by 3, then add 15 back."],
"source": "MGS 2023 P6 Prelim P2 Q3",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 70 min. Answer in minutes."
},
{
"n": 34,
"type_id": 2,
"question": "In the figure, PQRT and PRSU are rectangles. PQ = 8 cm, QR = 6 cm and PR = 10 cm. Find the length of RS. [?]",
"answer0": "4.8",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Area of rectangle PQRT = \\(\\dfrac{1}{2}\\times8\\times6\\times2\\); using triangle PQR area = \\(\\dfrac{1}{2}\\times8\\times6=24\\) cm². Triangle PRS shares this area: \\(\\dfrac{1}{2}\\times10\\times RS=24\\), so RS = 48 ÷ 10 = 4.8 cm.",
"hints": ["Find the area of triangle PQR using legs 8 and 6.", "Use PR = 10 as the base to find RS."],
"source": "MGS 2023 P6 Prelim P2 Q4",
"image_needed": true,
"image_options": false,
"image_file": "q34.png",
"image_page": 21,
"image_bbox": [0.16, 0.50, 0.48, 0.72],
"image_loc": "rectangles PQRT and PRSU with 8cm, 6cm, 10cm marked, middle-left of question",
"notes": "Key: 4.8 cm. Decimal answer."
},
{
"n": 35,
"type_id": 1,
"question": "The cube in Figure 1 is formed by folding the net shown in Figure 2. The face marked X in Figure 1 is the front face. Which of the faces is represented by X in Figure 1?",
"answer0": "Checkered pattern",
"answer1": "Circle (target) pattern",
"answer2": "Four-pointed star",
"answer3": "Diagonal-hatch pattern",
"correct_answer": 2,
"skill_id": 233,
"difficulty_id": 2,
"explanation": "Folding the net so the cube matches Figure 1, the face in the X position corresponds to the four-pointed star face on the net.",
"hints": ["Visualise folding the net into a cube.", "Track which net square lands in the X (front) position."],
"source": "MGS 2023 P6 Prelim P2 Q5",
"image_needed": true,
"image_options": false,
"image_file": "q35.png",
"image_page": 22,
"image_bbox": [0.22, 0.13, 0.70, 0.30],
"image_loc": "Figure 1 cube with face X and Figure 2 net with 4 patterns, top of question",
"notes": "Original is a 'circle your answer' task between 4 picture faces; converted to MCQ with text labels for the four pattern faces. Key (answer-key diagram): the four-pointed star face. The 4 option pictures could optionally be cropped (image_options) but text labels are provided. Verified against key page (Paper 2 Q5 shows the hatched star face shaded)."
},
{
"n": 36,
"type_id": 2,
"question": "Mr Raja paid a total of $1406.40 for a laptop and a camera at a sale. The price of the camera before discount was $864. Sale terms: 1st item 10% discount; 2nd item 20% discount (price of the 2nd item must be equal to or less than the 1st item). What was the price of the laptop before discount? $[?]",
"answer0": "786",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "The camera ($864) is the cheaper 2nd item at 20% off: 90% of $864 is the 1st item only if it is the 1st. Here camera at 10%? Key: 1st item (laptop) at 10% off = 90% × $864? No — work: 90% × $864 = $777.60 is the discounted 1st item portion attributed; $1406.40 − $777.60 = $628.80 is the laptop at 80%. Laptop before discount = $628.80 ÷ 80 × 100 = $786.",
"hints": ["The cheaper item gets 20% off, the dearer 10% off.", "Subtract the camera's discounted price, then reverse the 20% discount on the laptop."],
"source": "MGS 2023 P6 Prelim P2 Q6",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key working: 90% × $864 = $777.60; $1406.40 − $777.60 = $628.80; $628.80 ÷ 80 × 100 = $786. Answer $786."
},
{
"n": 37,
"type_id": 2,
"question": "A tank with a capacity of 1200 ℓ was \\(\\dfrac{1}{10}\\) filled with water at first. Then, Tony turned on the tap to add more water to the tank. The line graph shows the volume of water in the tank over 12 minutes after the tap was turned on.
(a) What was the volume of the water in the tank at first? [?] ℓ
(b) What was the volume of water in the tank after 18 minutes? [?] ℓ",
"answer0": "120",
"answer1": "660",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 191,
"difficulty_id": 3,
"explanation": "(a) \\(\\dfrac{1}{10}\\times1200=120\\) ℓ. (b) From the graph the volume rises from 120 ℓ to 180 ℓ over 2 min, i.e. 30 ℓ/min. In 18 min: 18 × 30 = 540 ℓ added, so total = 540 + 120 = 660 ℓ.",
"hints": ["(a) Find \\(\\dfrac{1}{10}\\) of 1200.", "(b) Read the rate per minute from the graph, then extend to 18 min."],
"source": "MGS 2023 P6 Prelim P2 Q7",
"image_needed": true,
"image_options": false,
"image_file": "q37.png",
"image_page": 24,
"image_bbox": [0.17, 0.20, 0.82, 0.48],
"image_loc": "line graph of volume vs time (0–12 min), upper part of question",
"notes": "Key: (a) 120 ℓ, (b) 660 ℓ. Both integer answers in litres."
},
{
"n": 38,
"type_id": 2,
"question": "Kelly bought a total of 40 pieces of squares and rectangular craft paper. She cut all the squares into 3 rectangles. She now has a total of 92 rectangles. How many pieces of rectangular craft paper did she buy? [?]",
"answer0": "14",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 241,
"difficulty_id": 3,
"explanation": "Each square becomes 3 rectangles, adding 2 extra pieces per square. Total increase = 92 − 40 = 52, so squares = 52 ÷ 2 = 26. Rectangular papers = 40 − 26 = 14.",
"hints": ["Cutting a square into 3 adds 2 extra pieces.", "Find the number of squares first, then subtract from 40."],
"source": "MGS 2023 P6 Prelim P2 Q8",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 14."
},
{
"n": 39,
"type_id": 2,
"question": "The graph shows the mass of a cup when empty and when different combinations of objects A, B and C are placed in the cup.
(a) What is the mass of the empty cup? [?] g
(b) What is the mass of object A? [?] g
(c) What is the average mass of objects A, B and C? [?] g",
"answer0": "70",
"answer1": "120",
"answer2": "130",
"answer3": null,
"correct_answer": null,
"skill_id": 205,
"difficulty_id": 3,
"explanation": "(a) Empty cup = 70 g (first bar). (b) Cup+B+A = 280, Cup+C+A = 370, Cup+C+B = 340. A+B = 210, A+C = 300, B+C = 270. Adding: 2(A+B+C) = 780, so A+B+C = 390. A = 390 − (B+C) = 390 − 270 = 120 g. (c) Average = 390 ÷ 3 = 130 g.",
"hints": ["Read each bar's total mass and subtract the empty cup.", "Set up A+B, A+C, B+C, then solve."],
"source": "MGS 2023 P6 Prelim P2 Q9",
"image_needed": true,
"image_options": false,
"image_file": "q39.png",
"image_page": 26,
"image_bbox": [0.17, 0.13, 0.80, 0.46],
"image_loc": "bar graph of cup mass with object combinations, upper part of question",
"notes": "Key: (a) 70 g, (b) 120 g, (c) 130 g. All integers in grams."
},
{
"n": 40,
"type_id": 2,
"question": "In the figure, PQRS is a rhombus and STUV is a parallelogram. PSV is a straight line. \\(\\angle PSQ = 48°\\), \\(\\angle RTS = 21°\\) and \\(\\angle STU = 116°\\).
(a) Find \\(\\angle QPS\\). [?]
(b) Find \\(\\angle RST\\). [?]
(c) Find \\(\\angle QRT\\). [?]",
"answer0": "84",
"answer1": "20",
"answer2": "137",
"answer3": null,
"correct_answer": null,
"skill_id": 230,
"difficulty_id": 3,
"explanation": "(a) In rhombus PQRS, triangle PQS is isosceles (PQ = QS not assumed; PS = QS) with base angles 48°, so ∠QPS = 180° − 48° − 48° = 84°. (b) ∠TSV = 180° − 116° = 64° (parallelogram co-interior); ∠RST = 180° − 64° − 48° − 48° = 20°. (c) ∠SRT = 180° − 21° − 20° = 139°; ∠QRT = 360° − 84° − 139° = 137°.",
"hints": ["Use the isosceles triangles formed by the rhombus diagonals.", "Use co-interior angles for the parallelogram, then angles around a point."],
"source": "MGS 2023 P6 Prelim P2 Q10",
"image_needed": true,
"image_options": false,
"image_file": "q40.png",
"image_page": 27,
"image_bbox": [0.16, 0.13, 0.72, 0.36],
"image_loc": "rhombus PQRS and parallelogram STUV with angles marked, upper part of question",
"notes": "Key: (a) 84°, (b) 20°, (c) 137°. All integer degree answers."
},
{
"n": 41,
"type_id": 2,
"question": "Tom wanted to buy a new television and started a 4-month savings plan. The line graph shows the total amount of savings at the start of each month (Jan $0, Feb $300, Mar $1300, Apr $2700, May $3600). What was the percentage increase in the amount of savings from the end of January to the end of February? [?] %",
"answer0": "333.33",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 208,
"difficulty_id": 3,
"explanation": "Savings at end of Jan = $300, end of Feb = $1300, so the increase = $1000. Percentage increase = \\(\\dfrac{1000}{300}\\times100\\% = 333\\dfrac{1}{3}\\% \\approx 333.33\\%\\). Part (a) of the original (labelling the pie chart) is a drawing task and is omitted here.",
"hints": ["Increase = Feb amount − Jan amount.", "Percentage increase = increase ÷ original × 100%."],
"source": "MGS 2023 P6 Prelim P2 Q11",
"image_needed": true,
"image_options": false,
"image_file": "q41.png",
"image_page": 28,
"image_bbox": [0.17, 0.16, 0.82, 0.55],
"image_loc": "line graph of savings Jan–May, upper part of question",
"notes": "Original Q11 has part (a) label-the-pie-chart (drawing, skipped) and part (b) percentage increase = 333 1/3% (key). Stem reduced to part (b). Answer is recurring; FIB stores 333.33 (rounded 2dp). Flag: exact value 333 1/3%."
},
{
"n": 42,
"type_id": 2,
"question": "The figure shows a cylinder which is hollow in the middle and has a thickness of 10 cm. (Taking \\(\\pi = 3.14\\)) The outer diameter is 60 cm, the height is 42 cm.
(a) Find the area of the shaded face. [?] cm²
(b) Randall dipped the entire cylinder into red paint. What is the surface area of the cylinder that is painted red? [?] cm²",
"answer0": "1570",
"answer1": "16328",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 222,
"difficulty_id": 3,
"explanation": "Outer radius = 30 cm, inner radius = 30 − 10 = 20 cm. (a) Shaded ring face = \\(3.14\\times30^2 - 3.14\\times20^2 = 2826 - 1256 = 1570\\) cm². (b) Two ring faces = 1570 × 2 = 3140; outer curved surface = \\(3.14\\times60\\times42 = 7912.8\\); inner curved surface = \\(3.14\\times40\\times42 = 5275.2\\). Total = 3140 + 7912.8 + 5275.2 = 16 328 cm².",
"hints": ["Ring area = outer circle − inner circle.", "Painted area = 2 ring faces + outer curved + inner curved surfaces."],
"source": "MGS 2023 P6 Prelim P2 Q12",
"image_needed": true,
"image_options": false,
"image_file": "q42.png",
"image_page": 30,
"image_bbox": [0.45, 0.16, 0.75, 0.34],
"image_loc": "hollow cylinder with 42cm, 10cm thickness, 60cm diameter marked, upper-right of question",
"notes": "Key: (a) 1570 cm², (b) 16 328 cm². Both integers."
},
{
"n": 43,
"type_id": 2,
"question": "A post office and a library are 360 m apart. They are located between Ali's house and Nelson's house. The post office is exactly half-way in between Ali's house and Nelson's house. One day, Ali and Nelson started jogging from their own house towards the library at the same time. They met each other at the library. Nelson jogged at 85 m/min while Ali jogged at a speed 40 m/min faster than Nelson.
(a) How much further did Ali jog than Nelson? [?] m
(b) How far is Nelson's house from the library? [?] m",
"answer0": "720",
"answer1": "1530",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 219,
"difficulty_id": 3,
"explanation": "(a) The post office is the midpoint, and the library is 360 m past it (towards Nelson). So Ali's distance is 360 × 2 = 720 m more than Nelson's. (b) They jog for the same time. Ali's speed = 85 + 40 = 125 m/min. Ali jogs 720 m further, and the speed difference is 40 m/min, so time = 720 ÷ 40 = 18 min. Nelson's distance = 85 × 18 = 1530 m.",
"hints": ["(a) The library is 360 m beyond the midpoint on Nelson's side.", "(b) Time = extra distance ÷ speed difference, then Nelson's distance = 85 × time."],
"source": "MGS 2023 P6 Prelim P2 Q13",
"image_needed": true,
"image_options": false,
"image_file": "q43.png",
"image_page": 31,
"image_bbox": [0.16, 0.18, 0.82, 0.27],
"image_loc": "diagram of Ali's house, Post Office, Library, Nelson's house with 360m, near top of question",
"notes": "Key: (a) 720 m, (b) 1530 m. Both integers in metres. Speed topic (moved to Sec 1 in 2026) but on this 2023 paper."
},
{
"n": 44,
"type_id": 2,
"question": "Six identical rectangular boxes can be stored in a cupboard 1.5 m high. Two arrangements are shown. The arrangement in figure A leaves a 30-cm gap at the side. The arrangement in figure B leaves a 13-cm gap at the side and another gap at the top.
(a) In the arrangement shown in Figure B, what is the width of the gap at the top? [?] cm
(b) What is the width of the cupboard in metres? [?] m",
"answer0": "34",
"answer1": "1.17",
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 138,
"difficulty_id": 3,
"explanation": "Length of 1 box = 150 ÷ 2 = 75 cm. The difference of (1 length − 2 breadths) shows up as the side-gap difference: 30 − 13 = 17 cm = 1 length − 2 breadths. (a) Top gap = 17 × 2 = 34 cm. (b) Breadth of 1 box = (75 − 17) ÷ 2 = 29 cm; cupboard width = 75 + 29 + 13 = 117 cm = 1.17 m.",
"hints": ["The two arrangements share the same cupboard width.", "Set up length and breadth from the 30 cm and 13 cm side gaps."],
"source": "MGS 2023 P6 Prelim P2 Q14",
"image_needed": true,
"image_options": false,
"image_file": "q44.png",
"image_page": 32,
"image_bbox": [0.17, 0.20, 0.72, 0.46],
"image_loc": "Figure A and Figure B box arrangements with 30cm and 13cm gaps, upper part of question",
"notes": "Key: (a) 34 cm, (b) 1.17 m."
},
{
"n": 45,
"type_id": 1,
"question": "The ratio of the number of girls to boys in Hall A is 7 : 3. The ratio of the number of girls to boys in Hall B is 2 : 7. The total number of pupils in Hall A is \\(\\dfrac{2}{3}\\) of the total number of pupils in Hall B. What is the ratio of the number of boys in Hall A to the number of boys in Hall B? Express your answer in the simplest form.",
"answer0": "9 : 35",
"answer1": "3 : 7",
"answer2": "7 : 9",
"answer3": "21 : 10",
"correct_answer": 0,
"skill_id": 214,
"difficulty_id": 3,
"explanation": "Total A : Total B = 2 : 3 = 30 : 45 (using units). Hall A girls:boys = 7:3 → scale total 10 to 30: 21 : 9. Hall B girls:boys = 2:7 → scale total 9 to 45: 10 : 35. Boys A : Boys B = 9 : 35.",
"hints": ["Make the hall totals 30 and 45 (since 2 : 3).", "Split each total by its girls:boys ratio."],
"source": "MGS 2023 P6 Prelim P2 Q15a",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 9 : 35. Ratio answer -> MCQ. Part (a) of paper-2 Q15."
},
{
"n": 46,
"type_id": 2,
"question": "The ratio of the number of girls to boys in Hall A is 7 : 3. The ratio of the number of girls to boys in Hall B is 2 : 7. The total number of pupils in Hall A is \\(\\dfrac{2}{3}\\) of the total number of pupils in Hall B. The number of boys in Hall A to boys in Hall B is 9 : 35. After a total of 375 boys left the hall, the percentage of all the girls became 62%. How many boys remained in the hall? [?]",
"answer0": "285",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 209,
"difficulty_id": 3,
"explanation": "Total girls : total boys across both halls = (21+10) : (9+35) = 31 : 44, total 75 units. After 375 boys leave, girls are 62%, so boys = 38%. Girls 62% → 31 units, so 1% = \\(\\dfrac{1}{2}\\) unit; boys 38% = 19 units. Boys who left = 44u − 19u = 25u = 375, so 1u = 15. Boys remaining = 19 × 15 = 285.",
"hints": ["Total girls = 31 units, total boys = 44 units (from the two halls combined).", "After boys leave, girls 62% → 31u; find unit value from the 375 boys who left."],
"source": "MGS 2023 P6 Prelim P2 Q15b",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 285. Part (b) of paper-2 Q15; gives part-(a) ratio (9:35) as context in stem."
},
{
"n": 47,
"type_id": 2,
"question": "At a concert, $9180 was collected from the sale of adult and child tickets. The ratio of the money collected from adult to child tickets is 14 : 3. \\(\\dfrac{1}{5}\\) of the tickets sold were child tickets. Each adult ticket is $9 more than each child ticket. How many child tickets were sold? [?]",
"answer0": "30",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 214,
"difficulty_id": 3,
"explanation": "Money A : C = 14 : 3, total 17 units = $9180, so 1 unit = $540. Adult money = $7560, child money = $1620. \\(\\dfrac{1}{5}\\) of tickets are child, so adults : children = 4 : 1; adult ticket price = $7560 ÷ 4u and child = $1620 ÷ 1u, with adult − child = $9. Solving: child tickets = 30.",
"hints": ["Find the money from adult and child tickets using 14 : 3.", "Use the ticket-count ratio (4 : 1) and the $9 price difference."],
"source": "MGS 2023 P6 Prelim P2 Q16",
"image_needed": false,
"image_options": false,
"image_file": null,
"notes": "Key: 30 child tickets. (Full key working: 17u=$9180, 1u=$540; $7560÷4=$1890; $1890−$1620=$270; $270÷$9=30.)"
},
{
"n": 48,
"type_id": 2,
"question": "At a bakery, cupcakes are sold in boxes of 4 at $2.10 and tarts are sold in boxes of 3 at $1.60. Mrs Lee spent a total of $203.60 on some cupcakes and tarts at the bakery. She repacks them onto trays such that there are 3 cupcakes and 5 tarts on each tray for a party. How many tarts did she buy from the bakery? [?]",
"answer0": "240",
"answer1": null,
"answer2": null,
"answer3": null,
"correct_answer": null,
"skill_id": 152,
"difficulty_id": 3,
"explanation": "Per tray, cupcakes : tarts = 3 : 5. To buy whole boxes (cupcakes in 4s, tarts in 3s), scale to 36 : 60 (multiples of 4 and 3). One such set = 9 boxes of cupcakes + 20 boxes of tarts = $2.10×9 + $1.60×20 = $18.90 + $32.00 = $50.90. $203.60 ÷ $50.90 = 4 sets. Tarts = 4 × 60 = 240.",
"hints": ["Match the 3 : 5 tray ratio to whole boxes: 36 : 60.", "Find the cost of one set, divide the total, then count tarts."],
"source": "MGS 2023 P6 Prelim P2 Q17",
"image_needed": true,
"image_options": false,
"image_file": "q48.png",
"image_page": 35,
"image_bbox": [0.18, 0.15, 0.76, 0.24],
"image_loc": "table of cupcakes (4 for $2.10) and tarts (3 for $1.60) with pictures, top of question",
"notes": "Key: 240 tarts. Picture table is decorative; prices are in the stem."
}
]
}