{ "paper": { "school": "St Nicholas", "year": 2025, "level": "P3", "label": "End of Year Exam", "source_prefix": "St Nicholas 2025 P3 End of Year Exam", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "2000 + 40 + 1 =", "answer0": "241", "answer1": "2041", "answer2": "2401", "answer3": "2410", "correct_answer": 1, "skill_id": 66, "difficulty_id": 1, "explanation": "Expanded form: 2000 + 40 + 1 means 2 thousands, 0 hundreds, 4 tens, 1 one. 2000 + 40 = 2040, then 2040 + 1 = 2041.", "hints": ["Add the place values together.", "There are no hundreds, so the hundreds digit is 0: 2041."], "source": "St Nicholas 2025 P3 End of Year Exam Q1", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 = 2041." }, { "n": 2, "type_id": 1, "question": "Which one of the following statements is true?", "answer0": "1/4 < 1/7", "answer1": "2/5 < 6/10", "answer2": "5/8 > 3/4", "answer3": "6/9 > 2/3", "correct_answer": 1, "skill_id": 79, "difficulty_id": 2, "explanation": "Convert to compare. 2/5 = 4/10, and 4/10 < 6/10 is true. Check others: 1/4 = 7/28 > 4/28 = 1/7 (false); 5/8 = 0.625 < 0.75 = 3/4 (false); 6/9 = 2/3, so 6/9 > 2/3 is false (they are equal).", "hints": ["Make the denominators the same before comparing.", "2/5 = 4/10. Is 4/10 less than 6/10?"], "source": "St Nicholas 2025 P3 End of Year Exam Q2", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2." }, { "n": 3, "type_id": 1, "question": "Which of the following shows an obtuse angle?", "answer0": "Angle 1", "answer1": "Angle 2", "answer2": "Angle 3", "answer3": "Angle 4", "correct_answer": 3, "skill_id": 99, "difficulty_id": 2, "explanation": "An obtuse angle is greater than a right angle (90 degrees) but less than a straight angle (180 degrees). Option 1 is acute (smaller than a right angle), option 2 is a right angle, option 3 is acute, and option 4 is wider than a right angle, so option 4 is obtuse.", "hints": ["An obtuse angle is bigger than a right-angle corner but not a straight line.", "Compare each angle to the corner of a square."], "source": "St Nicholas 2025 P3 End of Year Exam Q3", "image_needed": true, "image_options": true, "image_file": null, "image_page": 4, "image_bbox": [0.27, 0.13, 0.52, 0.82], "image_loc": "four angle diagrams stacked vertically down the left-centre of the page, labelled (1)-(4)", "notes": "Key: option 4. Image-option MCQ - four angle figures to be cropped to q3_opt0.png..q3_opt3.png. Opt0 page4 bbox ~[0.30,0.14,0.50,0.30]; opt1 ~[0.30,0.31,0.52,0.46]; opt2 ~[0.30,0.49,0.50,0.63]; opt3 ~[0.30,0.66,0.52,0.82]." }, { "n": 4, "type_id": 1, "question": "Which figure has the greatest perimeter?", "answer0": "Figure 1 (arrow-shaped hexagon: 9, 5, 5, 9, 5, 5 cm)", "answer1": "Figure 2 (rectangle 15 cm by 3 cm)", "answer2": "Figure 3 (triangle 15, 15, 18 cm)", "answer3": "Figure 4 (regular pentagon, side 8 cm)", "correct_answer": 2, "skill_id": 96, "difficulty_id": 2, "explanation": "Add up the sides of each figure. Figure 1: 9+5+5+9+5+5 = 38 cm. Figure 2: 15+3+15+3 = 36 cm. Figure 3: 15+15+18 = 48 cm. Figure 4: 8x5 = 40 cm. The greatest is Figure 3 at 48 cm.", "hints": ["Perimeter is the total length around a figure - add every side.", "Don't forget the rectangle has two long and two short sides."], "source": "St Nicholas 2025 P3 End of Year Exam Q4", "image_needed": true, "image_options": true, "image_file": null, "image_page": 5, "image_bbox": [0.25, 0.12, 0.60, 0.83], "image_loc": "four labelled figures stacked down the centre of the page with side lengths marked", "notes": "Key: option 3. Image-option MCQ - crop each figure to q4_opt0.png..q4_opt3.png. Opt0 page5 ~[0.27,0.13,0.58,0.30]; opt1 ~[0.30,0.36,0.58,0.44]; opt2 ~[0.30,0.46,0.58,0.66]; opt3 ~[0.30,0.66,0.58,0.83]." }, { "n": 5, "type_id": 1, "question": "There are 53 Art Club members. Mr Bala gave 6 sheets of drawing paper to each of the Art Club members. He had 9 sheets of drawing paper left. How many sheets of drawing paper did Mr Bala have at first?", "answer0": "318", "answer1": "327", "answer2": "477", "answer3": "483", "correct_answer": 1, "skill_id": 76, "difficulty_id": 2, "explanation": "Sheets given out = 53 x 6 = 318. He had 9 left over, so at first he had 318 + 9 = 327 sheets.", "hints": ["First find how many sheets were given out: 53 x 6.", "Add the leftover 9 sheets to the sheets given out."], "source": "St Nicholas 2025 P3 End of Year Exam Q5", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 = 327." }, { "n": 6, "type_id": 1, "question": "Find the value of 1/2 - 4/12 . Express the answer in its simplest form.", "answer0": "1/4", "answer1": "1/6", "answer2": "3/10", "answer3": "5/14", "correct_answer": 1, "skill_id": 81, "difficulty_id": 2, "explanation": "Make the denominators the same: 1/2 = 6/12. Then 6/12 - 4/12 = 2/12. Simplify by dividing top and bottom by 2: 2/12 = 1/6.", "hints": ["Rewrite 1/2 as twelfths: 1/2 = 6/12.", "Subtract, then simplify the result."], "source": "St Nicholas 2025 P3 End of Year Exam Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 = 1/6." }, { "n": 7, "type_id": 1, "question": "Siew Mei went to the supermarket. She was there for 1 h 50 min. She left the supermarket at 4:00 pm. What time did she reach the supermarket?", "answer0": "2:10 pm", "answer1": "2:30 pm", "answer2": "2:50 pm", "answer3": "3:50 pm", "correct_answer": 0, "skill_id": 92, "difficulty_id": 2, "explanation": "Work backwards from the leaving time. 4:00 pm minus 1 hour = 3:00 pm. Then minus 50 minutes = 2:10 pm.", "hints": ["Start at 4:00 pm and count backwards.", "Take off 1 hour first, then 50 minutes."], "source": "St Nicholas 2025 P3 End of Year Exam Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 1 = 2:10 pm." }, { "n": 8, "type_id": 2, "question": "How many more children bought vanilla ice-cream than strawberry ice-cream?", "answer0": "7", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 104, "difficulty_id": 1, "explanation": "Read the bar graph: vanilla = 35 children, strawberry = 28 children. Difference = 35 - 28 = 7 more children bought vanilla.", "hints": ["Read the length of the vanilla bar and the strawberry bar.", "Subtract the smaller from the larger: 35 - 28."], "source": "St Nicholas 2025 P3 End of Year Exam Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 8, "image_bbox": [0.20, 0.27, 0.88, 0.58], "image_loc": "horizontal bar graph titled 'Ice-cream bought by children' in the upper half of the page", "notes": "Key: 35 - 28 = 7." }, { "n": 9, "type_id": 2, "question": "1352 , 1382 , [?] , 1442 , 1472 , 1502", "answer0": "1412", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 69, "difficulty_id": 1, "explanation": "The numbers go up by 30 each time (1382 - 1352 = 30). So the missing number = 1382 + 30 = 1412.", "hints": ["Find the step size: how much is added each time?", "1382 + 30 = 1412."], "source": "St Nicholas 2025 P3 End of Year Exam Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 1382 + 30 = 1412." }, { "n": 10, "type_id": 1, "question": "(a) 6 x 5 is 5 [BLANK] than 7 x 5. (b) 9 x 9 is 9 [BLANK] than 8 x 9. Choose 'more' or 'less' for (a) then (b).", "answer0": "(a) less, (b) less", "answer1": "(a) less, (b) more", "answer2": "(a) more, (b) less", "answer3": "(a) more, (b) more", "correct_answer": 1, "skill_id": 73, "difficulty_id": 2, "explanation": "(a) 6x5 = 30 and 7x5 = 35; 30 is 5 less than 35, so 'less'. (b) 9x9 = 81 and 8x9 = 72; 81 is 9 more than 72, so 'more'.", "hints": ["Work out both products in each part and compare.", "6x5=30 vs 7x5=35; 9x9=81 vs 8x9=72."], "source": "St Nicholas 2025 P3 End of Year Exam Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Word fill-in ('more'/'less') converted to MCQ per spec (no word FIB). Key: a) less, b) more = option 2 (index 1)." }, { "n": 11, "type_id": 2, "question": "Find the sum of $7.65 and $99.55.", "answer0": "$107.20", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 82, "difficulty_id": 1, "explanation": "Add the two amounts: $7.65 + $99.55 = $107.20. (Add the cents: 65 + 55 = 120 cents = $1.20; add the dollars: 7 + 99 = 106; total $106 + $1.20 = $107.20.)", "hints": ["Line up the decimal points and add.", "65 cents + 55 cents = 120 cents, which carries over a dollar."], "source": "St Nicholas 2025 P3 End of Year Exam Q11", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 99.55 + 7.65 = $107.20." }, { "n": 12, "type_id": 2, "question": "Jia Jia bought a wallet for $84. She gave the cashier 2 pieces of $50 notes. The cashier gave her the change in $2 notes. How many $2 notes did Jia Jia receive?", "answer0": "8", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 83, "difficulty_id": 2, "explanation": "She gave 2 x $50 = $100. Change = $100 - $84 = $16. In $2 notes: $16 ÷ $2 = 8 notes.", "hints": ["First find the change: $100 - $84.", "Divide the change by $2 to count the notes."], "source": "St Nicholas 2025 P3 End of Year Exam Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 50x2=100, 100-84=16, 16/2=8." }, { "n": 13, "type_id": 2, "question": "(a) Measure Line XY. Length = [?] cm. (b) The table shows the volume of water in each container (F = 3 l 2 ml, G = 3200 ml, H = 3 l 20 ml, J = 3002 ml). Which container has the same amount of water as Container F? Container [?]", "answer0": "6", "answer1": "J", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 86, "difficulty_id": 2, "explanation": "(a) Line XY measures 6 cm. (b) Container F = 3 l 2 ml = 3000 + 2 = 3002 ml. Compare: G = 3200 ml, H = 3 l 20 ml = 3020 ml, J = 3002 ml. Container J also equals 3002 ml, so J matches F.", "hints": ["For (a) line up the ruler's 0 mark with point X.", "For (b) convert 3 l 2 ml to millilitres: 3000 + 2 = 3002 ml."], "source": "St Nicholas 2025 P3 End of Year Exam Q13", "image_needed": true, "image_options": false, "image_file": "q13.png", "image_page": 11, "image_bbox": [0.30, 0.18, 0.66, 0.25], "image_loc": "the short slanted line segment XY near the top of the page (part a); the container table is text and not needed as an image", "notes": "Key: a) 6 cm; b) Container J. Two blanks: line measurement then container letter. Crop only line XY for q13.png." }, { "n": 14, "type_id": 1, "question": "Which two lines are parallel to each other?", "answer0": "PQ and UT", "answer1": "PR and QS", "answer2": "RU and ST", "answer3": "PU and QT", "correct_answer": 0, "skill_id": 100, "difficulty_id": 2, "explanation": "On the square grid, lines PQ and UT run in the same direction and stay the same distance apart everywhere, so they never meet - they are parallel. The answer is PQ and UT.", "hints": ["Parallel lines stay the same distance apart and never meet.", "Look for two lines that slope the same way on the grid."], "source": "St Nicholas 2025 P3 End of Year Exam Q14", "image_needed": true, "image_options": false, "image_file": "q14.png", "image_page": 12, "image_bbox": [0.34, 0.13, 0.63, 0.34], "image_loc": "square grid with labelled points P, Q, R, S, T, U and line segments near the top of the page", "notes": "Key: PQ and UT. Converted to MCQ (line-pair answer is not numeric/symbolic); distractor pairs are plausible lines from the figure. Correct = option 1 (index 0)." }, { "n": 15, "type_id": 2, "question": "The table shows the timings for the animal shows at a zoo theatre. First Show: 10 45. Second Show: 12 15. Mr Lee and his family wanted to watch the second show. They arrived at the zoo theatre 25 minutes after the first show started. How long did Mr Lee and his family wait for the second show to start? [?] h [?] min", "answer0": "1", "answer1": "5", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 93, "difficulty_id": 2, "explanation": "First show started at 10:45. They arrived 25 minutes later, at 11:10. The second show starts at 12:15. Waiting time from 11:10 to 12:15: 11:10 to 12:10 is 1 hour, then 12:10 to 12:15 is 5 minutes. Total = 1 h 5 min.", "hints": ["First find their arrival time: 10:45 + 25 min.", "Then count the time from arrival (11:10) up to 12:15."], "source": "St Nicholas 2025 P3 End of Year Exam Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: arrive 11:10, wait to 12:15 = 1 h 5 min. Two blanks: hours then minutes." }, { "n": 16, "type_id": 2, "question": "The graphs show the number of T-shirts sold at two different shops (Shop A bar graph; Shop B pictogram, each star = 6 T-shirts). (a) Which shop sold fewer white T-shirts? Shop [?] (b) Find the total number of black T-shirts sold in Shop A and Shop B. [?]", "answer0": "A", "answer1": "68", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 104, "difficulty_id": 2, "explanation": "(a) Shop A white = 22 (bar graph); Shop B white = 4 stars x 6 = 24. 22 is fewer than 24, so Shop A sold fewer white T-shirts. (b) Shop A black = 32 (bar graph); Shop B black = 6 stars x 6 = 36. Total = 32 + 36 = 68.", "hints": ["Each star in the pictogram stands for 6 T-shirts, so multiply.", "For (b) add Shop A black (bar) and Shop B black (stars x 6)."], "source": "St Nicholas 2025 P3 End of Year Exam Q16", "image_needed": true, "image_options": false, "image_file": "q16.png", "image_page": 13, "image_bbox": [0.18, 0.16, 0.86, 0.66], "image_loc": "Shop A bar graph and Shop B pictogram (with star key) stacked in the upper-middle of the page", "notes": "Key: a) Shop A (22<24); b) 32+36=68. Two blanks: shop letter then total. Picture needed for both graphs incl. the 'each star = 6' key." }, { "n": 17, "type_id": 2, "question": "Arrange the fractions from the greatest to the smallest. 1/2 , 5/6 , 4/9. [?] , [?] , [?]", "answer0": "5/6", "answer1": "1/2", "answer2": "4/9", "answer3": null, "correct_answer": null, "skill_id": 79, "difficulty_id": 2, "explanation": "Compare the fractions. 5/6 is more than 1/2 (since 5/6 is close to 1). 4/9 is less than 1/2 (since half of 9 is 4.5, and 4 is below that). Order from greatest to smallest: 5/6, 1/2, 4/9.", "hints": ["Compare each fraction to 1/2 first.", "5/6 is nearly a whole; 4/9 is just under a half."], "source": "St Nicholas 2025 P3 End of Year Exam Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 5/6, 1/2, 4/9 (greatest to smallest). Ordering task as FIB with three blanks in order." }, { "n": 18, "type_id": 2, "question": "Mrs Davi hung 12 identical shapes in a straight line. All the shapes were at an equal distance of 2 m apart from each other. What was the distance between the 1st and 12th shape? [?] m", "answer0": "22", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 71, "difficulty_id": 2, "explanation": "With 12 shapes in a row, there are 12 - 1 = 11 gaps between them. Each gap is 2 m, so the distance from the 1st to the 12th shape = 11 x 2 = 22 m.", "hints": ["The number of gaps is one less than the number of shapes.", "11 gaps x 2 m each."], "source": "St Nicholas 2025 P3 End of Year Exam Q18", "image_needed": true, "image_options": false, "image_file": "q18.png", "image_page": 14, "image_bbox": [0.20, 0.51, 0.85, 0.66], "image_loc": "row of hanging star shapes labelled 1st, 2nd, 3rd ... 12th with 2 m spacing marked, in the lower-middle of the page", "notes": "Key: 12-1=11 gaps, 11x2=22 m." }, { "n": 19, "type_id": 2, "question": "A shop was giving 3 free highlighters for every 4 boxes of pens bought. Zen bought some boxes of pens and received 12 free highlighters. What was the least number of boxes of pens Zen bought?", "answer0": "16", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 76, "difficulty_id": 2, "explanation": "Every 3 highlighters needs 4 boxes. To get 12 highlighters: 12 ÷ 3 = 4 sets. Each set needs 4 boxes, so 4 x 4 = 16 boxes.", "hints": ["How many groups of 3 highlighters make 12? 12 ÷ 3.", "Each group of 3 free highlighters comes from 4 boxes."], "source": "St Nicholas 2025 P3 End of Year Exam Q19", "image_needed": false, "image_options": false, "image_file": null, "image_page": 15, "image_bbox": [0.22, 0.16, 0.66, 0.40], "image_loc": "'Special Offer!' poster showing pen boxes and highlighters", "notes": "Key: 12/3=4, 4x4=16. Poster is decorative - the offer (3 highlighters per 4 boxes) is fully stated in the text, so image not required for solving; image_needed=false." }, { "n": 20, "type_id": 2, "question": "Box A has a mass of 3 kg. It is 390 g lighter than Box B. Box C is 620 g heavier than Box B. What is the mass of Box C? Leave your answer in kilograms and grams. [?] kg [?] g", "answer0": "4", "answer1": "10", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 87, "difficulty_id": 3, "explanation": "Box A = 3 kg = 3000 g. Box A is 390 g lighter than Box B, so Box B = 3000 + 390 = 3390 g. Box C is 620 g heavier than Box B, so Box C = 3390 + 620 = 4010 g = 4 kg 10 g.", "hints": ["Convert 3 kg to grams first: 3000 g.", "Box B is heavier than A by 390 g; Box C is heavier than B by 620 g."], "source": "St Nicholas 2025 P3 End of Year Exam Q20", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: B=3390, C=4010=4 kg 10 g. Two blanks: kg then g." }, { "n": 21, "type_id": 2, "question": "John had $156. He wanted to buy a soccer ball which cost $79 and a jacket that cost $150. How much more money would John need to save in order to buy these two items?", "answer0": "73", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 83, "difficulty_id": 2, "explanation": "Total cost of both items = $79 + $150 = $229. John has $156, so he still needs $229 - $156 = $73 more.", "hints": ["Add the two prices first: $79 + $150.", "Subtract what John already has: $229 - $156."], "source": "St Nicholas 2025 P3 End of Year Exam Q21", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 79+150=229, 229-156=$73." }, { "n": 22, "type_id": 2, "question": "The figure is made up of 3 identical squares. The length of the square is 8 cm. (a) What is the area of one square? [?] cm2 (b) What is the area of the figure? [?] cm2", "answer0": "64", "answer1": "192", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 97, "difficulty_id": 2, "explanation": "(a) Area of one square = side x side = 8 x 8 = 64 cm2. (b) The figure is 3 identical squares, so area = 64 x 3 = 192 cm2.", "hints": ["Area of a square = side x side.", "There are 3 equal squares, so multiply one square's area by 3."], "source": "St Nicholas 2025 P3 End of Year Exam Q22", "image_needed": true, "image_options": false, "image_file": "q22.png", "image_page": 18, "image_bbox": [0.34, 0.19, 0.56, 0.32], "image_loc": "L-shaped figure of two squares in a row with a third square below, marked 8 cm, upper-middle of the page", "notes": "Key: a) 8x8=64 cm2; b) 64x3=192 cm2. Two blanks." }, { "n": 23, "type_id": 2, "question": "Xiao Ming bought 7 boxes of fruit tarts for a party. Each box contained 24 fruit tarts. Then she unpacked all the fruit tarts and placed them equally on 4 trays. (a) How many fruit tarts did Xiao Ming buy? (b) How many fruit tarts were on each tray?", "answer0": "168", "answer1": "42", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 76, "difficulty_id": 2, "explanation": "(a) Total fruit tarts = 7 boxes x 24 = 168. (b) Placed equally on 4 trays: 168 ÷ 4 = 42 fruit tarts on each tray.", "hints": ["For (a) multiply boxes by tarts per box: 7 x 24.", "For (b) divide the total by the number of trays: 168 ÷ 4."], "source": "St Nicholas 2025 P3 End of Year Exam Q23", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: a) 24x7=168; b) 168/4=42. Two blanks." }, { "n": 24, "type_id": 2, "question": "In the hall, there were 465 grey chairs and some blue chairs at first. Another 45 grey chairs were added. In the end, there were 5 times as many grey chairs as blue chairs. (a) How many blue chairs were there? (b) How many chairs were there altogether in the hall at first?", "answer0": "102", "answer1": "567", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 76, "difficulty_id": 3, "explanation": "(a) After adding 45, grey chairs = 465 + 45 = 510. Grey is 5 times the blue, so 5 units = 510, meaning 1 unit (blue) = 510 ÷ 5 = 102 blue chairs. The number of blue chairs did not change. (b) At first there were 465 grey + 102 blue = 567 chairs altogether.", "hints": ["First find the final number of grey chairs: 465 + 45.", "Grey = 5 x blue, so blue = grey ÷ 5. Then add the original grey for the total."], "source": "St Nicholas 2025 P3 End of Year Exam Q24", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: a) 5u=510 so 1u=102; b) 465+102=567." }, { "n": 25, "type_id": 2, "question": "Beth, Katie and Pamela had some cards. Beth had 69 fewer cards than Katie. Beth and Katie had a total of 277 cards. Pamela had as many cards as Beth. (a) How many cards did Pamela have? (b) Pamela gave 41 cards to Katie. How many more cards did Katie have than Pamela in the end?", "answer0": "104", "answer1": "151", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 71, "difficulty_id": 3, "explanation": "(a) Beth + Katie = 277, and Beth is 69 fewer than Katie. Remove the difference: 277 - 69 = 208, which is 2 equal parts (2 x Beth). So Beth = 208 ÷ 2 = 104. Pamela has as many as Beth, so Pamela = 104. (b) Katie = 104 + 69 = 173. After Pamela gives 41 to Katie: Katie = 173 + 41 = 214, Pamela = 104 - 41 = 63. Difference = 214 - 63 = 151. (Equivalently, the gap changes by 2 x 41 = 82, and Katie was already 69 ahead of Pamela: 69 + 82 = 151.)", "hints": ["For (a) subtract the difference from the total, then split into two equal parts.", "For (b) every card moved from Pamela to Katie widens the gap by 2: 69 + (2 x 41)."], "source": "St Nicholas 2025 P3 End of Year Exam Q25", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: a) 277-69=208, 208/2=104; b) 41x2=82, 82+69=151." } ] }