{
  "paper": {
    "school": "Nanyang",
    "year": 2023,
    "level": "P6",
    "label": "Weighted Assessment 1",
    "source_prefix": "Nanyang 2023 P6 Weighted Assessment 1",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Janice is \\(\\dfrac{5}{7}\\) as tall as Xiao Ming. What is the ratio of Xiao Ming's height to Janice's height?",
      "answer0": "5 : 7",
      "answer1": "7 : 5",
      "answer2": "5 : 12",
      "answer3": "7 : 12",
      "correct_answer": 1,
      "skill_id": 210,
      "difficulty_id": 1,
      "explanation": "Janice : Xiao Ming = 5 : 7. So Xiao Ming : Janice = 7 : 5.",
      "hints": ["Janice's height is 5 units, Xiao Ming's is 7 units.", "Reverse the order asked: Xiao Ming to Janice."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer (2)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "A pail contains 28 ℓ of water. A tank contains 800 times as much water as the pail. How many litres of water are there in the tank?",
      "answer0": "16 400 ℓ",
      "answer1": "22 400 ℓ",
      "answer2": "64 400 ℓ",
      "answer3": "224 000 ℓ",
      "correct_answer": 1,
      "skill_id": 152,
      "difficulty_id": 1,
      "explanation": "28 × 800 = 28 × 8 × 100 = 224 × 100 = 22 400 ℓ.",
      "hints": ["Multiply 28 by 800.", "28 × 8 = 224, then × 100."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer (2) = 22 400 ℓ."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "What is the value of \\(\\dfrac{2}{3}+\\dfrac{1}{5}\\)?",
      "answer0": "\\(\\dfrac{3}{8}\\)",
      "answer1": "\\(\\dfrac{3}{15}\\)",
      "answer2": "\\(\\dfrac{2}{15}\\)",
      "answer3": "\\(\\dfrac{13}{15}\\)",
      "correct_answer": 3,
      "skill_id": 159,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{2}{3}+\\dfrac{1}{5}=\\dfrac{10}{15}+\\dfrac{3}{15}=\\dfrac{13}{15}\\).",
      "hints": ["Find a common denominator of 15.", "10/15 + 3/15."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer (4)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "In the number line, what is the value of X?",
      "answer0": "\\(2\\dfrac{1}{4}\\)",
      "answer1": "\\(2\\dfrac{3}{15}\\)",
      "answer2": "\\(2\\dfrac{5}{16}\\)",
      "answer3": "\\(2\\dfrac{1}{2}\\)",
      "correct_answer": 2,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "The interval from 2 to \\(2\\dfrac{3}{8}\\) is divided into equal parts. X sits at \\(2\\dfrac{5}{16}\\) on the marked scale.",
      "hints": ["The marks between 2 and 2 3/8 are equal.", "Read the position of X carefully."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 4,
      "image_bbox": [0.20, 0.46, 0.82, 0.58],
      "image_loc": "number line with marks from 2 to 2 3/8 and arrow labelled X, upper-middle of page",
      "notes": "Key answer (3) = 2 5/16."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "What is the value of \\(\\dfrac{3}{7}\\times\\dfrac{5}{2}\\)?",
      "answer0": "\\(\\dfrac{8}{9}\\)",
      "answer1": "\\(\\dfrac{15}{14}\\)",
      "answer2": "\\(\\dfrac{15}{9}\\)",
      "answer3": "\\(\\dfrac{6}{35}\\)",
      "correct_answer": 1,
      "skill_id": 162,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{3}{7}\\times\\dfrac{5}{2}=\\dfrac{15}{14}\\).",
      "hints": ["Multiply numerators and denominators.", "3×5 = 15, 7×2 = 14."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer (2)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "\\(\\dfrac{3}{4}\\) of a pizza was shared equally among 5 people. What fraction of the pizza did each person receive?",
      "answer0": "\\(\\dfrac{3}{20}\\)",
      "answer1": "\\(\\dfrac{4}{15}\\)",
      "answer2": "\\(\\dfrac{20}{3}\\)",
      "answer3": "\\(\\dfrac{7}{45}\\)",
      "correct_answer": 0,
      "skill_id": 164,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{3}{4}\\div 5=\\dfrac{3}{4}\\times\\dfrac{1}{5}=\\dfrac{3}{20}\\).",
      "hints": ["Divide 3/4 by 5.", "Dividing by 5 is multiplying by 1/5."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer (1)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Express 10.01 kg in kilograms and grams.",
      "answer0": "1 kg 1 g",
      "answer1": "10 kg 1 g",
      "answer2": "10 kg 10 g",
      "answer3": "100 kg 10 g",
      "correct_answer": 2,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "0.01 kg = 0.01 × 1000 g = 10 g. So 10.01 kg = 10 kg 10 g.",
      "hints": ["1 kg = 1000 g.", "0.01 × 1000 = 10."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer (3)."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Ninety identical pencils cost $57.60. What is the cost of one such pencil?",
      "answer0": "$0.54",
      "answer1": "$0.64",
      "answer2": "$0.74",
      "answer3": "$6.40",
      "correct_answer": 1,
      "skill_id": 167,
      "difficulty_id": 1,
      "explanation": "$57.60 ÷ 90 = ($57.60 ÷ 9) ÷ 10 = $6.40 ÷ 10 = $0.64.",
      "hints": ["Divide $57.60 by 90.", "57.60 ÷ 9 = 6.40, then ÷ 10."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer (2)."
    },
    {
      "n": 9,
      "type_id": 1,
      "question": "Sathya had 250 fruits. 50 of them were papayas, 110 of them were mangoes and the rest were pears. What percentage of her fruits were pears?",
      "answer0": "20%",
      "answer1": "36%",
      "answer2": "44%",
      "answer3": "64%",
      "correct_answer": 1,
      "skill_id": 171,
      "difficulty_id": 1,
      "explanation": "Pears = 250 − 50 − 110 = 90. Percentage = \\(\\dfrac{90}{250}\\times100\\% = 36\\%\\).",
      "hints": ["Find the number of pears first.", "Express 90 out of 250 as a percentage."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer (2)."
    },
    {
      "n": 10,
      "type_id": 1,
      "question": "Which one of the following is likely to be the mass of a honeydew sold in a supermarket?",
      "answer0": "2.5 g",
      "answer1": "25 g",
      "answer2": "2.5 kg",
      "answer3": "250 kg",
      "correct_answer": 2,
      "skill_id": 184,
      "difficulty_id": 1,
      "explanation": "A honeydew melon's mass is realistically about 2.5 kg.",
      "hints": ["Think about how heavy a melon really is.", "A few grams is too light; hundreds of kilograms too heavy."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q10",
      "image_needed": true,
      "image_options": false,
      "image_file": "q10.png",
      "image_page": 7,
      "image_bbox": [0.38, 0.15, 0.62, 0.30],
      "image_loc": "drawing of a honeydew melon below the question, upper-middle of page",
      "notes": "Key answer (3) = 2.5 kg."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "The length, breadth and height of a box are in the ratio 3 : 2 : 1 respectively. The length of the box is 6 cm. Find the volume of the box.",
      "answer0": "12 cm³",
      "answer1": "18 cm³",
      "answer2": "36 cm³",
      "answer3": "48 cm³",
      "correct_answer": 3,
      "skill_id": 190,
      "difficulty_id": 2,
      "explanation": "3 units = 6 cm, so 1 unit = 2 cm. Length = 6 cm, breadth = 2×2 = 4 cm, height = 1×2 = 2 cm. Volume = 6 × 4 × 2 = 48 cm³.",
      "hints": ["Find the value of 1 unit from the length.", "Volume = length × breadth × height."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer (4)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The solid is made up of 1-cm cubes. How many more 1-cm cubes must be added to the solid to make it a cuboid measuring 4 cm by 3 cm by 4 cm?",
      "answer0": "27",
      "answer1": "28",
      "answer2": "29",
      "answer3": "30",
      "correct_answer": 0,
      "skill_id": 188,
      "difficulty_id": 2,
      "explanation": "Cuboid volume = 4 × 3 × 4 = 48 cubes. The solid has 1 + 4 + 6 + 10 = 21 cubes. Cubes to add = 48 − 21 = 27.",
      "hints": ["Count the cubes in the given solid layer by layer.", "Cuboid needs 48 cubes; subtract what is there."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q12.png",
      "image_page": 8,
      "image_bbox": [0.30, 0.22, 0.66, 0.42],
      "image_loc": "isometric drawing of a stepped solid made of unit cubes, middle of page",
      "notes": "Key answer (1) = 27. Solid count 1+4+6+10 = 21 per key."
    },
    {
      "n": 13,
      "type_id": 1,
      "question": "The table shows the number of bicycles sold each month by a shop. January 53, February 150, March 124, April 76, May 99. Which of the following bar graphs best represents the information in the table?",
      "answer0": "Graph (1)",
      "answer1": "Graph (2)",
      "answer2": "Graph (3)",
      "answer3": "Graph (4)",
      "correct_answer": 3,
      "skill_id": 147,
      "difficulty_id": 2,
      "explanation": "The bars must follow the order Jan (lowest, 53), Feb (highest, 150), Mar (124), Apr (76), May (99). Graph (4) matches: lowest in January, highest in February.",
      "hints": ["January is the smallest value; February is the largest.", "Match each bar's height to the table values."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q13",
      "image_needed": true,
      "image_options": true,
      "image_file": null,
      "image_page": 9,
      "image_bbox": [0.22, 0.34, 0.85, 0.92],
      "image_loc": "four candidate bar graphs (1)-(4) stacked vertically below the data table",
      "notes": "Key answer (4). Options are bar-graph images; crop each option q13_opt0..3. Data table values: Jan 53, Feb 150, Mar 124, Apr 76, May 99."
    },
    {
      "n": 14,
      "type_id": 1,
      "question": "Sally had some apples. \\(\\dfrac{3}{5}\\) of the apples were red. She then gave \\(\\dfrac{1}{2}\\) of the red apples to her sister. What fraction of Sally's apples were given to her sister?",
      "answer0": "\\(\\dfrac{1}{5}\\)",
      "answer1": "\\(\\dfrac{5}{6}\\)",
      "answer2": "\\(\\dfrac{1}{10}\\)",
      "answer3": "\\(\\dfrac{3}{10}\\)",
      "correct_answer": 3,
      "skill_id": 161,
      "difficulty_id": 1,
      "explanation": "\\(\\dfrac{3}{5}\\times\\dfrac{1}{2}=\\dfrac{3}{10}\\) of the apples were given to her sister.",
      "hints": ["Find 1/2 of 3/5.", "Multiply the two fractions."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer (4)."
    },
    {
      "n": 15,
      "type_id": 1,
      "question": "The first 15 numbers of a number pattern are given.<br>9 , 0 , 8 , 6 , 9 , 0 , 8 , 6 , 9 , 0 , 8 , 6 , 9 , 0 , 8 , …<br>What is the 274th number?",
      "answer0": "0",
      "answer1": "6",
      "answer2": "8",
      "answer3": "9",
      "correct_answer": 0,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "The pattern repeats in blocks of 4: 9, 0, 8, 6. 274 ÷ 4 = 68 remainder 2, so the 274th number is the 2nd in the block = 0.",
      "hints": ["The numbers repeat every 4 terms.", "Find the remainder when 274 is divided by 4."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer (1) = 0; 274 ÷ 4 = 68 R2."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "Find the value of 72 ÷ 8 − 2 × 3 + 77.<br>[?]",
      "answer0": "80",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 1,
      "explanation": "72 ÷ 8 − 2 × 3 + 77 = 9 − 6 + 77 = 3 + 77 = 80.",
      "hints": ["Do division and multiplication first.", "9 − 6 + 77."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer 80."
    },
    {
      "n": 17,
      "type_id": 1,
      "question": "The breadth of a rectangle is \\(\\dfrac{5}{6}\\) m and its area is 2 m². Find the length of the rectangle. Express your answer as a mixed number in its simplest form.",
      "answer0": "\\(2\\dfrac{2}{5}\\) m",
      "answer1": "\\(1\\dfrac{2}{3}\\) m",
      "answer2": "\\(2\\dfrac{1}{6}\\) m",
      "answer3": "\\(\\dfrac{5}{12}\\) m",
      "correct_answer": 0,
      "skill_id": 164,
      "difficulty_id": 2,
      "explanation": "Length = area ÷ breadth = \\(2\\div\\dfrac{5}{6}=\\dfrac{2}{1}\\times\\dfrac{6}{5}=\\dfrac{12}{5}=2\\dfrac{2}{5}\\) m.",
      "hints": ["Length = area ÷ breadth.", "Dividing by 5/6 means multiplying by 6/5."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer 2 2/5 m — mixed-number answer so rendered as MCQ; distractors are plausible wrong values."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "The ratio of Shina's test marks to Kyle's test marks was 3 : 7. Shina scored 16 fewer marks than Kyle. How many marks did Kyle score?<br>[?]",
      "answer0": "28",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 182,
      "difficulty_id": 2,
      "explanation": "Difference = 7 − 3 = 4 units = 16 marks, so 1 unit = 4 marks. Kyle = 7 units = 7 × 4 = 28 marks.",
      "hints": ["The difference in units corresponds to 16 marks.", "Find 1 unit, then Kyle's 7 units."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer 28."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Round 199.99 to 1 decimal place.<br>[?]",
      "answer0": "200.0",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 168,
      "difficulty_id": 1,
      "explanation": "The second decimal digit is 9, so round up: 199.99 ≈ 200.0.",
      "hints": ["Look at the second decimal place.", "9 rounds the first decimal up, carrying over."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer 200.0."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "Mrs Pereira baked 400 tarts. 45% of the tarts she baked were egg tarts while the rest were chocolate tarts. How many chocolate tarts did Mrs Pereira bake?<br>[?]",
      "answer0": "220",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 174,
      "difficulty_id": 1,
      "explanation": "Chocolate tarts = 100% − 45% = 55% of 400 = \\(\\dfrac{55}{100}\\times400 = 220\\).",
      "hints": ["Chocolate tarts are 55% of the total.", "Find 55% of 400."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer 220."
    },
    {
      "n": 21,
      "type_id": 2,
      "question": "75% of a number is 36. What is the number?<br>[?]",
      "answer0": "48",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 207,
      "difficulty_id": 1,
      "explanation": "75% → 36, so 25% → 36 ÷ 3 = 12. 100% → 12 × 4 = 48.",
      "hints": ["Find 25% first.", "100% is four times 25%."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q21",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer 48."
    },
    {
      "n": 22,
      "type_id": 1,
      "question": "Derinda had 25 m of ribbon. She used it to make as many flowers as possible. She used \\(\\dfrac{2}{3}\\) m of ribbon to make each flower. How many metres of the ribbon were left?",
      "answer0": "\\(\\dfrac{1}{3}\\) m",
      "answer1": "\\(\\dfrac{2}{3}\\) m",
      "answer2": "\\(\\dfrac{1}{2}\\) m",
      "answer3": "\\(\\dfrac{1}{4}\\) m",
      "correct_answer": 0,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "25 ÷ \\(\\dfrac{2}{3}\\) = \\(\\dfrac{25}{1}\\times\\dfrac{3}{2}=\\dfrac{75}{2}=37\\dfrac{1}{2}\\) flowers, so 37 whole flowers. The leftover \\(\\dfrac{1}{2}\\) of a flower uses \\(\\dfrac{1}{2}\\times\\dfrac{2}{3}=\\dfrac{1}{3}\\) m of ribbon left over.",
      "hints": ["Divide 25 by 2/3 to find how many flowers.", "Convert the fractional flower back into metres of ribbon."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q22",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer 1/3 m — fraction answer so rendered as MCQ."
    },
    {
      "n": 23,
      "type_id": 1,
      "question": "Brenda had 6 ℓ of orange juice. She drank \\(\\dfrac{1}{2}\\) of it in the morning and gave \\(\\dfrac{1}{4}\\) ℓ of it to her brother. How much orange juice did she have left in the end?",
      "answer0": "\\(2\\dfrac{3}{4}\\) ℓ",
      "answer1": "\\(3\\dfrac{1}{4}\\) ℓ",
      "answer2": "\\(2\\dfrac{1}{4}\\) ℓ",
      "answer3": "\\(3\\dfrac{3}{4}\\) ℓ",
      "correct_answer": 0,
      "skill_id": 160,
      "difficulty_id": 2,
      "explanation": "Morning: \\(\\dfrac{1}{2}\\times6 = 3\\) ℓ. Left = 6 − 3 − \\(\\dfrac{1}{4}\\) = 3 − \\(\\dfrac{1}{4}\\) = \\(2\\dfrac{3}{4}\\) ℓ.",
      "hints": ["Half of 6 ℓ is drunk in the morning.", "Subtract the morning amount and the 1/4 ℓ given away."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q23",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer 2 3/4 ℓ — mixed number so rendered as MCQ."
    },
    {
      "n": 24,
      "type_id": 1,
      "question": "In a camp, the number of children is \\(\\dfrac{3}{8}\\) of the number of adults. \\(\\dfrac{2}{9}\\) of the children are boys and there is an equal number of men and women. What is the ratio of the number of girls to the number of women?",
      "answer0": "7 : 12",
      "answer1": "7 : 9",
      "answer2": "2 : 9",
      "answer3": "12 : 7",
      "correct_answer": 0,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Children : Adults = 3 : 8. Take children = 9 units (so adults = 24). Boys : Girls : Children = 2 : 7 : 9, so girls = 7 units. Women = 24 ÷ 2 = 12 units. Girls : Women = 7 : 12.",
      "hints": ["Pick children as 9 units so 2/9 are boys works evenly.", "Equal men and women means women is half the adults."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q24",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer 7 : 12 — ratio answer so rendered as MCQ."
    },
    {
      "n": 25,
      "type_id": 2,
      "question": "Clarence, Amir and Jun Wei received some stickers. The ratio of the number of stickers that Clarence received to the number of stickers Amir received was 4 : 9. The ratio of the number of stickers Jun Wei received to the number of stickers Amir received was 4 : 3. Clarence received 24 stickers. How many stickers did Jun Wei receive?<br>[?]",
      "answer0": "72",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Clarence : Amir = 4 : 9. Clarence = 24, so 4 units = 24, 1 unit = 6, Amir = 9 units = 54. Jun Wei : Amir = 4 : 3 = 12 : 9, so Jun Wei = 12 units = 12 × 6 = 72.",
      "hints": ["Make Amir the common quantity in both ratios.", "Find 1 unit from Clarence's 24 stickers."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q25",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer 72."
    },
    {
      "n": 26,
      "type_id": 2,
      "question": "The ratio of the number of sweets Rachel had to the number of sweets Euodia had was 2 : 3 at first. After Rachel bought 8 more sweets, the ratio of the number of sweets Rachel had to the number of sweets Euodia had became 5 : 6. How many sweets did Euodia have?<br>[?]",
      "answer0": "48",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Euodia is unchanged. At first Rachel : Euodia = 2 : 3 = 4 : 6; after = 5 : 6. The difference 5 − 4 = 1 unit (of the 6-part scale) = 8 sweets. Euodia = 6 units = 6 × 8 = 48.",
      "hints": ["Euodia's amount stays the same, so make her share equal in both ratios.", "The 8 extra sweets equal the change in Rachel's units."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q26",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer 48. Common Euodia = 6 parts; 1 part = 8."
    },
    {
      "n": 27,
      "type_id": 2,
      "question": "Mr Tan had $20 more than Mr Lee at first. After Mr Tan spent $50 and Mr Lee spent half of his money, both of them had the same amount of money left. How much money did Mr Lee have at first?<br>$[?]",
      "answer0": "60",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 241,
      "difficulty_id": 3,
      "explanation": "Let Mr Lee have 2 units. Mr Tan has 2 units + $20. Mr Lee left = 1 unit; Mr Tan left = 2 units + $20 − $50 = 2 units − $30. Equal: 1 unit = 2 units − $30, so 1 unit = $30. Mr Lee at first = 2 units = $60.",
      "hints": ["Let Mr Lee's money be 2 units so half is a whole unit.", "Set the two 'left' amounts equal."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q27",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer $60."
    },
    {
      "n": 28,
      "type_id": 2,
      "question": "Diane wanted to train for a marathon. She started by running 1.6 km in the first week. She increased her distance by 1.2 km every week from the previous week. Find the total distance that she ran in the first 5 weeks.<br>[?]",
      "answer0": "20",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Weeks: 1.6, 2.8, 4.0, 5.2, 6.4 km. Total = (1.6 × 5) + (1.2 × 10) = 8 + 12 = 20 km.",
      "hints": ["List the distance each week (add 1.2 km each time).", "Sum the five weekly distances."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q28",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key answer 20 km."
    },
    {
      "n": 29,
      "type_id": 2,
      "question": "A wire 210 cm long was cut into 2 pieces and bent to form a rectangle and a square. The length of the rectangle is 48.5 cm and its breadth is 38.5 cm. Find the length of one side of the square.<br>[?]",
      "answer0": "9",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 137,
      "difficulty_id": 2,
      "explanation": "Perimeter of rectangle = (48.5 + 38.5) × 2 = 87 × 2 = 174 cm. Wire for square = 210 − 174 = 36 cm. One side = 36 ÷ 4 = 9 cm.",
      "hints": ["Find the rectangle's perimeter first.", "The rest of the wire forms the square's 4 equal sides."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q29",
      "image_needed": true,
      "image_options": false,
      "image_file": "q29.png",
      "image_page": 18,
      "image_bbox": [0.14, 0.18, 0.74, 0.36],
      "image_loc": "labelled rectangle (48.5 cm by 38.5 cm) and a small square with a '?' side, upper part of page",
      "notes": "Key answer 9 cm."
    },
    {
      "n": 30,
      "type_id": 0,
      "question": "The table shows the number of toys collected by Sunshine Centre in Year 2021 and Year 2022. Part of the table is covered by an ink blot. The number of soft toys collected and the total number of toys collected were both three-digit numbers. (Wooden 2021:121, 2022:80; Electronic 2021:65, 2022:74; Soft 2021:18_ , 2022:200; Total 2021:3__ , 2022:354.) For each statement, decide True / False / Not possible to tell: (i) In Year 2021, more than 50% of the toys collected were soft toys. (ii) In Year 2021, 20% of the toys collected were electronic toys. (iii) In Year 2022, the number of wooden toys collected was 40% of the number of soft toys collected.",
      "answer0": null,
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 171,
      "difficulty_id": 3,
      "explanation": "Soft toys 2021 is 18_ (180–189) and total is 3__ , at least 121+65+180 = 366. (i) Not possible to tell — soft toys could be just under or over half, undetermined. (ii) False — electronic 65 out of at least 366 is about 18%, not 20%. (iii) True — 2022 wooden 80 is 40% of soft 200.",
      "hints": ["Use the constraint that soft toys and total are three-digit numbers.", "Check each percentage statement against possible values."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Q30",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Interactive tick-the-box (True/False/Not possible) format with no app question type — type_id 0, skipped on insert. Key: (i) Not possible to tell, (ii) False, (iii) True."
    },
    {
      "n": 31,
      "type_id": 1,
      "question": "Jasper ran \\(6\\dfrac{1}{10}\\) km. Irfan ran \\(2\\dfrac{7}{16}\\) km more than Jasper. How far did they run altogether?",
      "answer0": "\\(14\\dfrac{51}{80}\\) km",
      "answer1": "\\(8\\dfrac{43}{80}\\) km",
      "answer2": "\\(14\\dfrac{43}{80}\\) km",
      "answer3": "\\(12\\dfrac{51}{80}\\) km",
      "correct_answer": 0,
      "skill_id": 160,
      "difficulty_id": 2,
      "explanation": "Irfan = \\(6\\dfrac{1}{10}+2\\dfrac{7}{16}=8\\dfrac{43}{80}\\) km. Altogether = \\(8\\dfrac{43}{80}+6\\dfrac{1}{10}=14\\dfrac{51}{80}\\) km.",
      "hints": ["Find Irfan's distance first.", "Add both distances using a common denominator of 80."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q1. Key answer 14 51/80 km — mixed number so MCQ."
    },
    {
      "n": 32,
      "type_id": 2,
      "question": "The mass of each sack of rice is \\(4\\dfrac{1}{5}\\) kg. Find the total mass of 45 such sacks of rice.<br>[?]",
      "answer0": "189",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 163,
      "difficulty_id": 1,
      "explanation": "\\(4\\dfrac{1}{5}\\times45=\\dfrac{21}{5}\\times45=21\\times9=189\\) kg.",
      "hints": ["Convert 4 1/5 to an improper fraction.", "45 ÷ 5 = 9, then × 21."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q2. Answer 189 kg (whole number) so FIB. Key answer 189."
    },
    {
      "n": 33,
      "type_id": 2,
      "question": "Joy had a meal that cost $32.50 before GST at a restaurant. What was the cost of her meal after adding 8% GST?<br>$[?]",
      "answer0": "35.10",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "After GST = 108% of $32.50 = \\(\\dfrac{108}{100}\\times32.50 = $35.10\\).",
      "hints": ["The total is 100% + 8% = 108% of the price.", "Multiply $32.50 by 1.08."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q3. Key answer $35.10."
    },
    {
      "n": 34,
      "type_id": 2,
      "question": "Danny's scores for 5 games are 8, 0, 7, 16 and 9. Find his average score.<br>[?]",
      "answer0": "8",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 203,
      "difficulty_id": 1,
      "explanation": "Average = \\(\\dfrac{8+0+7+16+9}{5}=\\dfrac{40}{5}=8\\).",
      "hints": ["Add all five scores.", "Divide the total by 5."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q4. Scores from table: 8,0,7,16,9. Key answer 8."
    },
    {
      "n": 35,
      "type_id": 2,
      "question": "Siti has the exact amount of money to buy 84 bottled drinks or 126 canned drinks. She has already spent some of the money to buy 39 canned drinks and 42 bottled drinks. How many more bottled drinks can she buy with the remaining money?<br>[?]",
      "answer0": "16",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "84 bottled = 126 canned, so 1 bottled = \\(\\dfrac{126}{84}=1.5\\) canned. 39 canned = 39 ÷ 1.5 = 26 bottled-equivalents. Total bottled-equivalents spent = 26 + 42 = 68. Remaining bottled = 84 − 68 = 16.",
      "hints": ["Find how many canned drinks equal one bottled drink.", "Convert everything to bottled-drink units."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q5. Key answer 16."
    },
    {
      "n": 36,
      "type_id": 2,
      "question": "Miss Wong bought two identical suitcases at a year-end sale (40% discount for all suitcases). The two suitcases cost $174 after discount. Find the price of one such suitcase before discount.<br>$[?]",
      "answer0": "145",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 207,
      "difficulty_id": 2,
      "explanation": "One suitcase after discount = $174 ÷ 2 = $87. This is 60% of the original (100% − 40%). 60% → $87, so 10% → $14.50, 100% → $145.",
      "hints": ["Find the after-discount price of one suitcase.", "$87 is 60% of the original price."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q6. 'YEAR-END SALE 40% discount' banner is decorative; discount value is in the stem. Key answer $145."
    },
    {
      "n": 37,
      "type_id": 2,
      "question": "Mr Mohammad took a taxi from home to his office. His taxi fare was based on the charges: first 1 kilometre or less $4.30; every additional 400 m or less $0.24; every 45 seconds of waiting or less $0.24. The taxi stopped once at a traffic light and travelled a total distance of 7 km to reach his office. Mr Mohammad paid $9.10. What was the longest possible duration the taxi stopped at the traffic light?<br>[?] s",
      "answer0": "225",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 167,
      "difficulty_id": 3,
      "explanation": "Distance after first 1 km = 7 − 1 = 6 km = 6000 m. 6000 ÷ 400 = 15 blocks → 15 × $0.24 = $3.60. Distance fare = $3.60 + $4.30 = $7.90. Waiting fare = $9.10 − $7.90 = $1.20. Blocks = $1.20 ÷ $0.24 = 5. Longest duration = 5 × 45 = 225 s.",
      "hints": ["Work out the fare for the distance first.", "The remaining fare is for waiting time in 45-second blocks."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q7. Charges table values embedded in stem. Key answer 225 s."
    },
    {
      "n": 38,
      "type_id": 2,
      "question": "A rectangular tank measuring 32.5 cm by 22.5 cm by 18 cm was \\(\\dfrac{5}{9}\\)-filled with water. When Kamala poured 7 litres of water into the tank, some water overflowed. Find the volume of water that overflowed. Give your answer in litres.<br>[?] ℓ",
      "answer0": "1.15",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 191,
      "difficulty_id": 3,
      "explanation": "Tank volume = 32.5 × 22.5 × 18 = 13 162.5 cm³. Empty space = \\(1-\\dfrac{5}{9}=\\dfrac{4}{9}\\), so space = \\(\\dfrac{4}{9}\\times13162.5 = 5850\\) cm³. Poured 7 ℓ = 7000 cm³. Overflow = 7000 − 5850 = 1150 cm³ = 1.15 ℓ.",
      "hints": ["Find the volume of the empty space (4/9 of the tank).", "Overflow = poured volume − empty space; 1000 cm³ = 1 ℓ."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q8",
      "image_needed": true,
      "image_options": false,
      "image_file": "q38.png",
      "image_page": 25,
      "image_bbox": [0.28, 0.22, 0.72, 0.42],
      "image_loc": "labelled cuboid tank (32.5 cm, 22.5 cm, 18 cm) shaded part-full of water, upper-middle of page",
      "notes": "Paper 2 Q8. Key answer 1.15 ℓ."
    },
    {
      "n": 39,
      "type_id": 2,
      "question": "Amrit had some sugar at first. He used 275 g of sugar to bake some muffins and \\(\\dfrac{3}{5}\\) of the remaining sugar to bake some cookies. In the end, he had \\(\\dfrac{1}{8}\\) of the sugar left. How much sugar did he have at first?<br>[?] g",
      "answer0": "400",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Let total = 8 units (1/8 left). After muffins the remainder R: cookies = 3/5 R, left = 2/5 R = 1 unit. So R = \\(\\dfrac{5}{2}\\) units. Muffins (275 g) = 8 − 2.5×... using key: 1/8 of sugar = 2 units, full = 16 units, remainder after muffins gives left 2/5 = 2 units → remainder = 5 units of 16-scale... 16 − 5 = 11 units = 275 g, 1 unit = 25 g, total 16 units = 400 g.",
      "hints": ["Let the total be a number of units so 1/8 and 2/5 are whole units.", "The 275 g equals the units used for muffins."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q9. Key answer 400 g (model: total 16 units, 1/8 left = 2 units, remainder = 5 units, muffins = 11 units = 275 g, 1 unit = 25 g)."
    },
    {
      "n": 40,
      "type_id": 2,
      "question": "In a class of 42 children, the average mass of the children was 37.5 kg. The average mass of the girls in the class was 36.7 kg. The average mass of the boys in the class was 38.8 kg. How many more girls than boys were there in the class?<br>[?]",
      "answer0": "10",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 205,
      "difficulty_id": 3,
      "explanation": "By the supposition method: if all 42 were girls, total deficit per child below boys etc. Using the key: 13 × 2 = 26 girls and 8 × 2 = 16 boys (37.5−36.7 = 0.8 per girl, 38.8−37.5 = 1.3 per boy; 13:8 ratio of girls to boys → 26 girls, 16 boys). 26 − 16 = 10 more girls than boys.",
      "hints": ["Compare each group's average to the overall average.", "The 'top-up' and 'take-away' amounts balance, giving the girl:boy ratio."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q10. Key answer 10 (26 girls, 16 boys)."
    },
    {
      "n": 41,
      "type_id": 2,
      "question": "A group of children is put into 2 halls, hall A and hall B. The ratio of the number of children in hall A to the number of children in hall B is 3 : 8. In hall A, the ratio of the number of boys to the number of girls is 5 : 2. There are 18 girls in hall A. Find the total number of children in both halls.<br>[?]",
      "answer0": "231",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Hall A boys:girls = 5:2, total 7 parts; girls = 2 parts = 18, so 1 part = 9, hall A total = 7 × 9 = 63. A:B = 3:8 → A = 3 units = 63, 1 unit = 21, total = 11 units = 21 × 11 = 231.",
      "hints": ["Find the total in hall A from the boys:girls ratio.", "Use A:B = 3:8 to scale up to both halls."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q11. Key answer 231."
    },
    {
      "n": 42,
      "type_id": 2,
      "question": "ABCD is a trapezium. APB, DQC, RCS and PQR are straight lines. APB is parallel to DQC and AD is parallel to PQR. ∠BCS = 50°, ∠BCQ = 90° and ∠QRC = 95°.<br>(a) Find ∠DQP. [?]<br>(b) Find ∠ADQ. [?]",
      "answer0": "45",
      "answer1": "135",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 230,
      "difficulty_id": 3,
      "explanation": "(a) ∠RCQ = 180° − 90° − 50° = 40° (angles on straight line RCS at C). In triangle QRC, ∠RQC = 180° − 95° − 40° = 45°, and ∠DQP = ∠RQC = 45° (vertically opposite). (b) AD is parallel to PQR, so ∠ADQ and ∠DQP are interior angles: ∠ADQ = 180° − 45° = 135°.",
      "hints": ["Use angles on a straight line at C to find ∠RCQ.", "Angle sum of triangle QRC gives ∠RQC; then use parallel lines."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q12",
      "image_needed": true,
      "image_options": false,
      "image_file": "q42.png",
      "image_page": 29,
      "image_bbox": [0.30, 0.21, 0.78, 0.42],
      "image_loc": "trapezium ABCD with straight lines APB, DQC, RCS, PQR and marked angles 50°, 95°, upper-middle of page",
      "notes": "Paper 2 Q12. Two FIB blanks (a)=45°, (b)=135°. Key answers (a) 45, (b) 135."
    },
    {
      "n": 43,
      "type_id": 2,
      "question": "Ashraf had some money at first. He spent 15% of it on food and $810 on a new laptop. He then gave 20% of the remainder to his brother. In the end, he had $304 left.<br>(a) How much money did Ashraf give to his brother? $[?]<br>(b) How much money did Ashraf have at first? $[?]",
      "answer0": "76",
      "answer1": "1400",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "(a) After giving 20% of the remainder, 80% of the remainder = $304, so 20% (given to brother) = $304 ÷ 4 = $76. (b) Remainder = $76 × 5 = $380. This remainder = 85% of original − $810 (after 15% food and the laptop): 85% → $380 + $810 = $1190, 1% → $14, 100% → $1400.",
      "hints": ["$304 is 80% of the remainder; the brother got 20%.", "Work back to the original: 85% remained after the 15% food spend, then subtract the laptop."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q13. Two FIB blanks: (a) $76, (b) $1400. Key answers match."
    },
    {
      "n": 44,
      "type_id": 2,
      "question": "Susan had 117 beads and marbles altogether. The beads and marbles were either white or black. 20% of the beads and 50% of the marbles were white. There were as many black beads as black marbles. How many beads did Susan have?<br>[?]",
      "answer0": "45",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "Black beads = 80% of beads = \\(\\dfrac{4}{5}\\) beads; black marbles = 50% of marbles = \\(\\dfrac{1}{2}\\) marbles. Equal black: \\(\\dfrac{4}{5}B=\\dfrac{1}{2}M\\). Taking beads = 5 units (black 4 units) and marbles = 8 units (black 4 units): total 5 + 8 = 13 units = 117, 1 unit = 9. Beads = 5 units = 45.",
      "hints": ["Black beads = 4/5 of beads; black marbles = 1/2 of marbles; set them equal.", "Pick units so both black amounts match, then split the 117 total."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q14. Part (a) is a circle-the-phrase task (answer: 'fewer than'), recorded here in notes; the served FIB is part (b) = 45 beads. Key answer (b) 45."
    },
    {
      "n": 45,
      "type_id": 2,
      "question": "Christopher and Helen had 1044 erasers altogether at first. Christopher gave \\(\\dfrac{4}{5}\\) of his erasers to his brother. Helen gave \\(\\dfrac{5}{8}\\) of her erasers to her sister. In the end, Helen had 150 erasers more than Christopher. How many erasers did Christopher have at first?<br>[?]",
      "answer0": "420",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Christopher left = \\(\\dfrac{1}{5}\\) of his; Helen left = \\(\\dfrac{3}{8}\\) of hers. Make a common unit (15 parts): Christopher = 15 units → left 3 units; Helen = 8 units → left 3 units. Helen 150 more: difference. Using the key model, 1 unit = 28, Christopher = 15 units = 28 × 15 = 420.",
      "hints": ["Christopher keeps 1/5; Helen keeps 3/8.", "Use a common unit so the kept amounts compare cleanly; the 150 difference fixes 1 unit."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q15. Key answer 420 (1 unit = 28, Christopher 15 units)."
    },
    {
      "n": 46,
      "type_id": 2,
      "question": "The figure is made up of 2 squares, ABCD and DEFG. X is a point on GD and Y is a point on DE. BC = 7 cm, FE = 6 cm and XD = DY = YE.<br>(a) Find the total area of the shaded parts. [?] cm²<br>(b) What fraction of the figure is unshaded? [?]",
      "answer0": "38",
      "answer1": "\\(\\dfrac{47}{85}\\)",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 138,
      "difficulty_id": 3,
      "explanation": "(a) Square ABCD side 7, square DEFG side 6. YE = 6 ÷ 3 = 2, so DY = XD = 2. Shaded ACD-triangle area = 1/2 × 7 × 7 = 24.5. Shaded XYF region = square DEFG (36) − triangle DXY (1/2×2×2=... ) − triangle YEF (1/2×6×6=18) etc.; per key: area of triangle ABCD-part 24.5 plus XYF region 13.5 = 38 cm². (b) Total figure area = 7×7 + 6×6 = 49 + 36 = 85. Unshaded = 85 − 38 = 47, fraction = \\(\\dfrac{47}{85}\\).",
      "hints": ["Each square's area is side × side; use XD = DY = YE to find the small lengths.", "Unshaded fraction = (total − shaded) ÷ total."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q46.png",
      "image_page": 33,
      "image_bbox": [0.28, 0.15, 0.72, 0.35],
      "image_loc": "two adjoining squares ABCD and DEFG with shaded triangles, points X and Y marked, upper part of page",
      "notes": "Paper 2 Q16. (a) 38 cm² is a whole number; (b) is a fraction 47/85 — second blank's answer is fractional, but it sits in a single multi-part FIB. Key answers (a) 38 cm², (b) 47/85."
    },
    {
      "n": 47,
      "type_id": 2,
      "question": "The table shows the number of clips in different coloured containers: White 30 per container, Blue 50 per container, Green 60 per container.<br>(a) Gwen has a total of 10 white containers and green containers. What is the smallest possible difference between the total number of clips in Gwen's white containers and the total number of clips in her green containers? [?]<br>(b) Clement has some white containers and some blue containers. The ratio of the total number of clips in Clement's white containers to the total number of clips in his blue containers is 3 : 2. Express the number of his blue containers as a fraction of the total number of his containers. [?]",
      "answer0": "30",
      "answer1": "\\(\\dfrac{2}{7}\\)",
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 213,
      "difficulty_id": 3,
      "explanation": "(a) Green clips (60) is twice white clips (30), so for every 2 white containers to 1 green container the difference is 0. With 10 containers split to minimise: closest split gives smallest difference 30 (using the key's 7 white + 3 green: 7×30 = 210 vs 3×60 = 180, difference 30). (b) White clips : blue clips = 3 : 2 → 150 : 100. White containers = 150 ÷ 30 = 5; blue containers = 100 ÷ 50 = 2. Total = 7. Blue fraction = \\(\\dfrac{2}{7}\\).",
      "hints": ["(a) One green container (60) equals two white containers (30 each), so balance them.", "(b) Convert the clip ratio to actual container counts using clips-per-container."],
      "source": "Nanyang 2023 P6 Weighted Assessment 1 Paper 2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Paper 2 Q17. (a) 30 (whole number); (b) 2/7 (fraction) within multi-part FIB. Key answers (a) 30, (b) 2/7."
    }
  ]
}