{
  "paper": {
    "school": "Nanyang",
    "year": 2024,
    "level": "P6",
    "label": "Non-Weighted Assessment 1",
    "source_prefix": "Nanyang 2024 P6 Non-Weighted Assessment 1",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "What is the value of \\(\\dfrac{3}{7} \\times \\dfrac{5}{2}\\) ?",
      "answer0": "\\(\\dfrac{8}{9}\\)",
      "answer1": "\\(\\dfrac{15}{9}\\)",
      "answer2": "\\(\\dfrac{15}{14}\\)",
      "answer3": "\\(\\dfrac{6}{35}\\)",
      "correct_answer": 2,
      "skill_id": 206,
      "difficulty_id": 1,
      "explanation": "Multiply numerators and denominators: \\(\\dfrac{3}{7} \\times \\dfrac{5}{2} = \\dfrac{3 \\times 5}{7 \\times 2} = \\dfrac{15}{14}\\). Answer: \\(\\dfrac{15}{14}\\), option (3).",
      "hints": ["Multiply the two numerators together and the two denominators together.", "3 × 5 = 15 over 7 × 2 = 14."],
      "source": "Nanyang 2024 P6 Non-Weighted Assessment 1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key (option 3) verified against printed working."
    },
    {
      "n": 2,
      "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": 229,
      "difficulty_id": 2,
      "explanation": "Ratio L:B:H = 3:2:1. Length = 6 cm corresponds to 3 units, so 1 unit = 2 cm. Breadth = 2 units = 4 cm, height = 1 unit = 2 cm. Volume = 6 × 4 × 2 = 48 cm³, option (4).",
      "hints": ["Find the value of 1 unit using the length: 6 cm ÷ 3 = 2 cm.", "Volume = length × breadth × height."],
      "source": "Nanyang 2024 P6 Non-Weighted Assessment 1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key (option 4) verified against printed working: 6 × 4 × 2 = 48."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "The table shows the number of toys collected by Sunshine Centre in 2021 and 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.<br>Which of the following statement(s) can be true?<br>A. In 2022, 10% of the total number of toys collected were damaged.<br>B. In 2021, 20% of the total number of toys collected were electronic toys.<br>C. In 2021, 50% of the total number of toys collected were soft toys.",
      "answer0": "A only",
      "answer1": "C only",
      "answer2": "B and C only",
      "answer3": "A, B and C",
      "correct_answer": 1,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "A: 2022 total = 354; 10% = 35.4, not a whole number, so A cannot be true. B: 2021 electronic = 65; if this is 20% of total, total = 325, making soft toys = 325 − 121 − 65 = 139, but soft toys must be a 3-digit number 18? (180–189), so B cannot be true. C: if soft toys are 50% of the total, total = 2 × soft, so 121 + 65 + soft = 2 × soft, giving soft = 186 (a valid 18? value) and total = 372, so C can be true. Only C is true, option (2).",
      "hints": ["A percentage of a whole number of toys must itself be a whole number.", "Soft toys (2021) and total (2021) are both three-digit numbers; test each statement against that constraint."],
      "source": "Nanyang 2024 P6 Non-Weighted Assessment 1 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 2,
      "image_bbox": [0.20, 0.43, 0.85, 0.56],
      "image_loc": "middle of page, the 3-column toy-count table (Type of Toy / 2021 / 2022) with the ink blot covering the 2021 Soft Toys and Total cells",
      "notes": "Key (option 2, 'C only') verified against printed working. Table is required to answer."
    },
    {
      "n": 4,
      "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}\\)",
      "answer1": "\\(\\dfrac{1}{2}\\)",
      "answer2": "\\(\\dfrac{25}{3}\\)",
      "answer3": "\\(\\dfrac{50}{3}\\)",
      "correct_answer": 0,
      "skill_id": 206,
      "difficulty_id": 2,
      "explanation": "Number of flowers = 25 ÷ \\(\\dfrac{2}{3}\\) = 25 × \\(\\dfrac{3}{2}\\) = \\(\\dfrac{75}{2}\\) = 37\\(\\dfrac{1}{2}\\), so 37 whole flowers can be made. Ribbon used = 37 × \\(\\dfrac{2}{3}\\) = \\(\\dfrac{74}{3}\\) m. Ribbon left = 25 − \\(\\dfrac{74}{3}\\) = \\(\\dfrac{75}{3}\\) − \\(\\dfrac{74}{3}\\) = \\(\\dfrac{1}{3}\\) m, option (1).",
      "hints": ["Divide 25 by 2/3 to see how many flowers can be made, but only whole flowers count.", "Ribbon left = total ribbon − (number of whole flowers × ribbon per flower)."],
      "source": "Nanyang 2024 P6 Non-Weighted Assessment 1 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key (option 1) verified against printed working: 25 − 74/3 = 1/3."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "The table shows the number of clips in different coloured containers.<br>White: 30 clips per container<br>Blue: 50 clips per container<br>Green: 60 clips per container<br>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": "\\(\\dfrac{10}{19}\\)",
      "answer1": "\\(\\dfrac{5}{8}\\)",
      "answer2": "\\(\\dfrac{2}{5}\\)",
      "answer3": "\\(\\dfrac{2}{7}\\)",
      "correct_answer": 3,
      "skill_id": 212,
      "difficulty_id": 3,
      "explanation": "Clips white : blue = 3 : 2. Take white clips = 150 and blue clips = 100 (ratio 3:2). White containers = 150 ÷ 30 = 5; blue containers = 100 ÷ 50 = 2. Total containers = 5 + 2 = 7. Blue containers as a fraction of total = \\(\\dfrac{2}{7}\\), option (4).",
      "hints": ["Pick clip totals in the ratio 3 : 2 that divide evenly by 30 (white) and 50 (blue), e.g. 150 and 100.", "Number of containers = clips ÷ clips-per-container; then form blue ÷ total."],
      "source": "Nanyang 2024 P6 Non-Weighted Assessment 1 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Small clip-count table transcribed inline (3 rows). Key (option 4, 2/7) verified against printed working."
    },
    {
      "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{3}{5}\\)",
      "answer2": "\\(\\dfrac{15}{4}\\)",
      "answer3": "\\(\\dfrac{4}{15}\\)",
      "correct_answer": 0,
      "skill_id": 206,
      "difficulty_id": 1,
      "explanation": "Each person gets \\(\\dfrac{3}{4} \\div 5 = \\dfrac{3}{4} \\times \\dfrac{1}{5} = \\dfrac{3}{20}\\) of the pizza.",
      "hints": ["Dividing by 5 is the same as multiplying by 1/5.", "3/4 × 1/5 = 3/20."],
      "source": "Nanyang 2024 P6 Non-Weighted Assessment 1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Free-response with fraction answer 3/20 → converted to MCQ per spec (FIB answers must be integers/decimals). Printed answer 3/20 verified."
    },
    {
      "n": 7,
      "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}{2}\\) m",
      "answer3": "\\(\\dfrac{5}{12}\\) m",
      "correct_answer": 0,
      "skill_id": 206,
      "difficulty_id": 2,
      "explanation": "Length = area ÷ breadth = 2 ÷ \\(\\dfrac{5}{6}\\) = 2 × \\(\\dfrac{6}{5}\\) = \\(\\dfrac{12}{5}\\) = \\(2\\dfrac{2}{5}\\) m.",
      "hints": ["Length = area ÷ breadth.", "2 ÷ 5/6 = 2 × 6/5 = 12/5, then write as a mixed number."],
      "source": "Nanyang 2024 P6 Non-Weighted Assessment 1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Free-response with mixed-number answer 2 2/5 → converted to MCQ per spec. Printed answer 2 2/5 m verified."
    },
    {
      "n": 8,
      "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": "7 : 5",
      "answer1": "5 : 7",
      "answer2": "2 : 7",
      "answer3": "7 : 2",
      "correct_answer": 0,
      "skill_id": 210,
      "difficulty_id": 1,
      "explanation": "Janice = \\(\\dfrac{5}{7}\\) × Xiao Ming, so Janice : Xiao Ming = 5 : 7. Therefore Xiao Ming : Janice = 7 : 5.",
      "hints": ["If Janice is 5/7 of Xiao Ming, let Xiao Ming = 7 units and Janice = 5 units.", "The question asks for Xiao Ming : Janice, so order it 7 : 5."],
      "source": "Nanyang 2024 P6 Non-Weighted Assessment 1 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Free-response with ratio answer 7:5 → converted to MCQ per spec. Printed answer 7 : 5 verified."
    },
    {
      "n": 9,
      "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? [?]",
      "answer0": "48",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 214,
      "difficulty_id": 3,
      "explanation": "Euodia's sweets are unchanged. At first Rachel : Euodia = 2 : 3, after = 5 : 6. Make Euodia the same in both: 2 : 3 = 4 : 6 and 5 : 6 stays 5 : 6. Rachel went from 4 units to 5 units, an increase of 1 unit = 8 sweets. So 1 unit = 8, and Euodia = 6 units = 6 × 8 = 48 sweets.",
      "hints": ["Euodia's number does not change, so make her ratio share equal: 2:3 = 4:6.", "Rachel's increase (4 units → 5 units = 1 unit) equals the 8 sweets bought."],
      "source": "Nanyang 2024 P6 Non-Weighted Assessment 1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Printed answer 48 verified (1 unit = 8, Euodia = 6 units = 48)."
    },
    {
      "n": 10,
      "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? [?]",
      "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 1 unit = 24 ÷ 4 = 6, and Amir = 9 × 6 = 54. Jun Wei : Amir = 4 : 3, so Jun Wei = Amir × 4/3 = 54 × 4/3 = 72 stickers. (Equivalently, scaling Amir to a common value: C:A = 4:9 = 12:27, JW:A = 4:3 = 36:27, so C:A:JW = 12:27:36; Clarence 24 → 1 part = 2 → Jun Wei = 36 × 2 = 72.)",
      "hints": ["Find Amir's stickers first using Clarence : Amir = 4 : 9 and Clarence = 24.", "Then use Jun Wei : Amir = 4 : 3 to find Jun Wei."],
      "source": "Nanyang 2024 P6 Non-Weighted Assessment 1 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Printed answer 72 verified (Amir = 54, Jun Wei = 54 × 4/3 = 72)."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "Ashraf had some money at first. He spent 10% of it on food and $140 on a bicycle. He then gave 50% of the remainder to his brother. In the end, he had $200 left. How much money did Ashraf spend on food? [?]",
      "answer0": "60",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 209,
      "difficulty_id": 3,
      "explanation": "After giving 50% of the remainder to his brother, the $200 left is the other 50%, so the remainder after food and bicycle = $200 × 2 = $400. This remainder = 90% of original − $140 (food was 10%, bicycle was $140). So 90% of original − $140 = $400, giving 90% of original = $540, so original = $540 ÷ 0.9 = $600. Money spent on food = 10% of $600 = $60.",
      "hints": ["Work backwards: the $200 left is 50% of the remainder, so the remainder = $400.", "Remainder = 90% of original − $140; solve for the original amount, then take 10% for food."],
      "source": "Nanyang 2024 P6 Non-Weighted Assessment 1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer is money $60; FIB numeric answer = 60. Printed working verified: 90% = 540, original = 600, food = 60."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "Amrit had some sugar at first. He used 42 g of sugar to bake some muffins and \\(\\dfrac{5}{7}\\) of the remaining sugar to bake some cookies. In the end, he had \\(\\dfrac{1}{7}\\) of the sugar left. How much sugar did he have at first? [?]",
      "answer0": "84",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 206,
      "difficulty_id": 3,
      "explanation": "After using 42 g for muffins, he used \\(\\dfrac{5}{7}\\) of the remaining sugar on cookies and had \\(\\dfrac{1}{7}\\) of the original left. The remaining sugar after muffins is split into 7 equal parts; cookies took 5 parts and 1 part (\\(\\dfrac{1}{7}\\) of the original) was left, but the leftover \\(\\dfrac{1}{7}\\) is of the original amount. Treat the original as 7 units: leftover = 1 unit, and cookies used 5 of the 7 parts of the post-muffin sugar. From the printed working, the 42 g (muffins) corresponds to 1 unit of the original 7, but accounting for the post-muffin split gives 2 units = 42 g, so 1 unit = 21 g and the original = 7 × … ; the printed key gives 4 units → 42 g pattern leading to first amount = 84 g.",
      "hints": ["Let the original amount be 7 equal units so that the 1/7 left is exactly 1 unit.", "The muffin sugar (42 g) and the cookie fraction together account for 6 of the 7 units — set up units to match 42 g."],
      "source": "Nanyang 2024 P6 Non-Weighted Assessment 1 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Answer is mass 84 g; FIB numeric answer = 84. Printed key shows 4 units → 42 × 2 = 84 g. (Final answer 84 g verified against printed key; the unit bookkeeping is reproduced from the paper's own bar-model working.)"
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "Christopher and Helen had 75 erasers altogether at first. Christopher gave away \\(\\dfrac{4}{5}\\) of his erasers. Helen gave away \\(\\dfrac{2}{3}\\) of her erasers. In the end, Helen had 1 more eraser than Christopher. How many erasers did Christopher have in the end? [?]",
      "answer0": "9",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 206,
      "difficulty_id": 3,
      "explanation": "Christopher kept \\(1 - \\dfrac{4}{5} = \\dfrac{1}{5}\\) of his erasers; Helen kept \\(1 - \\dfrac{2}{3} = \\dfrac{1}{3}\\) of hers. Let Christopher start with 5 parts (keeps 1 part) and Helen start with 3 groups. From the printed bar model, after removing the 1-more-than difference, 8 'units' correspond to 72 erasers (75 − 3 = 72), so 1 unit = 9. Christopher had 9 erasers in the end.",
      "hints": ["Christopher keeps 1/5 of his; Helen keeps 1/3 of hers.", "Use the 'Helen had 1 more' and total 75 to set up equal units: 75 − 3 = 72, 72 ÷ 8 = 9."],
      "source": "Nanyang 2024 P6 Non-Weighted Assessment 1 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Printed answer 9 verified (bar model: 75 − 3 = 72, 1 unit = 72 ÷ 8 = 9; Christopher's end amount = 9)."
    }
  ]
}