{
  "paper": {
    "school": "ACS Junior",
    "year": 2025,
    "level": "P6",
    "label": "WA1",
    "source_prefix": "ACS Junior 2025 P6 WA1",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "\\(\\dfrac{5}{8} \\div \\dfrac{1}{2} = \\) ______",
      "answer0": "\\(\\dfrac{5}{16}\\)",
      "answer1": "\\(\\dfrac{4}{5}\\)",
      "answer2": "\\(1\\dfrac{1}{4}\\)",
      "answer3": "\\(3\\dfrac{1}{5}\\)",
      "correct_answer": 2,
      "skill_id": 206,
      "difficulty_id": 1,
      "explanation": "Dividing by \\(\\dfrac{1}{2}\\) is multiplying by 2: \\(\\dfrac{5}{8} \\times 2 = \\dfrac{10}{8} = \\dfrac{5}{4} = 1\\dfrac{1}{4}\\). Answer: \\(1\\dfrac{1}{4}\\).",
      "hints": ["To divide by a fraction, multiply by its reciprocal.", "\\(\\dfrac{5}{8} \\times \\dfrac{2}{1} = \\dfrac{10}{8} = 1\\dfrac{1}{4}\\)."],
      "source": "ACS Junior 2025 P6 WA1 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q1 = option 3 (1 1/4)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "Find the value of \\(16 \\times 3 + (18 + 33) \\div 3\\).",
      "answer0": "65",
      "answer1": "77",
      "answer2": "288",
      "answer3": "320",
      "correct_answer": 0,
      "skill_id": 155,
      "difficulty_id": 1,
      "explanation": "Order of operations: brackets first, (18 + 33) = 51; then \\(51 \\div 3 = 17\\) and \\(16 \\times 3 = 48\\); finally 48 + 17 = 65. Answer: 65.",
      "hints": ["Do the brackets first, then multiply and divide before adding.", "16 x 3 = 48 and 51 / 3 = 17, so 48 + 17 = 65."],
      "source": "ACS Junior 2025 P6 WA1 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q2 = option 1 (65)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "\\(\\dfrac{1}{2}\\) of P is equal to \\(\\dfrac{1}{5}\\) of Q. What is the ratio of P : Q?",
      "answer0": "1 : 5",
      "answer1": "1 : 7",
      "answer2": "2 : 5",
      "answer3": "2 : 7",
      "correct_answer": 2,
      "skill_id": 181,
      "difficulty_id": 2,
      "explanation": "\\(\\dfrac{1}{2}P = \\dfrac{1}{5}Q\\). Cross-multiply: \\(5P = 2Q\\), so \\(P : Q = 2 : 5\\). Answer: 2 : 5.",
      "hints": ["Set 1/2 of P equal to 1/5 of Q and cross-multiply.", "5P = 2Q means P : Q = 2 : 5."],
      "source": "ACS Junior 2025 P6 WA1 Q3",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q3 = option 3 (2 : 5)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "Mr Wong had \\(\\dfrac{1}{4}\\) litres of paint. He used \\(\\dfrac{1}{3}\\) of it to paint a chair. How many litres of paint was he left with?",
      "answer0": "\\(\\dfrac{1}{6}\\)",
      "answer1": "\\(\\dfrac{1}{12}\\)",
      "answer2": "\\(\\dfrac{7}{12}\\)",
      "answer3": "\\(\\dfrac{11}{12}\\)",
      "correct_answer": 0,
      "skill_id": 161,
      "difficulty_id": 2,
      "explanation": "He used \\(\\dfrac{1}{3} \\times \\dfrac{1}{4} = \\dfrac{1}{12}\\) litres. Left: \\(\\dfrac{1}{4} - \\dfrac{1}{12} = \\dfrac{3}{12} - \\dfrac{1}{12} = \\dfrac{2}{12} = \\dfrac{1}{6}\\) litres. Answer: \\(\\dfrac{1}{6}\\).",
      "hints": ["Used = 1/3 of 1/4 = 1/12 litres.", "Left = 1/4 - 1/12 = 1/6 litres."],
      "source": "ACS Junior 2025 P6 WA1 Q4",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q4 = option 1 (1/6)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "91% of the participants at a carnival were children. There were 316 men and 503 women at the carnival. How many participants were there altogether?",
      "answer0": "819",
      "answer1": "900",
      "answer2": "8281",
      "answer3": "9100",
      "correct_answer": 3,
      "skill_id": 207,
      "difficulty_id": 2,
      "explanation": "Adults = 316 + 503 = 819, which is 100% - 91% = 9% of all participants. So 9% = 819, meaning 1% = 91, and 100% = 9100. Answer: 9100.",
      "hints": ["Children are 91%, so adults (men + women) make up 9%.", "Adults = 316 + 503 = 819 = 9%; total = 819 / 9 x 100 = 9100."],
      "source": "ACS Junior 2025 P6 WA1 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q5 = option 4 (9100)."
    },
    {
      "n": 6,
      "type_id": 1,
      "question": "The ratio of Ahmad's savings to Ben's savings is 2 : 3. The ratio of Ahmad's savings to Chong's savings is 3 : 5. What is the ratio of Ben's savings to Chong's savings?",
      "answer0": "2 : 5",
      "answer1": "3 : 5",
      "answer2": "5 : 8",
      "answer3": "9 : 10",
      "correct_answer": 3,
      "skill_id": 178,
      "difficulty_id": 2,
      "explanation": "Make Ahmad's terms equal. A : B = 2 : 3 = 6 : 9; A : C = 3 : 5 = 6 : 10. So B : C = 9 : 10. Answer: 9 : 10.",
      "hints": ["Make Ahmad's value the same in both ratios (LCM of 2 and 3 = 6).", "A:B = 6:9 and A:C = 6:10, so B:C = 9:10."],
      "source": "ACS Junior 2025 P6 WA1 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q6 = option 4 (9 : 10)."
    },
    {
      "n": 7,
      "type_id": 1,
      "question": "Mariam was given \\(\\dfrac{3}{8}\\) of a cake and Nathan was given \\(\\dfrac{3}{10}\\) of the remaining cake. The rest of the cake was shared equally between their two friends. What fraction of the cake did each friend get?",
      "answer0": "\\(\\dfrac{3}{16}\\)",
      "answer1": "\\(\\dfrac{7}{16}\\)",
      "answer2": "\\(\\dfrac{7}{32}\\)",
      "answer3": "\\(\\dfrac{9}{32}\\)",
      "correct_answer": 2,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Remaining after Mariam = \\(1 - \\dfrac{3}{8} = \\dfrac{5}{8}\\). Nathan took \\(\\dfrac{3}{10} \\times \\dfrac{5}{8} = \\dfrac{15}{80} = \\dfrac{3}{16}\\). Left = \\(\\dfrac{5}{8} - \\dfrac{3}{16} = \\dfrac{10}{16} - \\dfrac{3}{16} = \\dfrac{7}{16}\\). Each friend got \\(\\dfrac{7}{16} \\div 2 = \\dfrac{7}{32}\\). Answer: \\(\\dfrac{7}{32}\\).",
      "hints": ["After Mariam, 5/8 remains; Nathan takes 3/10 of that = 3/16.", "Remaining 7/16 is split between 2 friends: 7/16 / 2 = 7/32 each."],
      "source": "ACS Junior 2025 P6 WA1 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q7 = option 3 (7/32)."
    },
    {
      "n": 8,
      "type_id": 2,
      "question": "A piece of cloth is 6 m long. Kelly cut it into smaller pieces of length \\(\\dfrac{1}{8}\\) m to make rags. How many pieces of rags did she get? [?]",
      "answer0": "48",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 206,
      "difficulty_id": 1,
      "explanation": "Number of pieces = \\(6 \\div \\dfrac{1}{8} = 6 \\times 8 = 48\\). Answer: 48.",
      "hints": ["Divide the total length by the length of each piece.", "6 / (1/8) = 6 x 8 = 48 pieces."],
      "source": "ACS Junior 2025 P6 WA1 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q8 = 48."
    },
    {
      "n": 9,
      "type_id": 2,
      "question": "27 : [?] : 54 = 3 : 7 : 6",
      "answer0": "63",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 178,
      "difficulty_id": 1,
      "explanation": "27 corresponds to 3, so the multiplier is \\(27 \\div 3 = 9\\) (check: \\(6 \\times 9 = 54\\), correct). The middle term = \\(7 \\times 9 = 63\\). Answer: 63.",
      "hints": ["27 maps to 3, so each part is multiplied by 9.", "Middle term = 7 x 9 = 63."],
      "source": "ACS Junior 2025 P6 WA1 Q9",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q9 = 63. The box is the answer-entry blank ([?]); the 27, 54 and 3:7:6 are given."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "Find the value of \\(7840 \\div 40\\). [?]",
      "answer0": "196",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 151,
      "difficulty_id": 1,
      "explanation": "\\(7840 \\div 40 = 784 \\div 4 = 196\\). Answer: 196.",
      "hints": ["Divide both 7840 and 40 by 10 first: 784 / 4.", "784 / 4 = 196."],
      "source": "ACS Junior 2025 P6 WA1 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q10 = 196."
    },
    {
      "n": 11,
      "type_id": 2,
      "question": "In a class of 40 students, 15 students take the school bus to school. What percentage of the students take the school bus to school? [?]%",
      "answer0": "37.5",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 171,
      "difficulty_id": 1,
      "explanation": "Percentage = \\(\\dfrac{15}{40} \\times 100\\% = 37.5\\%\\). Answer: 37.5%.",
      "hints": ["Percentage = (part / whole) x 100%.", "15 / 40 x 100% = 37.5%."],
      "source": "ACS Junior 2025 P6 WA1 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q11 = 37.5%. Answer entered as a decimal (37.5)."
    },
    {
      "n": 12,
      "type_id": 1,
      "question": "The ratio of the length of a rectangle to its breadth is 4 : 3. Express the length of the rectangle as a fraction of its perimeter. Give your answer in its simplest form.",
      "answer0": "\\(\\dfrac{2}{7}\\)",
      "answer1": "\\(\\dfrac{4}{7}\\)",
      "answer2": "\\(\\dfrac{4}{3}\\)",
      "answer3": "\\(\\dfrac{4}{14}\\)",
      "correct_answer": 0,
      "skill_id": 210,
      "difficulty_id": 2,
      "explanation": "Length = 4u, breadth = 3u. Perimeter = 2(4u + 3u) = 14u. Length / perimeter = \\(\\dfrac{4u}{14u} = \\dfrac{2}{7}\\). Answer: \\(\\dfrac{2}{7}\\).",
      "hints": ["Let length = 4 units, breadth = 3 units; perimeter = 2(4+3) = 14 units.", "Length / perimeter = 4/14 = 2/7."],
      "source": "ACS Junior 2025 P6 WA1 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q12 = 2/7. Made MCQ because the answer is a fraction (FIB is integer/decimal only)."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "\\(\\dfrac{2}{9}\\) of a number is 50. What is the \\(\\dfrac{1}{5}\\) of the number? [?]",
      "answer0": "45",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "If \\(\\dfrac{2}{9}\\) of the number is 50, the number = \\(50 \\div \\dfrac{2}{9} = 50 \\times \\dfrac{9}{2} = 225\\). Then \\(\\dfrac{1}{5}\\) of 225 = 45. Answer: 45.",
      "hints": ["First find the whole number: 50 / (2/9) = 225.", "1/5 of 225 = 45."],
      "source": "ACS Junior 2025 P6 WA1 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q13 = 45."
    },
    {
      "n": 14,
      "type_id": 2,
      "question": "Mason and Peter had a total of 210 stickers. Mason had 6 times as many stickers as Peter. How many more stickers did Mason have than Peter? [?]",
      "answer0": "150",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Total units = 6 + 1 = 7 units = 210, so 1 unit = 30. Difference = 6 - 1 = 5 units = 5 x 30 = 150. Answer: 150.",
      "hints": ["Mason = 6 units, Peter = 1 unit, total 7 units = 210, so 1 unit = 30.", "Difference = 5 units = 5 x 30 = 150."],
      "source": "ACS Junior 2025 P6 WA1 Q14",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q14 = 150."
    },
    {
      "n": 15,
      "type_id": 2,
      "question": "ABC Mega Mall had a storewide sale of 70%. Mrs Suresh paid $570 for a laptop during the sale. What was the usual price of the laptop? $[?]",
      "answer0": "1900",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "A 70% discount means she paid 30% of the usual price. 30% = $570, so 1% = $19 and 100% = $1900. Answer: $1900.",
      "hints": ["A 70% sale means she paid 100% - 70% = 30% of the usual price.", "30% = $570, so usual price = $570 / 30 x 100 = $1900."],
      "source": "ACS Junior 2025 P6 WA1 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q15 = $1900."
    },
    {
      "n": 16,
      "type_id": 1,
      "question": "The table shows the prices of 3 rice dishes. Uncle Roger ordered two different types of rice dishes and paid a total of $13.08, including 9% GST. Which 2 rice dishes did he order?<br>Chicken Rice $5.00<br>Duck Rice $6.00<br>Fried Rice $7.00",
      "answer0": "Chicken Rice and Fried Rice",
      "answer1": "Chicken Rice and Duck Rice",
      "answer2": "Duck Rice and Fried Rice",
      "answer3": "Chicken Rice and Chicken Rice",
      "correct_answer": 0,
      "skill_id": 176,
      "difficulty_id": 2,
      "explanation": "Total before GST = \\($13.08 \\div 1.09 = $12.00\\). Two different dishes summing to $12.00: Chicken Rice ($5.00) + Fried Rice ($7.00) = $12.00. Answer: Chicken Rice and Fried Rice.",
      "hints": ["Remove the 9% GST: $13.08 / 1.09 = $12.00 before GST.", "Two different dishes adding to $12.00 are Chicken Rice ($5) and Fried Rice ($7)."],
      "source": "ACS Junior 2025 P6 WA1 Q16",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q16 = Chicken Rice and Fried Rice. Originally a two-blank fill-in; made MCQ because the answer is a pair of dish names (word answers are fragile as FIB). Prices embedded in stem since the table is plain text."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Ali, Ben and Carl shared 390 stamps. Each of them received another 44 stamps. In the end, the ratio of the number of stamps shared by Ali, Ben and Carl was 2 : 3 : 4. How many stamps did Carl have in the end? [?]",
      "answer0": "232",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Total at the end = 390 + (3 x 44) = 522 stamps. Ratio 2 : 3 : 4 has 9 units, so 1 unit = 522 / 9 = 58. Carl = 4 units = 4 x 58 = 232. Answer: 232.",
      "hints": ["Total in the end = 390 + 3 x 44 = 522 stamps; ratio total = 2+3+4 = 9 units.", "1 unit = 522 / 9 = 58; Carl = 4 units = 232."],
      "source": "ACS Junior 2025 P6 WA1 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q17 working: 9u = 522, u = 58, 58 x 4 = 232."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Mrs Lee bought some muffins from a shop. The cost of each muffin is $2. For every 4 muffins she bought, 1 muffin was given free. Mrs Lee paid $252 altogether. What was the greatest number of muffins Mrs Lee would get from the shop? [?]",
      "answer0": "157",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "She paid for $252 / $2 = 126 muffins. Bundles: every 4 paid muffins give 1 free, so each group of 4 paid = 5 muffins. 126 / 4 = 31 groups remainder 2. 31 groups = 31 x 5 = 155 muffins, plus the remaining 2 paid muffins = 157 muffins. Answer: 157.",
      "hints": ["Paid muffins = $252 / $2 = 126.", "Per 4 paid muffins, get 1 free (5 total): 126 = 31 x 4 + 2, so 31 x 5 + 2 = 157."],
      "source": "ACS Junior 2025 P6 WA1 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q18 working: 252/2 = 126 paid; 4x2=8 ($8 per bundle of 5); 252/8 = 31 R4; 31x5 = 155; 155+2 = 157."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "The figure shows Oval A overlapping Oval B. The ratio of the area of Oval A to the shaded area is 7 : 1. The ratio of the area of Oval B to the shaded area is 9 : 2. The area of the shaded area is 8 cm². Find the area of the whole figure. [?]",
      "answer0": "84",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 221,
      "difficulty_id": 3,
      "explanation": "Shaded = 8 cm². Oval A : shaded = 7 : 1, so Oval A = 7 x 8 = 56 cm². Oval B : shaded = 9 : 2, so 2 units = 8 cm² (1 unit = 4 cm²), Oval B = 9 x 4 = 36 cm². Whole figure = Oval A + Oval B - shaded (counted once) = 56 + 36 - 8 = 84 cm². Answer: 84 cm².",
      "hints": ["Oval A = 7 x shaded = 56 cm²; Oval B: 2 units = 8, so Oval B = 9 x 4 = 36 cm².", "Whole figure = A + B - overlap = 56 + 36 - 8 = 84 cm²."],
      "source": "ACS Junior 2025 P6 WA1 Q19",
      "image_needed": true,
      "image_options": false,
      "image_file": "q19.png",
      "image_page": 10,
      "image_bbox": [0.26, 0.18, 0.47, 0.27],
      "image_loc": "two overlapping ovals labelled A and B with a hatched (shaded) overlap region, upper-left below the question text on page 10",
      "notes": "Key: Q19 working: 2u = 8 cm², u = 4 cm², total 21u x 4 = 84 cm². Answer in units = 84 (cm²)."
    },
    {
      "n": 20,
      "type_id": 2,
      "question": "A bookshop had 654 more pencils than erasers. After \\(\\dfrac{2}{3}\\) of the pencils and \\(\\dfrac{1}{2}\\) of the erasers were sold, the total number of pencils and erasers left was 508. How many pencils and erasers did the bookshop have at first? [?]",
      "answer0": "1350",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Let erasers = E, pencils = E + 654. Pencils left = \\(\\dfrac{1}{3}(E + 654)\\); erasers left = \\(\\dfrac{1}{2}E\\). Sum = \\(\\dfrac{1}{3}(E + 654) + \\dfrac{1}{2}E = 508\\). Multiply by 6: \\(2(E + 654) + 3E = 3048\\); \\(2E + 1308 + 3E = 3048\\); \\(5E = 1740\\); \\(E = 348\\). Pencils = 348 + 654 = 1002. Total at first = 348 + 1002 = 1350. Answer: 1350.",
      "hints": ["Let erasers = E, pencils = E + 654; pencils left = 1/3 of pencils, erasers left = 1/2 of erasers.", "1/3(E+654) + 1/2 E = 508 gives E = 348, pencils = 1002, total = 1350."],
      "source": "ACS Junior 2025 P6 WA1 Q20",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "notes": "Key: Q20 = 1350."
    }
  ]
}