{
  "source_prefix": "Maris Stella 2024 P6 Prelim",
  "models": [
    {
      "n": 12,
      "answer": "90",
      "answer_matches_key": true,
      "working": "The 60 blue chairs do not change. Since red becomes 60% of the total, blue is 40% (4 units). 4 units \\(= 60\\), so 1 unit \\(= 15\\) and the total \\(= 10\\) units \\(= 150\\). Red chairs \\(= 150 - 60 = 90\\).",
      "spec": {
        "unit_px": 60,
        "bars": [
          {"label": "Blue", "segments": [
            {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}],
           "brace": {"text": "60 (40%)"}},
          {"label": "Red", "segments": [
            {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}],
           "brace": {"text": "? (60%)"}}
        ],
        "total": {"text": "150 chairs", "bars": [0, 1]}
      }
    },
    {
      "n": 21,
      "answer": "11",
      "answer_matches_key": true,
      "working": "The two whole numbers have sum 19 and product 60, so they are 15 and 4 (\\(15 \\times 4 = 60\\), \\(15 + 4 = 19\\)). Drawing them as two bars, the difference \\(= 15 - 4 = 11\\).",
      "spec": {
        "unit_px": 30,
        "bars": [
          {"label": "Larger", "segments": [{"u": 4, "text": "4", "fill": "#dbe9ff"}, {"u": 11, "text": "?", "fill": "#dbe9ff"}]},
          {"label": "Smaller", "segments": [{"u": 4, "text": "4", "fill": "#ffe7c2"}]}
        ],
        "total": {"text": "sum = 19", "bars": [0, 1]}
      }
    },
    {
      "n": 25,
      "answer": "\\($12\\)",
      "answer_matches_key": true,
      "working": "Ali spent \\(\\dfrac{3}{5}\\), so he kept \\(\\dfrac{2}{5}\\) (2 units) \\(= \\$72\\); 1 unit \\(= \\$36\\) and Ali had 5 units \\(= \\$180\\). Bala spent \\(\\dfrac{4}{7}\\), so he kept \\(\\dfrac{3}{7}\\) (3 units) \\(= \\$72\\); 1 unit \\(= \\$24\\) and Bala had 7 units \\(= \\$168\\). Difference \\(= 180 - 168 = \\$12\\).",
      "spec": {
        "unit_px": 78,
        "bars": [
          {"label": "Ali", "segments": [
            {"u": 1, "fill": "#ffd6d6"}, {"u": 1, "fill": "#ffd6d6"}, {"u": 1, "fill": "#ffd6d6"},
            {"u": 1, "text": "$72", "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}],
           "brace": {"text": "$180"}},
          {"label": "Bala", "segments": [
            {"u": 1, "fill": "#ffd6d6"}, {"u": 1, "fill": "#ffd6d6"}, {"u": 1, "fill": "#ffd6d6"}, {"u": 1, "fill": "#ffd6d6"},
            {"u": 1, "text": "$72", "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}],
           "brace": {"text": "$168"}}
        ]
      }
    },
    {
      "n": 29,
      "answer": "96",
      "answer_matches_key": true,
      "working": "Picture the number as 24 equal units. Dividing by 8 gives 3 units; dividing by 6 gives 4 units. The wrong answer is 1 unit more than the correct one, and that 1 unit \\(= 4\\). So the number \\(= 24\\) units \\(= 24 \\times 4 = 96\\).",
      "spec": {
        "unit_px": 22,
        "bars": [
          {"label": "\\(\\div 8\\)", "segments": [
            {"u": 8, "fill": "#dbe9ff"}, {"u": 8, "fill": "#dbe9ff"}, {"u": 8, "fill": "#dbe9ff"}],
           "brace": {"text": "3 units"}},
          {"label": "\\(\\div 6\\)", "segments": [
            {"u": 6, "fill": "#ffe7c2"}, {"u": 6, "fill": "#ffe7c2"}, {"u": 6, "fill": "#ffe7c2"}, {"u": 6, "text": "4", "fill": "#ffd6d6"}],
           "brace": {"text": "4 units (extra unit = 4)"}}
        ],
        "total": {"text": "number = 24 units = 96", "bars": [0, 1]}
      }
    },
    {
      "n": 40,
      "answer": "688",
      "answer_matches_key": true,
      "working": "Total boys \\(= 2298 - 1118 = 1180\\). Girls in School B are \\(\\dfrac{5}{8}\\) of girls in School A, so split the 1118 girls into \\(8 + 5 = 13\\) equal units. 13 units \\(= 1118\\), 1 unit \\(= 86\\). Girls in School A \\(= 8\\) units \\(= 688\\). (Boys + girls in School A \\(= 637 + 688 = 1325\\).)",
      "spec": {
        "unit_px": 60,
        "bars": [
          {"label": "Girls A", "segments": [
            {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"},
            {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}],
           "brace": {"text": "? (8 units)"}},
          {"label": "Girls B", "segments": [
            {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}],
           "brace": {"text": "5 units"}}
        ],
        "total": {"text": "1118 girls", "bars": [0, 1]}
      }
    },
    {
      "n": 42,
      "answer": "18",
      "answer_matches_key": true,
      "working": "Total height over the 4 months \\(= 16.5 \\times 4 = 66\\) cm. From the graph the heights are in the ratio \\(2 : 3 : 6 : 11\\) (Jan : Feb : Mar : Apr), a total of \\(2 + 3 + 6 + 11 = 22\\) units. 22 units \\(= 66\\) cm, so 1 unit \\(= 3\\) cm. March \\(= 6\\) units \\(= 18\\) cm.",
      "spec": {
        "unit_px": 26,
        "bars": [
          {"label": "Jan", "segments": [{"u": 2, "fill": "#dbe9ff"}], "brace": {"text": "2u"}},
          {"label": "Feb", "segments": [{"u": 3, "fill": "#dbe9ff"}], "brace": {"text": "3u"}},
          {"label": "Mar", "segments": [{"u": 6, "text": "?", "fill": "#ffe7c2"}], "brace": {"text": "6u"}},
          {"label": "Apr", "segments": [{"u": 11, "fill": "#dbe9ff"}], "brace": {"text": "11u"}}
        ],
        "total": {"text": "total = 66 cm (22 units)", "bars": [0, 1, 2, 3]}
      }
    },
    {
      "n": 45,
      "answer": "90",
      "answer_matches_key": true,
      "working": "Children boys : girls \\(= 10 : 7\\), so \\(10 + 7 = 17\\) units. Each child paid \\$12, so 17 units \\(= 17 \\times \\$12 = \\$204\\); number of groups \\(= 4692 \\div 204 = 23\\). Boys \\(= 23 \\times 10 = 230\\). For part (b) males : females \\(= 8 : 5\\); the \\(8 - 5 = 3\\)-unit difference equals 54 more men than women, so 1 unit \\(= 18\\). Females \\(= 5\\) units \\(= 90\\) (key reports 90).",
      "spec": {
        "unit_px": 26,
        "bars": [
          {"label": "Males", "segments": [
            {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"},
            {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}, {"u": 1, "fill": "#dbe9ff"}],
           "brace": {"text": "8 units"}},
          {"label": "Females", "segments": [
            {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}, {"u": 1, "fill": "#ffe7c2"}],
           "brace": {"text": "? = 5 units"}}
        ],
        "total": {"text": "difference = 3 units = 54", "bars": [0]}
      }
    },
    {
      "n": 47,
      "answer": "67",
      "answer_matches_key": true,
      "working": "Match the 20¢ coins with an equal number of 10¢ coins; the 10¢ bar has 34 extra coins worth \\(34 \\times 10\\text{¢} = 340\\text{¢} = \\$3.40\\). Remove that: \\(\\$13.30 - \\$3.40 = \\$9.90\\). The matched coins cost \\(10\\text{¢} + 20\\text{¢} = 30\\text{¢}\\) per pair, so pairs \\(= \\$9.90 \\div \\$0.30 = 33\\). Number of 10¢ coins \\(= 33 + 34 = 67\\).",
      "spec": {
        "unit_px": 22,
        "bars": [
          {"label": "10¢ coins", "segments": [
            {"u": 6, "fill": "#dbe9ff"}, {"u": 4, "text": "+34 = $3.40", "fill": "#ffd6d6"}],
           "brace": {"text": "67 coins"}},
          {"label": "20¢ coins", "segments": [{"u": 6, "fill": "#ffe7c2"}], "brace": {"text": "33 coins"}}
        ],
        "total": {"text": "10¢ + 20¢ value = $13.30", "bars": [0, 1]}
      }
    }
  ]
}