{
  "Id": "7ad1e666-5ed0-483d-ad97-b6fe6bcfb2fb",
  "Title": "Playing With Numbers: Class 6 Mixed Practice",
  "Subject": "Mathematics",
  "Topic": "Number systems, numeration, factors and multiples, properties, and Roman numerals",
  "Instructions": "Read each question carefully and answer to the best of your ability. Show all working for word problems.",
  "EstimatedMinutes": 45,
  "StudentProfileId": "dd186faa-f489-46ee-84e4-26e2d01e2691",
  "SourceFileName": "manual-input",
  "SessionMaterialId": "1709fa47-6ae0-4890-aa7c-914f6f2e622b",
  "GeneratedAt": "2026-09-07T23:50:10.945188Z",
  "Questions": [
    {
      "Id": 1,
      "Type": "true_false",
      "Text": "Zero is a whole number.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 2,
      "Type": "true_false",
      "Text": "In the set of whole numbers, 0 has a predecessor.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 3,
      "Type": "true_false",
      "Text": "Addition of whole numbers is commutative.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 4,
      "Type": "true_false",
      "Text": "Subtraction of whole numbers is associative.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 5,
      "Type": "true_false",
      "Text": "Whole numbers are closed under multiplication.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 6,
      "Type": "true_false",
      "Text": "In the Indian system, the number 12,34,567 is correctly grouped with commas.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 7,
      "Type": "true_false",
      "Text": "The number 1 is a prime number.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 8,
      "Type": "true_false",
      "Text": "Every even number is divisible by 4.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 9,
      "Type": "true_false",
      "Text": "999 rounded to the nearest thousand is 1000.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 10,
      "Type": "true_false",
      "Text": "A number is divisible by 3 if the sum of its digits is a multiple of 3.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 11,
      "Type": "multiple_choice",
      "Text": "Which number is the greatest?",
      "Options": [
        "A. 607",
        "B. 670",
        "C. 706",
        "D. 760"
      ],
      "Answer": "D. 760",
      "Points": 2
    },
    {
      "Id": 12,
      "Type": "multiple_choice",
      "Text": "In 3,58,241 (Indian system), the place value of the digit 5 is:",
      "Options": [
        "A. 5,000",
        "B. 50,000",
        "C. 500",
        "D. 5,00,000"
      ],
      "Answer": "B. 50,000",
      "Points": 2
    },
    {
      "Id": 13,
      "Type": "multiple_choice",
      "Text": "Write 27,05,300 (Indian system) in the International system.",
      "Options": [
        "A. 270,530",
        "B. 2,705,300",
        "C. 27,053,00",
        "D. 27,530,0"
      ],
      "Answer": "B. 2,705,300",
      "Points": 2
    },
    {
      "Id": 14,
      "Type": "multiple_choice",
      "Text": "Round 46,372 to the nearest 1,000.",
      "Options": [
        "A. 46,300",
        "B. 46,000",
        "C. 47,000",
        "D. 46,500"
      ],
      "Answer": "B. 46,000",
      "Points": 2
    },
    {
      "Id": 15,
      "Type": "multiple_choice",
      "Text": "Evaluate: 18 \u2212 [6 \u002B 2 \u00D7 (7 \u2212 4)]",
      "Options": [
        "A. 0",
        "B. 3",
        "C. 6",
        "D. 12"
      ],
      "Answer": "C. 6",
      "Points": 2
    },
    {
      "Id": 16,
      "Type": "multiple_choice",
      "Text": "Which is the correct Roman numeral for 90?",
      "Options": [
        "A. IC",
        "B. LXXXX",
        "C. XC",
        "D. VC"
      ],
      "Answer": "C. XC",
      "Points": 2
    },
    {
      "Id": 17,
      "Type": "multiple_choice",
      "Text": "Which of the following is a prime number?",
      "Options": [
        "A. 77",
        "B. 97",
        "C. 91",
        "D. 121"
      ],
      "Answer": "B. 97",
      "Points": 2
    },
    {
      "Id": 18,
      "Type": "multiple_choice",
      "Text": "Which number is divisible by 9?",
      "Options": [
        "A. 7,245",
        "B. 8,137",
        "C. 9,114",
        "D. 7,001"
      ],
      "Answer": "A. 7,245",
      "Points": 2
    },
    {
      "Id": 19,
      "Type": "multiple_choice",
      "Text": "The HCF of 36 and 60 is:",
      "Options": [
        "A. 6",
        "B. 12",
        "C. 18",
        "D. 24"
      ],
      "Answer": "B. 12",
      "Points": 2
    },
    {
      "Id": 20,
      "Type": "multiple_choice",
      "Text": "How many 4-digit numbers exist?",
      "Options": [
        "A. 900",
        "B. 999",
        "C. 9,000",
        "D. 10,000"
      ],
      "Answer": "C. 9,000",
      "Points": 2
    },
    {
      "Id": 21,
      "Type": "fill_blank",
      "Text": "Zero is the smallest _____ number.",
      "Options": [],
      "Answer": "whole",
      "Points": 2
    },
    {
      "Id": 22,
      "Type": "fill_blank",
      "Text": "The successor of 4,999 is _____.",
      "Options": [],
      "Answer": "5000",
      "Points": 2
    },
    {
      "Id": 23,
      "Type": "fill_blank",
      "Text": "In the Indian system, 1,00,000 is called one _____.",
      "Options": [],
      "Answer": "lakh",
      "Points": 2
    },
    {
      "Id": 24,
      "Type": "fill_blank",
      "Text": "The additive identity for whole numbers is _____.",
      "Options": [],
      "Answer": "0",
      "Points": 2
    },
    {
      "Id": 25,
      "Type": "fill_blank",
      "Text": "300 \u002B 20 \u002B 5 in standard form is _____.",
      "Options": [],
      "Answer": "325",
      "Points": 2
    },
    {
      "Id": 26,
      "Type": "fill_blank",
      "Text": "A number divisible by 2 and 5 is always divisible by _____.",
      "Options": [],
      "Answer": "10",
      "Points": 2
    },
    {
      "Id": 27,
      "Type": "fill_blank",
      "Text": "The prime factorization of 84 is 2 \u00D7 2 \u00D7 3 \u00D7 _____.",
      "Options": [],
      "Answer": "7",
      "Points": 2
    },
    {
      "Id": 28,
      "Type": "fill_blank",
      "Text": "In Roman numerals, 40 is written as _____.",
      "Options": [],
      "Answer": "XL",
      "Points": 2
    },
    {
      "Id": 29,
      "Type": "fill_blank",
      "Text": "The place value of 9 in 5,19,804 (Indian system) is _____.",
      "Options": [],
      "Answer": "9000",
      "Points": 2
    },
    {
      "Id": 30,
      "Type": "fill_blank",
      "Text": "On a number line, moving 7 units left from 15 lands on _____.",
      "Options": [],
      "Answer": "8",
      "Points": 2
    },
    {
      "Id": 31,
      "Type": "word_problem",
      "Text": "On Saturday, 48,376 people visited a fair, and on Sunday, 51,942 people visited. Estimate the total number of visitors to the nearest thousand. Show your working.",
      "Options": [],
      "Answer": "Step 1: Round each to the nearest 1,000: 48,376 \u2192 48,000 and 51,942 \u2192 52,000\nStep 2: Add the rounded numbers: 48,000 \u002B 52,000 = 100,000\nAnswer: Approximately 100,000 visitors",
      "Points": 5
    },
    {
      "Id": 32,
      "Type": "word_problem",
      "Text": "A teacher has 84 pencils and 126 erasers. She wants to make identical sets with no items left over. What is the maximum number of sets she can make, and how many pencils and erasers will each set contain? Show your working.",
      "Options": [],
      "Answer": "Step 1: Prime factorize: 84 = 2 \u00D7 2 \u00D7 3 \u00D7 7; 126 = 2 \u00D7 3 \u00D7 3 \u00D7 7\nStep 2: HCF = 2 \u00D7 3 \u00D7 7 = 42\nStep 3: Number of sets = 42; Pencils per set = 84 \u00F7 42 = 2; Erasers per set = 126 \u00F7 42 = 3\nAnswer: 42 sets; each set has 2 pencils and 3 erasers",
      "Points": 5
    },
    {
      "Id": 33,
      "Type": "word_problem",
      "Text": "Two shuttle buses leave a station at 8:00 AM. One returns every 12 minutes and the other every 15 minutes. At what time will they next arrive together? Show your working.",
      "Options": [],
      "Answer": "Step 1: Find LCM of 12 and 15: 12 = 2^2 \u00D7 3; 15 = 3 \u00D7 5 \u2192 LCM = 2^2 \u00D7 3 \u00D7 5 = 60\nStep 2: Add 60 minutes to 8:00 AM \u2192 9:00 AM\nAnswer: 9:00 AM",
      "Points": 5
    },
    {
      "Id": 34,
      "Type": "word_problem",
      "Text": "What is the least number that must be subtracted from 5,237 to make it divisible by 6? Show your working.",
      "Options": [],
      "Answer": "Step 1: For divisibility by 6, the number must be even and the sum of digits must be a multiple of 3\nStep 2: Try subtracting the smallest numbers:\n- 5,237 \u2212 1 = 5,236 (even), sum = 5\u002B2\u002B3\u002B6 = 16 (not multiple of 3)\n- 5,237 \u2212 2 = 5,235 (odd)\n- 5,237 \u2212 3 = 5,234 (even), sum = 14 (not multiple of 3)\n- 5,237 \u2212 4 = 5,233 (odd)\n- 5,237 \u2212 5 = 5,232 (even), sum = 5\u002B2\u002B3\u002B2 = 12 (multiple of 3)\nAnswer: 5",
      "Points": 5
    },
    {
      "Id": 35,
      "Type": "word_problem",
      "Text": "Find the LCM of 48 and 180 using prime factorization. Show your working.",
      "Options": [],
      "Answer": "Step 1: Prime factorize: 48 = 2^4 \u00D7 3; 180 = 2^2 \u00D7 3^2 \u00D7 5\nStep 2: Take highest powers: LCM = 2^4 \u00D7 3^2 \u00D7 5 = 16 \u00D7 9 \u00D7 5\nStep 3: Compute: 16 \u00D7 9 = 144; 144 \u00D7 5 = 720\nAnswer: 720",
      "Points": 5
    },
    {
      "Id": 36,
      "Type": "word_problem",
      "Text": "A shop calculates a bill as (250 \u002B 75) \u00D7 4 \u2212 180. Find the final amount. Show your working.",
      "Options": [],
      "Answer": "Step 1: Evaluate inside brackets: 250 \u002B 75 = 325\nStep 2: Multiply: 325 \u00D7 4 = 1,300\nStep 3: Subtract: 1,300 \u2212 180 = 1,120\nAnswer: 1,120",
      "Points": 5
    },
    {
      "Id": 37,
      "Type": "word_problem",
      "Text": "Convert the number 2,019 to Roman numerals. Show your working.",
      "Options": [],
      "Answer": "Step 1: Decompose 2,019 = 2,000 \u002B 10 \u002B 9\nStep 2: Convert each part: 2,000 = MM; 10 = X; 9 = IX\nStep 3: Combine: MM \u002B X \u002B IX = MMXIX\nAnswer: MMXIX",
      "Points": 5
    },
    {
      "Id": 38,
      "Type": "word_problem",
      "Text": "Write 4,57,20,608 (Indian system) in the International system with commas. Show your working.",
      "Options": [],
      "Answer": "Step 1: Interpret Indian groups: 4 crore = 40,000,000; 57 lakh = 5,700,000; 20 thousand = 20,000; plus 608\nStep 2: Add: 40,000,000 \u002B 5,700,000 = 45,700,000; \u002B20,000 = 45,720,000; \u002B608 = 45,720,608\nAnswer: 45,720,608",
      "Points": 5
    },
    {
      "Id": 39,
      "Type": "word_problem",
      "Text": "On a number line, starting at 0, make 5 jumps of 7 units to the right, then 3 jumps of 4 units to the left. Where do you land? Show your working.",
      "Options": [],
      "Answer": "Step 1: Rightward movement: 5 \u00D7 7 = 35 \u2192 position 35\nStep 2: Leftward movement: 3 \u00D7 4 = 12 \u2192 move to 35 \u2212 12\nStep 3: Compute: 35 \u2212 12 = 23\nAnswer: 23",
      "Points": 5
    },
    {
      "Id": 40,
      "Type": "word_problem",
      "Text": "In the 3\u00D73 grid below, a supercell is a number larger than all of its existing neighbors directly above, below, left, and right. Grid:\n12  35  18\n44  29  31\n27  33  20\nIdentify all supercells. Show your working.",
      "Options": [],
      "Answer": "Step 1: Check 35 (top middle): neighbors 12 (left), 18 (right), 29 (down) \u2192 35 \u003E 12, 18, 29 \u2192 supercell\nStep 2: Check 44 (middle left): neighbors 35 (right), 12 (up), 27 (down) \u2192 44 \u003E 35, 12, 27 \u2192 supercell\nStep 3: Check 31 (middle right): neighbors 29 (left), 18 (up), 20 (down) \u2192 31 \u003E 29, 18, 20 \u2192 supercell\nStep 4: Check 33 (bottom middle): neighbors 27 (left), 20 (right), 29 (up) \u2192 33 \u003E 27, 20, 29 \u2192 supercell\nAnswer: Supercells are 35, 44, 31, and 33",
      "Points": 5
    }
  ],
  "TotalPoints": 100
}