{
  "Id": "69a3a51b-af9f-4618-8f4b-89c97b2cd583",
  "Title": "Playing with Numbers: Place Value, Divisibility, and Number Sense \u2014 Practice Set",
  "Subject": "Mathematics",
  "Topic": "Whole numbers, place value, divisibility, factors and multiples (Class 6)",
  "Instructions": "Read each question carefully and answer to the best of your ability. Show all working for word problems.",
  "EstimatedMinutes": 35,
  "StudentProfileId": "dd186faa-f489-46ee-84e4-26e2d01e2691",
  "SourceFileName": "manual-input",
  "SessionMaterialId": "1709fa47-6ae0-4890-aa7c-914f6f2e622b",
  "GeneratedAt": "2026-08-16T10:15:43.657894Z",
  "Questions": [
    {
      "Id": 1,
      "Type": "true_false",
      "Text": "Zero is a whole number but not a natural number.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 2,
      "Type": "true_false",
      "Text": "The successor of 9,999 is 10,000.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 3,
      "Type": "true_false",
      "Text": "Whole numbers are closed under subtraction.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 4,
      "Type": "true_false",
      "Text": "In the Indian system, 1,00,000 is called one lakh.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 5,
      "Type": "true_false",
      "Text": "The Roman numeral XL represents 60.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 6,
      "Type": "true_false",
      "Text": "Every prime number greater than 2 is odd.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 7,
      "Type": "true_false",
      "Text": "If a number is divisible by 9, it is always divisible by 3.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 8,
      "Type": "true_false",
      "Text": "The number 1 has exactly two distinct factors.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 9,
      "Type": "true_false",
      "Text": "The additive identity for whole numbers is 1.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 10,
      "Type": "true_false",
      "Text": "Multiplication of whole numbers is commutative.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 11,
      "Type": "multiple_choice",
      "Text": "Which of the following is the greatest number?",
      "Options": [
        "A. 705,200",
        "B. 750,020",
        "C. 700,520",
        "D. 705,020"
      ],
      "Answer": "B. 750,020",
      "Points": 2
    },
    {
      "Id": 12,
      "Type": "multiple_choice",
      "Text": "In 403,506, what is the value of the digit 5?",
      "Options": [
        "A. 5",
        "B. 50",
        "C. 500",
        "D. 5,000"
      ],
      "Answer": "C. 500",
      "Points": 2
    },
    {
      "Id": 13,
      "Type": "multiple_choice",
      "Text": "Which number is divisible by 6?",
      "Options": [
        "A. 234",
        "B. 245",
        "C. 253",
        "D. 261"
      ],
      "Answer": "A. 234",
      "Points": 2
    },
    {
      "Id": 14,
      "Type": "multiple_choice",
      "Text": "Which Roman numeral equals 94?",
      "Options": [
        "A. LXLIV",
        "B. XCIV",
        "C. IC",
        "D. XCVIV"
      ],
      "Answer": "B. XCIV",
      "Points": 2
    },
    {
      "Id": 15,
      "Type": "multiple_choice",
      "Text": "The LCM of 12 and 15 is:",
      "Options": [
        "A. 30",
        "B. 45",
        "C. 60",
        "D. 120"
      ],
      "Answer": "C. 60",
      "Points": 2
    },
    {
      "Id": 16,
      "Type": "multiple_choice",
      "Text": "Which of the following is a composite number?",
      "Options": [
        "A. 29",
        "B. 31",
        "C. 37",
        "D. 39"
      ],
      "Answer": "D. 39",
      "Points": 2
    },
    {
      "Id": 17,
      "Type": "multiple_choice",
      "Text": "Starting at 0 on a number line, you make 4 jumps of size 7 to the right. Where do you land?",
      "Options": [
        "A. 21",
        "B. 28",
        "C. 35",
        "D. 42"
      ],
      "Answer": "B. 28",
      "Points": 2
    },
    {
      "Id": 18,
      "Type": "multiple_choice",
      "Text": "Round 8,649 to the nearest thousand.",
      "Options": [
        "A. 8,000",
        "B. 8,600",
        "C. 8,700",
        "D. 9,000"
      ],
      "Answer": "D. 9,000",
      "Points": 2
    },
    {
      "Id": 19,
      "Type": "multiple_choice",
      "Text": "Evaluate: 5 \u00D7 (12 \u2212 7) \u002B 3",
      "Options": [
        "A. 22",
        "B. 28",
        "C. 30",
        "D. 40"
      ],
      "Answer": "B. 28",
      "Points": 2
    },
    {
      "Id": 20,
      "Type": "multiple_choice",
      "Text": "Which is the correct Indian system grouping of 7,200,300?",
      "Options": [
        "A. 7,20,030",
        "B. 72,00,300",
        "C. 7,200,30",
        "D. 7,20,03,00"
      ],
      "Answer": "B. 72,00,300",
      "Points": 2
    },
    {
      "Id": 21,
      "Type": "fill_blank",
      "Text": "The predecessor of 10,000 is _____",
      "Options": [],
      "Answer": "9999",
      "Points": 2
    },
    {
      "Id": 22,
      "Type": "fill_blank",
      "Text": "The smallest whole number is _____",
      "Options": [],
      "Answer": "0",
      "Points": 2
    },
    {
      "Id": 23,
      "Type": "fill_blank",
      "Text": "The Roman numeral for 500 is _____",
      "Options": [],
      "Answer": "D",
      "Points": 2
    },
    {
      "Id": 24,
      "Type": "fill_blank",
      "Text": "A number divisible by 10 must end with _____",
      "Options": [],
      "Answer": "0",
      "Points": 2
    },
    {
      "Id": 25,
      "Type": "fill_blank",
      "Text": "According to the distributive property, a \u00D7 (b \u002B c) = a\u00D7b \u002B a\u00D7_____",
      "Options": [],
      "Answer": "c",
      "Points": 2
    },
    {
      "Id": 26,
      "Type": "fill_blank",
      "Text": "The place value of 7 in 7,046 is _____",
      "Options": [],
      "Answer": "7000",
      "Points": 2
    },
    {
      "Id": 27,
      "Type": "fill_blank",
      "Text": "The sum of the factors of a perfect number equals _____ times the number.",
      "Options": [],
      "Answer": "2",
      "Points": 2
    },
    {
      "Id": 28,
      "Type": "fill_blank",
      "Text": "Moving left three steps of size 4 on a number line decreases the value by _____",
      "Options": [],
      "Answer": "12",
      "Points": 2
    },
    {
      "Id": 29,
      "Type": "fill_blank",
      "Text": "A prime number has exactly _____ distinct factors.",
      "Options": [],
      "Answer": "2",
      "Points": 2
    },
    {
      "Id": 30,
      "Type": "fill_blank",
      "Text": "In the International system, 1,000,000 is read as _____",
      "Options": [],
      "Answer": "one million",
      "Points": 2
    },
    {
      "Id": 31,
      "Type": "word_problem",
      "Text": "You start at 18 on a number line. Move right 6 steps of 4 units each, then move left 5 steps of 3 units each. Where do you land? Show your working.",
      "Options": [],
      "Answer": "Step 1: Total right movement = 6 \u00D7 4 = 24\nStep 2: Total left movement = 5 \u00D7 3 = 15\nStep 3: Final position = 18 \u002B 24 \u2212 15 = 27\nAnswer: 27",
      "Points": 5
    },
    {
      "Id": 32,
      "Type": "word_problem",
      "Text": "Estimate the sum of 8,649 and 3,378 by rounding each number to the nearest thousand. What is the estimated total? Show your working.",
      "Options": [],
      "Answer": "Step 1: 8,649 rounds to 9,000 (nearest thousand)\nStep 2: 3,378 rounds to 3,000 (nearest thousand)\nStep 3: Estimated sum = 9,000 \u002B 3,000 = 12,000\nAnswer: 12,000",
      "Points": 5
    },
    {
      "Id": 33,
      "Type": "word_problem",
      "Text": "A school has 48 red chairs and 60 blue chairs. They want to arrange each color in rows with the same number of chairs and no chairs left over. What is the greatest number of chairs in each row? Show your working.",
      "Options": [],
      "Answer": "Step 1: Prime factors: 48 = 2\u2074 \u00D7 3; 60 = 2\u00B2 \u00D7 3 \u00D7 5\nStep 2: HCF = 2\u00B2 \u00D7 3 = 12\nStep 3: Therefore, maximum chairs per row = 12\nAnswer: 12",
      "Points": 5
    },
    {
      "Id": 34,
      "Type": "word_problem",
      "Text": "Three bells ring every 18, 24, and 30 minutes respectively. If they all ring together at 8:00 a.m., when will they ring together next? Show your working.",
      "Options": [],
      "Answer": "Step 1: Prime factors: 18 = 2 \u00D7 3\u00B2; 24 = 2\u00B3 \u00D7 3; 30 = 2 \u00D7 3 \u00D7 5\nStep 2: LCM = 2\u00B3 \u00D7 3\u00B2 \u00D7 5 = 8 \u00D7 9 \u00D7 5 = 360 minutes\nStep 3: 360 minutes = 6 hours; 8:00 a.m. \u002B 6 hours = 2:00 p.m.\nAnswer: 2:00 p.m.",
      "Points": 5
    },
    {
      "Id": 35,
      "Type": "word_problem",
      "Text": "A factory can pack items in boxes of 45 or in boxes of 60 with no leftovers in either case. What is the smallest number of items the factory can pack to satisfy both conditions? Show your working.",
      "Options": [],
      "Answer": "Step 1: Prime factors: 45 = 3\u00B2 \u00D7 5; 60 = 2\u00B2 \u00D7 3 \u00D7 5\nStep 2: LCM = 2\u00B2 \u00D7 3\u00B2 \u00D7 5 = 4 \u00D7 9 \u00D7 5 = 180\nStep 3: The smallest number of items that fits both box sizes exactly is the LCM\nAnswer: 180",
      "Points": 5
    },
    {
      "Id": 36,
      "Type": "word_problem",
      "Text": "Without long division, determine whether 8,415 is divisible by 9 and by 11. Show your working.",
      "Options": [],
      "Answer": "Step 1: Test for 9: Sum of digits = 8 \u002B 4 \u002B 1 \u002B 5 = 18 (divisible by 9)\nStep 2: Test for 11: (8 \u002B 1) \u2212 (4 \u002B 5) = 9 \u2212 9 = 0 (multiple of 11)\nStep 3: Therefore, 8,415 is divisible by both 9 and 11\nAnswer: Divisible by 9: Yes; Divisible by 11: Yes",
      "Points": 5
    },
    {
      "Id": 37,
      "Type": "word_problem",
      "Text": "Convert 3,06,50,090 (Indian system) to the International system and write it in words (International system). Show your working.",
      "Options": [],
      "Answer": "Step 1: 3,06,50,090 = 3 crore \u002B 6 lakh \u002B 50 thousand \u002B 90\nStep 2: 3 crore = 30,000,000; 6 lakh = 600,000; total = 30,600,000 \u002B 50,000 \u002B 90 = 30,650,090\nStep 3: In International format: 30,650,090 = thirty million six hundred fifty thousand ninety\nAnswer: 30,650,090; Thirty million six hundred fifty thousand ninety",
      "Points": 5
    },
    {
      "Id": 38,
      "Type": "word_problem",
      "Text": "Evaluate the expression using brackets: 7 \u00D7 (18 \u2212 5) \u2212 4 \u00D7 (6 \u002B 1). Show your working.",
      "Options": [],
      "Answer": "Step 1: Compute inside brackets: (18 \u2212 5) = 13 and (6 \u002B 1) = 7\nStep 2: Multiply: 7 \u00D7 13 = 91 and 4 \u00D7 7 = 28\nStep 3: Subtract: 91 \u2212 28 = 63\nAnswer: 63",
      "Points": 5
    },
    {
      "Id": 39,
      "Type": "word_problem",
      "Text": "In a 3\u00D73 grid, the numbers are:\nRow 1: 11, 14, 9\nRow 2: 8, 20, 13\nRow 3: 7, 16, 10\nA supercell is larger than its neighbors directly above, below, left, and right. Is 20 a supercell? Show your working.",
      "Options": [],
      "Answer": "Step 1: Identify neighbors of 20: up = 14, down = 16, left = 8, right = 13\nStep 2: Compare: 20 \u003E 14, 20 \u003E 16, 20 \u003E 8, 20 \u003E 13\nStep 3: Since 20 is greater than all four neighbors, it is a supercell\nAnswer: Yes, 20 is a supercell",
      "Points": 5
    },
    {
      "Id": 40,
      "Type": "word_problem",
      "Text": "Find the smallest 5-digit number that is divisible by both 12 and 15. Show your working.",
      "Options": [],
      "Answer": "Step 1: LCM(12, 15) = 60 (since 12 = 2\u00B2 \u00D7 3 and 15 = 3 \u00D7 5, LCM = 2\u00B2 \u00D7 3 \u00D7 5 = 60)\nStep 2: Smallest 5-digit number is 10,000; compute 10,000 \u00F7 60 \u2248 166.66, so take next whole number 167\nStep 3: 167 \u00D7 60 = 10,020\nAnswer: 10,020",
      "Points": 5
    }
  ],
  "TotalPoints": 100
}