Integer Division and Mod

All 15 integer division and mod questions

Work through the interactive quiz above first. This is the full integer division and mod question set with worked solutions, so students can review any question after attempting it.

1. 1.Code Tracing 01 - Integer Division and Mod: track the final printed value.

   int total = 18;
   int bonus = 5;
   int group = 3;
   int result = (total + bonus) / group;
   result = result * group + total % group;
   System.out.print(result);

   • 23
   • 7
   • 22
   • 21
   Show worked solution

   Correct answer: 21

   The first division uses integer division. The quotient is multiplied back by group, and the remainder from total is added.

2. 2.Code Tracing 12 - Integer Division and Mod: follow the variable updates.

   int views = 26;
   int added = 7;
   int pageSize = 5;
   int pages = views / pageSize;
   int leftover = (views + added) % pageSize;
   System.out.print(pages + leftover);

   • 8
   • 6
   • 1
   • 13
   Show worked solution

   Correct answer: 8

   Both / and % are integer operations here. The variables pages and leftover are computed separately before the final addition.

3. 3.Code Tracing 28 - Integer Division and Mod: trace the branch and loop path.

   int minutes = 38;
   int seconds = 10;
   int bucket = 3;
   int totalSeconds = minutes * 60 + seconds;
   System.out.print(totalSeconds / bucket);

   • 763
   • 1
   • 770
   • 764
   Show worked solution

   Correct answer: 763

   The multiplication and addition build totalSeconds first. Dividing two ints truncates any fractional part.

4. 4.Code Tracing 39 - Integer Division and Mod: watch the index changes.

   int x = 46;
   int y = 5;
   int group = 5;
   int cycle = 5;
   int value = (x + y) / group;
   System.out.print(value % cycle);

   • 2
   • 0
   • 1
   • 10
   Show worked solution

   Correct answer: 0

   The quotient is found first using integer division. The modulus is then applied to that quotient, not to the original sum.

5. 5.Code Tracing 50 - Integer Division and Mod: evaluate the state change step by step.

   int n = 54;
   int base = 3;
   int left = n / base;
   int right = n % base;
   System.out.print(left * 10 + right);

   • 179
   • The code does not compile.
   • 180
   • 54
   Show worked solution

   Correct answer: 180

   The quotient and remainder are computed separately. The quotient is scaled by 10 before the remainder is added.

6. 6.What is printed by the following code segment?

   int n = 3725;
   int sum = n / 1000 + n / 100 % 10 + n / 10 % 10 + n % 10;
   System.out.print(sum);

   • 15
   • 17
   • 3725
   • 20
   Show worked solution

   Correct answer: 17

   Each term isolates one digit of a four-digit number, and 3 + 7 + 2 + 5 is 17.

7. 7.What is printed by the following code segment?

   int total = 0;
   for (int i = 1; i <= 20; i++)
   {
       if (i % 3 == 0 && i % 5 != 0)
       {
           total += i;
       }
   }
   System.out.print(total);

   • 63
   • 78
   • 48
   • 33
   Show worked solution

   Correct answer: 48

   The multiples of 3 up to 20 are 3, 6, 9, 12, 15, and 18, and 15 is excluded because it is also a multiple of 5.

8. 8.What is printed by the following code segment?

   int mins = 545;
   int h = mins / 60;
   int rest = mins % 60;
   System.out.print(h + ":" + rest / 10 + rest % 10);

   • 9:5
   • 9:50
   • 8:65
   • 9:05
   Show worked solution

   Correct answer: 9:05

   The remainder is 5, so the tens digit is 0 and the ones digit is 5, printing a padded minute field.

9. 9.What is printed by the following code segment?

   int n = -14;
   int d = 4;
   System.out.print(n / d * d + n % d);

   • -14
   • -16
   • -12
   • -10
   Show worked solution

   Correct answer: -14

   Java guarantees that the quotient times the divisor plus the remainder returns the original value, even for negatives.

10. 10.What is printed by the following code segment?

    int count = 0;
    int n = 1;
    while (n <= 100)
    {
        if (n % 7 == 0 || n % 11 == 0)
        {
            count++;
        }
        n++;
    }
    System.out.print(count);

    • 23
    • 22
    • 14
    • 9
    Show worked solution

    Correct answer: 22

    There are 14 multiples of 7 and 9 of 11 up to 100, and 77 is counted once because || does not double count.

11. 11.What is printed by the following code segment?

    int n = 1024;
    int steps = 0;
    while (n % 2 == 0)
    {
        n /= 2;
        steps++;
    }
    System.out.print(n + " " + steps);

    • 2 9
    • 1 11
    • 1 10
    • 0 10
    Show worked solution

    Correct answer: 1 10

    Ten halvings reduce 1024 to 1, which is odd, so the loop stops there.

12. 12.What is printed by the following code segment?

    int a = 100;
    int b = 36;
    while (b != 0)
    {
        int t = a % b;
        a = b;
        b = t;
    }
    System.out.print(a);

    • 36
    • 100
    • 12
    • 4
    Show worked solution

    Correct answer: 4

    This is the Euclidean algorithm, and the greatest common divisor of 100 and 36 is 4.

13. 13.What is printed by the following code segment?

    int n = 6;
    int result = 1;
    while (n > 1)
    {
        result *= n % 4 == 0 ? 1 : n;
        n--;
    }
    System.out.print(result);

    • 180
    • 720
    • 30
    • 120
    Show worked solution

    Correct answer: 180

    The conditional operator replaces every multiple of 4 with 1, so 4 drops out and the product is 6 times 5 times 3 times 2, or 180.

14. 14.What is printed by the following code segment?

    int digits = 0;
    int n = 100000;
    while (n > 0)
    {
        digits++;
        n /= 10;
    }
    System.out.print(digits);

    • 5
    • 6
    • 7
    • 100000
    Show worked solution

    Correct answer: 6

    Each pass removes one digit, and 100000 has six of them before the value reaches 0.

15. 15.What is printed by the following code segment?

    int n = 255;
    String out = "";
    while (n > 0)
    {
        out = n % 2 + out;
        n /= 2;
    }
    System.out.print(out);

    • 255
    • 10000000
    • 11111111
    • 11111110
    Show worked solution

    Correct answer: 11111111

    Repeated division by 2 with the remainder prepended builds the binary form, and 255 is eight ones.