Multiple choice

When 125 is divided by a divisor d (where d ϵ N), the remainder is 5. How many values can d take?

  1. 1

  2. 11

  3. 16

  4. 120
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If 125 divided by d leaves a remainder of 5, then d must be a divisor of (125 - 5) = 120, and d must be greater than the remainder 5. The divisors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Divisors greater than 5 are 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120, which are 11 values.

AI explanation

If dividing 125 by d leaves a remainder of 5, then d must perfectly divide 125 minus 5, which is 120. The divisor d must also be strictly greater than the remainder 5. The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120, and the values among these that are greater than 5 are 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120, giving exactly 11 possible values.

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