Multiple choice

100 and 80 leave the same remainder when divided by a divisor d (where d ϵ N). How many values can d take?

  1. 1

  2. 3

  3. 6

  4. 20
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If 100 and 80 leave the same remainder when divided by d, then d must be a divisor of (100-80) = 20. The divisors of 20 are 1, 2, 4, 5, 10, 20. Since the remainder must be less than the divisor, for d=1, remainder is 0. For d=2, remainder is 0. For d=4, remainder is 0. For d=5, remainder is 0. For d=10, remainder is 0. For d=20, remainder is 0. All 6 divisors work.

AI explanation

When two numbers leave the same remainder when divided by a divisor, their difference must be exactly divisible by that divisor. The difference between 100 and 80 is 20. The divisor d must be a factor of 20, and because it leaves a remainder, d must be strictly greater than the remainder, meaning d must be greater than 0. The factors of 20 are 1, 2, 4, 5, 10, and 20, giving 6 possible values for d.

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