Multiple choice

If 5 divided the integer n, the remainder is 2. What will be the remainder if 7n is divided by 5?

  1. 1

  2. 2

  3. 3

  4. 4
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D Correct answer
Explanation

n = 5k + 2. Then 7n = 7(5k + 2) = 35k + 14 = 35k + 10 + 4 = 5(7k + 2) + 4. The remainder when divided by 5 is 4.

AI explanation

If n leaves a remainder of 2 when divided by 5, we can write n as 5k + 2 for some integer k. Multiplying this expression by 7 gives 7n = 35k + 14. When 35k + 14 is divided by 5, the term 35k is perfectly divisible by 5, leaving a remainder from 14 divided by 5, which is 4. The required remainder is 4.

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