ISEE Mathematics Achievement Question 8: Answer and Explanation

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Question: 8

8. If a and b each has a remainder of 4 when divided by 5, then which one of the following also has a remainder of 4 when divided by 5?

  • A. a – b
  • B. 2a – b
  • C. 2a + b
  • D. a + 2b

Correct Answer: B

Explanation:

B

For a number to have a remainder when divided by 5, it must be some factor of 5 plus 4. So let a and b each equal 5x + 4. Substitute this expression into each answer. For choice (A), the result is 0, which is not equivalent to some factor of 5 plus 4. For choice (B), the result is 2(5x + 4) – (5x + 4), which is 10x + 8 – (5x + 4), which is 5x + 4. This is a factor of 5 plus 4. If you check choice (C) out of caution, the result is 2(5x + 4) + (5x + 4), which is 10x + 8 + (5x + 4), which is 15x + 12. When 12 is divided by 5, the remainder is 2, not 4. Choice (D) yields the same result as choice (C).

If you are given a denominator of a quotient and a remainder, you can plug in for the numerator by adding the denominator and the remainder. In this case, you can set both a and b equal to 9 (4 + 5). Plug 9 into each answer (f

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