ISEE Word Problems Question 189: Answer and Explanation

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Question: 189

10. If each of p and q has a remainder of 3 when divided by 7, then which one of the following also has a remainder of 3 when divided by 7?

  • A. p – q
  • B. p + 3q
  • C. 3p + q
  • D. 3p – 2q

Correct Answer: D

Explanation:

The answer is D

For a number to have a remainder of 3 when divided by 7, it must be some factor of 7 plus 3. So let each of p and q = 7x + 3. Substitute this expression into each answer. For choice (A), the result is 0, which is not equivalent to some factor of 7 plus 3. For choice (B), the result is 7x + 3 + 3(7x + 3), which is 7x + 3 + (21x + 9), which is 28x + 12. When 12 is divided by 7, the remainder is 5. Choice (C) yields the same result. For choice (D), the result is 3(7x + 3) - 2(7x + 3), which is 21x + 9 - (14x + 6), which is 7x + 3. This is a factor of 7 plus 3.

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 p and q equal to 10 (7 + 3). Plug 10 into each answer (for p and q) and divide

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