ISEE Mathematics Achievement Question 310: Answer and Explanation

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Question: 310

10. If p is an odd integer, which of the following must be an odd integer?

  • A. p2 + 3
  • B. 2p + 1
  • C. p ÷ 3
  • D. p - 3

Correct Answer: B

Explanation:

B Since there are variables in the choices, Plug In a value for p, paying attention to the restrictions in the question. If p is an odd integer, make sure to Plug In an odd integer, for instance p = 3. Now, test the choices to see which one can be eliminated. Cross off (A) because (3)2 + 3 = 9 + 3 = 12, which is not odd. Choice (B) works since 2(3) + 1 = 6 + 1 = 7, which is odd. Choice (C) works since = 1. Choice (D) does not work since 3 - 3 = 0. Remember 0 is even, not odd. Plug In a second time for the remaining choices. Try p = 5. Choice (B) still works because 2(5) + 1 = 10 + 1 = 11, but eliminate (C) because is no longer an integer. The correct answer is (B).

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