ISEE Mathematics Achievement Question 311: Answer and Explanation

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Question: 311

11. If m is the sum of two positive even integers, which of the following CANNOT be true?

  • A. m < 5
  • B. 3m is odd.
  • C. m is even.
  • D. m3 is even.

Correct Answer: B

Explanation:

B The wording on this problem is tricky: it asks for which CANNOT be true, so try to find examples that COULD be true to eliminate choices. Pay attention to the restrictions in the problem, and Plug In two positive even integers: say 4 and 6. Thus, 4 + 6 = 10 = m. Next, eliminate choices that WORK. Choice (A) does not work since 10 is greater than 5. Keep it. Choice (B) does not work because 3(10) = 30, which is even, not odd. Keep it. Eliminate (C) because m = 10, which is even, so it works. Eliminate (D) as well because 103 ends in a zero, which is also even, so this statement works. Now, Plug In a second time for the remaining choices. Try new numbers, and remember that the numbers do not have to be distinct from one another. Try Plugging In 2 for both positive even integers. Thus, 2 + 2 = 4 = m. Check the remaining answers and eliminate the choices that WORK. For (A), 4 is less than 5. That works, so eliminate (A). For (B), 3(4) = 12, which does not work since it's even, so keep it. The only choice left is (B), which is the correct answer.

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