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If m is an integer, is m odd? @veritas

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Source: — Data Sufficiency |
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by DavidG@VeritasPrep » Sun Jan 10, 2016 9:16 am
Mechmeera wrote:If m is an integer, is m odd?

1. m/2 is not an even integer.
2. m - 3 is not an even integer.
Pick some simple numbers.

Statement 1
Case 1: m = 1. (1/2 is not an even integer, so this satisfies the statement.) YES, m is odd.
Case 2: m = 2 (2/2 is not an even integer, so this satisfies the statement.) NO, m is not odd.
Statement 1 is not sufficient.


Statement 2: If m has to be an integer, it's going to have to be even.
Reuse Case 2: m = 2. NO, m is not odd
If m is odd, m - 3 will be even, but we're told that m - 3 is NOT even. So if m must be EVEN, then the answer to the question will always be NO. So statement 2 alone is sufficient. Answer is B
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by GMATGuruNY » Sun Jan 10, 2016 9:57 am
If m is an integer, is m odd?
(1) m/2 is not an even integer
(2) m-3 is an even integer
Statement 1: m/2 is not an even integer.
It's possible that m=1, since 1/2 is not an even integer.
In this case, m is odd.
It's possible that m=2, since 2/2=1 is not an even integer.
In this case, m is even.
INSUFFICIENT.

Statement 2: m-3 is an even integer.
m - 3 = even.
Thus:
m = even + 3 = even + odd = odd.
SUFFICIENT.

The correct answer is B.
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by Scott@TargetTestPrep » Fri Dec 15, 2017 6:37 am
conquistador wrote:If m is an integer, is m odd?

1. m/2 is not an even integer.
2. m - 3 is not an even integer.
We need to determine whether integer m is odd.

Statement One Alone:

m/2 is not an even integer

This is not enough information, since m can be odd or even. For example, if m = 5, then m/2 = 5/2, which is not an even integer. Likewise, if m = 6, then m/2 = 3, which is not an even integer. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

m - 3 is an even integer

If m - 3 is an even integer, then m must be odd, since odd - odd = even. Statement two alone is sufficient to answer the question.

Answer: B

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