Official Guide Explanation:
Data Sufficiency #73




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Solution and Metadata

Question: 73
Page: 279
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Evens and Odds

Explanation: Treat the statements as equations. If ((m)/2) is not an even integer, then:

((m)/2) ≠ 2(\func{integer})    (An even integer is, by definition, twice some other integer.)

m ≠ 4(\func{integer})

In other words, (1) says that m is not a multiple of 4. If m is not a multiple of 4, it could be odd, but it could also be an even number such as 2 or 6, so the statement is insufficient.

Statement (2) can be analyzed the same way:

m - 3 = even

m = even + 3 = even + odd = odd

This statement is sufficient, so the correct choice is (B).

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