If m is an integer, is m odd? (1) 1 + m^2 is an odd integer. (2) 5m

Question

If m is an integer, is m odd?

(1) 1 + m^2 is an odd integer.

(2) 5m - 2 is an even integer.

IanStewart · Answer

If m^2 + 1 is odd, then m^2 is even, and m is even.

If 5m - 2 is even, then 5m is even, and m is even.

So each Statement alone is sufficient to give a "no" answer to the question, and the answer is D.

Archit3110 · Answer

#1
possible only when m is even
sufficient
#2
only possible when m is even , sufficient 
IMO D ,

Kinshook · Answer

Given:  m is an integer

Asked:  Is m odd?

(1) 1 + m^2 is an odd integer.
m^2 is even integer => m is even integer => m is NOT odd
SUFFICIENT

(2) 5m - 2 is an even integer.
5m is even integer => m is even integer => m is NOT odd
SUFFICIENT

IMO D

Bunuel · Answer

Official Explanation

We should be pleased to see a question about the odd and even properties of numbers, because we know that we can look at cases to summon the number properties rules. We know that m is an integer. Is it odd? On to the data statements, separately first. At a glance, we know they will both be separately sufficient, by the rules. In Statement (1), if 1 + m^2 is odd, it could be, say, 9. We see that's awkward. How about 37. Then m^2 = 36 and m is 6, which is even. This will hold up in other cases.

As a tidbit, another way to evaluate this would be to suppose the contrary. You can say, could m be odd? Using the rules, m^2 would then be an odd times and odd, so it must be odd. And adding 1 is adding an odd to an odd, so 1 + m^2 in that case would be even. But that outcome is not permitted by the data statement, which states that 1 + m^2 must be odd. Ergo m CANNOT be odd, which means that it must be even. That example shows another way of evaluating by cases: you can evaluate by cases whenever you can point to a finite number of possibilities that will cover the universe of possibilities--in this case, that m is odd or m is even.

Statement (2) is sufficient by the same logic.

The correct answer is (D).

Bunuel · Answer

Video Explanation

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bumpbot · Answer

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If m is an integer, is m odd? (1) 1 + m^2 is an odd integer. (2) 5m

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GMAT Data Sufficiency (DS) Questions

If m is an integer, is m odd? (1) 1 + m^2 is an odd integer. (2) 5m

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