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# M02-33

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Math Expert
Joined: 02 Sep 2009
Posts: 51301

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15 Sep 2014, 23:18
1
6
00:00

Difficulty:

35% (medium)

Question Stats:

58% (00:49) correct 42% (00:53) wrong based on 175 sessions

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If $$n$$ is an integer, is $$\frac{n^3}{16}$$ a positive integer?

(1) $$\frac{n}{4}$$ is an integer

(2) $$\frac{n^2}{16}$$ is a positive integer

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Math Expert
Joined: 02 Sep 2009
Posts: 51301

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15 Sep 2014, 23:18
Official Solution:

We need to know the sign of $$n$$ and its divisibility by 16 to answer the question.

Statement (1) by itself is insufficient. We know that $$n$$ is divisible by 4, but we do not know whether $$n$$ is positive or negative.

Statement (2) by itself is insufficient. Statement (2), is S1 squared and provides no new information. We know that $$\frac{n^2}{16}$$ is a positive integer, but we do not know whether $$n$$ is positive or negative.

Statements (1) and (2) combined are insufficient.

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Director
Joined: 11 Feb 2015
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06 Jul 2018, 07:15
1
The key to getting this question right is to read carefully. Note the use of "positive" integer & the implications of its usage in statement (2) and not in statement (1) and how the squares cancel out the use in statement (2).

In general, one could get many questions right just by reading them carefully.
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Manish

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Re: M02-33 &nbs [#permalink] 06 Jul 2018, 07:15
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# M02-33

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