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# Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an

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Math Expert
Joined: 02 Sep 2009
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Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an  [#permalink]

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28 Jan 2017, 11:17
alice7 wrote:
Hi, Bunel how could n2 could be 3 in your assumption. I think it has to be 1,2,4,9 which is sufficient.

Why cannot n^2 be 3? In this case $$n=\sqrt{3}$$ or $$-\sqrt{3}$$, so in this case n is an irrational number.

For more on number theory (for example on irrational numbers) check the following link: https://gmatclub.com/forum/math-number- ... 88376.html

Hope it helps.
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Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an  [#permalink]

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13 Dec 2017, 10:49
vwjetty wrote:
Is n an integer?

(1) $$n^2$$ is an integer

(2) $$\sqrt{n}$$ is an integer

We need to determine whether n is an integer.

Statement One Alone:

n^2 is an integer.

If n^2 is an integer, n may or may not be an integer. For instance, if n^2 = 4, then n is an integer (since n = 2 or -2). However, if n^2 = 5, then n is not an integer (since n = √5 or -√5). Statement one is not sufficient to answer the question.

Statement Two Alone:

√n is an integer.

In order for √n to be an integer, n must be an integer. This is because n = (√n)^2, and any integer squared is also an integer. Statement two is sufficient to answer the question.

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Re: Is n an integer? (1) n^2 is an integer (2) n^(1/2) is an &nbs [#permalink] 13 Dec 2017, 10:49

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