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# divisibility and primes

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Manager
Joined: 20 May 2006
Posts: 93

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27 Sep 2008, 12:55
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Is n an integer?

1. n^2 is an integer
2. sqrt(n) is an integer
Intern
Joined: 28 Sep 2008
Posts: 3

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28 Sep 2008, 19:21
govinam wrote:

Is n an integer?

1. n^2 is an integer
2. sqrt(n) is an integer

Here are two resources that I've found especially helpful for learning GMAT number properties and divisibility rules:

Statement 1 is insufficient because n could be sqrt(2), which is not an integer, or n could be 3, which is an integer. In both cases, n^2 is an integer. Insufficient.
Statement 2 is sufficient because the product of two integers is always an integer. Thus, if sqrt(n) is an integer, then sqrt(n)*sqrt(n) must an integer. Sufficient.

Since Statement (2) alone is sufficient, but Statement (1) alone is not sufficient, the correct answer is B.
Re: divisibility and primes   [#permalink] 28 Sep 2008, 19:21
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# divisibility and primes

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