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divisibility and primes

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Manager
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Joined: 20 May 2006
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divisibility and primes [#permalink]

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New post 27 Sep 2008, 12:55
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please explain each. thanks:

Is n an integer?

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

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Re: divisibility and primes [#permalink]

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New post 28 Sep 2008, 19:21
govinam wrote:
please explain each. thanks:

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.

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Re: divisibility and primes   [#permalink] 28 Sep 2008, 19:21
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divisibility and primes

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