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# If b is an integer, is sq(a^2+b^2) an integer? (1) a2 + b2

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Joined: 10 Feb 2011
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If b is an integer, is sq(a^2+b^2) an integer? (1) a2 + b2 [#permalink]  26 Feb 2011, 15:45
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76% (01:38) correct 24% (00:53) wrong based on 37 sessions
If b is an integer, is sq(a^2+b^2) an integer?

(1) a2 + b2 is an integer.
(2) a^2 – 3b^2 = 0
[Reveal] Spoiler: OA
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Joined: 02 Sep 2009
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Kudos [?]: 53413 [1] , given: 8160

Re: . If b is an integer, is sq(a^2+b^2) an integer? (1) a2 + b [#permalink]  26 Feb 2011, 15:55
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banksy wrote:
If b is an integer, is sq(a^2+b^2) an integer?
(1) a2 + b2 is an integer.
(2) a^2 – 3b^2 = 0

If b is an integer, is sqrt(a^2+b^2) an integer?

(1) a^2 + b^2 is an integer. Clearly insufficient: if a^2 + b^2 is a perfect square, say 4, then the answer is YES but if a^2 + b^2 is NOT a perfect square, say 5, then the answer is NO. Not sufficient.

(2) a^2 – 3b^2 = 0 --> $$a^2=3b^2$$ --> $$\sqrt{a^2+b^2}=\sqrt{3b^2+b^2}=\sqrt{4b^2}=2|b|=integer$$. Sufficient.

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Re: . If b is an integer, is sq(a^2+b^2) an integer? (1) a2 + b   [#permalink] 26 Feb 2011, 15:55
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