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Is k the square of an integer?

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Is k the square of an integer? [#permalink] New post 18 Dec 2012, 22:04
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Is k the square of an integer?

(1) k= t^2 * q^6 *r^10, where t, q and r are integers

(2) k= t^2 * m^15, where t and m are integers
[Reveal] Spoiler: OA

Last edited by jsphcal on 19 Dec 2012, 06:41, edited 3 times in total.
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Re: Is k the square of an integer? [#permalink] New post 18 Dec 2012, 22:18
jsphcal wrote:
Is k the square of an integer?

(1) k= t ^2 * q^6 * r^10 , where t, q and r are integers


(2) k= r ^2 * m^{15} , where r and m are integers


Please correct the typo in statement 1... :)

1) we havek={(tq^3r^5)}^2. Since t,q and r are intergers, k is the square of an integer. Sufficient.

2)m can take several values for k to not be the square of an integer. If m =1, k is the square of an integer. Insufficient.

Answer is A.

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Re: Is k the square of an integer? [#permalink] New post 19 Dec 2012, 02:05
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Is k the square of an integer?

We need to determine whether k is a perfect square.

(1) k = t^2*q^6*r^10, where t, q, and r are integers --> k=(tq^3r^5)^2=integer^2. Sufficient.

(2) k = t^2*m^15, where t and m are integers --> if m is a perfect square itself (say if m=n^2 for some integer n), then k will also be a perfect square but if m is NOT a perfect square, then k also will NOT be a perfect square. For example consider m=1 and m=2. Not sufficient.

Answer: A.

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Re: Is k the square of an integer?   [#permalink] 19 Dec 2012, 02:05
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