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If is an integer and xy2 = 36, how many values are possible

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If is an integer and xy2 = 36, how many values are possible [#permalink] New post 30 Aug 2018, 07:52
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If \(\sqrt{x}\) is an integer and \(xy^2 = 36\), how many values are possible for the integer y?

(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
[Reveal] Spoiler: OA

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Re: If is an integer and xy2 = 36, how many values are possible [#permalink] New post 07 Sep 2018, 19:19
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sandy wrote:
If \(\sqrt{x}\) is an integer and \(xy^2 = 36\), how many values are possible for the integer y?

(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight



\(\sqrt{x}\) = integer. It means that x is a perfect square.

Given,

\(xy^2 = 36\)

Possible combination:

\(1^26^2 = 36\)

\(2^23^2 = 36\)

\(6^21^2 = 36\)

\(3^22^2 = 36\)

Note: As x and y both are perfect square , we must consider negative values too. Then we have 4 sets of positive and 4 sets of negative values.

Total 8 sets of values. Thus possible values of y is 8. In perfect square negative value becomes positive one.***

The best answer is E.
Re: If is an integer and xy2 = 36, how many values are possible   [#permalink] 07 Sep 2018, 19:19
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If is an integer and xy2 = 36, how many values are possible

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