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If x and y are positive integers, what is the value of xy? (1) 3^(

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If x and y are positive integers, what is the value of xy? (1) 3^(  [#permalink]

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New post 21 Jul 2017, 10:11
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  85% (hard)

Question Stats:

25% (00:46) correct 75% (01:11) wrong based on 36 sessions

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If x and y are positive integers, what is the value of xy?

(1) 3^(x^2 – y^2) = 243
(2) 3^(x^2 + y^2) = 3^13

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Re: If x and y are positive integers, what is the value of xy? (1) 3^(  [#permalink]

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New post 21 Jul 2017, 14:32
i) 3^(x^2-y^2) = 243

=>3^(x^2-y^2) = 3^5
(x^2-y^2) = 5
(x-y)(x+y) = 5 since x,y are positive integers , the only combination for this is x = 3 and y =2
So A is sufficient xy = 6

ii) 3^(x^2+y^2) = 3^13

=> (x^2+y^2) = 13
the squares of positive integers 1,4,9,16,etc..
the values of x^2 and y^2 could be 4,9 only which would mean xy = 6
SO B is sufficient too.

Hence Answer is D. A and B independently can be used to answer this question.
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If x and y are positive integers, what is the value of xy? (1) 3^(  [#permalink]

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New post 22 Jul 2017, 00:08
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1.\(3^{x^2 – y^2} = 243\)

We know that \(x^2 – y^2 = (x+y)(x-y)\)
Also, \(3^5 = 243\)
The only possible value of x and y is 3 and 2 such that the resulting value of xy is 6(Sufficient)

2.\(3^{x^2 + y^2} = 3^13\)

We know that \(x^2 + y^2 = 13\)
This is only possible when x=2,y=3 or x=3,y=2.
In either case the value of xy is 6(Sufficient) (Option D)


--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.


If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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If x and y are positive integers, what is the value of xy? (1) 3^(   [#permalink] 22 Jul 2017, 00:08
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