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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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21 Jul 2017, 10:11
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Difficulty:

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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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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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)

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

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