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# If x and y are integers, what is the value of (2^x)^y (1) 2^x + 2^y =

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Math Expert
Joined: 02 Sep 2009
Posts: 61283
If x and y are integers, what is the value of (2^x)^y (1) 2^x + 2^y =  [#permalink]

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16 Dec 2019, 01:55
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45% (medium)

Question Stats:

67% (01:16) correct 33% (01:35) wrong based on 43 sessions

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If x and y are integers, what is the value of $$(2^x)^y$$

(1) $$2^x + 2^y = 9$$
(2) $$xy = 0$$

Are You Up For the Challenge: 700 Level Questions

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Joined: 08 Aug 2014
Posts: 8
GMAT Date: 10-02-2015
Re: If x and y are integers, what is the value of (2^x)^y (1) 2^x + 2^y =  [#permalink]

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16 Dec 2019, 03:02
I strongly believe the answer is D.

statement 1: 2^x + 2^y= 9

The only two conditions for this equation to equal 9, is if x=0 and Y=3, or X=3 and Y=0

Going by this analysis, we can find a unique solution for the expression (2^x)^y as 1.

Statement 1 --->> sufficient

From statement 2
xy=0

This equally gives us a unique solution to the equation as 1.
Because any number raised to the power of zero is 1

Statement 2---->> sufficient .

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Joined: 16 Feb 2015
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Re: If x and y are integers, what is the value of (2^x)^y (1) 2^x + 2^y =  [#permalink]

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16 Dec 2019, 03:04
Bunuel wrote:
If x and y are integers, what is the value of $$(2^x)^y$$

(1) $$2^x + 2^y = 9$$
(2) $$xy = 0$$

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Explanation:
Requirement: Value: (2^x)^y Given: x,y is integer
Statement 1: 2^x + 2^y = 9
Either of x or y have to be zero. By this we know (2^x)^y will be 1
Sufficient.
Statement 2: xy=0
Either of x or y have to be zero. By this we know (2^x)^y will be 1
Sufficient.

IMO-D
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Re: If x and y are integers, what is the value of (2^x)^y (1) 2^x + 2^y =  [#permalink]

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16 Dec 2019, 03:23
#1
$$2^x + 2^y = 9$$
possible when x=3/0 or y=0/3
so $$(2^x)^y$$ = 1
sufficient
#2
$$xy = 0$$
xy=0 so
$$(2^x)^y$$ = 1
sufficient
IMO D

Bunuel wrote:
If x and y are integers, what is the value of $$(2^x)^y$$

(1) $$2^x + 2^y = 9$$
(2) $$xy = 0$$

Are You Up For the Challenge: 700 Level Questions
Re: If x and y are integers, what is the value of (2^x)^y (1) 2^x + 2^y =   [#permalink] 16 Dec 2019, 03:23
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