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

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New post 16 Dec 2019, 01:55
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

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

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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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New post 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 .

Answer is 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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New post 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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New post 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
GMAT Club Bot
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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