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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 Updated on: 25 Jul 2018, 20:18
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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

Originally posted by Priya78240 on 25 Jul 2018, 16:51.
Last edited by Bunuel on 25 Jul 2018, 20:18, edited 1 time in total.
Renamed the topic and edited the question.
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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 25 Jul 2018, 18:29
1
Priya78240 wrote:
if x and y are integers ,what is the value of (2^x)^y

1. 2^x + 2^y = 9
2. x.y = 0

Posted from my mobile device



Statement 01 : \(2^x\) + \(2^y\) = \(9\) ==> as 9 is odd , and it is the sum of two number , either of them have to be odd.
Hence .... the possible values of x, y are : 0,3 or 3,0 . In each of the case \((2^x)^y\) = 1 ( as in the expression if either x or y is 0, the expression will become 1).....Sufficient

Statement 02 : x.y = 0 ==> there are 3 possibility : x=0 or y=0 or x and y both 0.
In each of the case \((2^x)^y\) = 1 ( as in the expression if either x or y is 0, the expression will become 1).................Sufficient


Hence D would be the answer.
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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 25 Jul 2018, 22:44
1
Priya78240 wrote:
if x and y are integers ,what is the value of (2^x)^y

1. 2^x + 2^y = 9
2. x.y = 0

Posted from my mobile device



First off, Welcome to GMATClub - Priya78240

Let's first set some basics straight - both a^0 1^a is always equal to 1

On analyzing the individual statements.

1. 2^x + 2^y = 9
Sum of two exponents whose base is even must be odd.
There is only one possibility for the base to be odd - when one of the two bases result
in an odd integer. The only possibility is when one of the even bases has 0 as a power,
making it the zero. If x = 0, \((2^x)^y\) will be 1^y which is 1. Also, if y = 0, the
expression \((2^x)^y\) will always yield a zero (Sufficient)

2. xy = 0
This is possible when x,y, or both have a value of 0.
Whichever case we consider, the value of \((2^x)^y\) will be 0 without fail. This
makes the details of the individual statement enough (Sufficient - Option D)
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If x and y are integers, what is the value of (2^x)^y (1) 2^x + 2^y = &nbs [#permalink] 25 Jul 2018, 22:44
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