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Math Expert V
Joined: 02 Sep 2009
Posts: 56370
What is the value of (2^x + 2^x)/2^y ?  [#permalink]

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1
3 00:00

Difficulty:   15% (low)

Question Stats: 80% (01:21) correct 20% (01:41) wrong based on 137 sessions

### HideShow timer Statistics Tough and Tricky questions: Exponents.

What is the value of (2^x + 2^x)/2^y ?

(1) x – y = 8
(2) x/y = -3

Kudos for a correct solution.

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Manager  Joined: 22 Sep 2012
Posts: 125
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
Re: What is the value of (2^x + 2^x)/2^y ?  [#permalink]

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2
2^x+2^x/2^y => 2^x-y+1

Statement 1 : x-y = 8

Therefore 2^x-y+1 = 2^9. Sufficient

Statemenet 2:
x/y = -3 -> x =-3y

2^x-y+1 = 2^-4y+1. Insufficient

Manager  Joined: 07 Oct 2014
Posts: 160
GMAT 1: 710 Q48 V39 WE: Sales (Other)
Re: What is the value of (2^x + 2^x)/2^y ?  [#permalink]

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What is the value of (2^x + 2^x)/2^y ?

(1) x – y = 8
(2) x/y = -3

1)
as we don't know if x and/or y are pos/neg there are too many possibilities... e.g. -6 + 14 = 8. 10 - 2) = 8, etc. can't do much with there. Insufficient

2) x/y = -3 means that either x or y is negative, and that absolute value of x is 3 times absolute value of y...way too many possibilities.

Combined:
only thing I can think of is : 6 - (-2) = 8 which makes the calc dobale, I can't think of any other solutions (am bad at equations ) so sufficient.

C
Intern  Joined: 03 Aug 2014
Posts: 16
Re: What is the value of (2^x + 2^x)/2^y ?  [#permalink]

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Hi Bunuel - can you provide an explanation for this question? I got (B) because I reduced the equation to 2(2^(x/y)) and I'd like to know what I'm doing wrong. Thanks.
EMPOWERgmat Instructor V
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: What is the value of (2^x + 2^x)/2^y ?  [#permalink]

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1
Hi revul,

You bring up an interesting point (that X and Y could be a variety of different values), but then you stopped working and immediately called Fact 1 INSUFFICIENT. If you do a bit more work, you'll find that that is NOT the case (the answer to the question stays the same....it's always 512).

Hi cg0588,

Here's how you can 'rewrite' the question:

First, it's important to realize that when you add two of the 'same thing' together, you can write the result as 2 "times"....

A + A = 2A
10 + 10 = 2(10)
Etc.

The question asks us for the value of (2^X + 2^X)/(2^Y)

2^X + 2^X = 2(2^X)

2(2^X) = (2^1)(2^X) = 2^(X+1)

Now, using exponent rules...since the numerator and denominator have the SAME BASE (2), we can SUBTRACT the exponents...

2^(X+1)/(2^Y) = 2^(X+1-Y)

So we're really asked for the value of 2^(X+1-Y).

From this, can you get to the question answer?

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Re: What is the value of (2^x + 2^x)/2^y ?  [#permalink]

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Hello from the GMAT Club BumpBot!

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_________________ Re: What is the value of (2^x + 2^x)/2^y ?   [#permalink] 22 Aug 2018, 14:32
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