how do i solve this?

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Source: — Data Sufficiency |

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by eagleeye » Sat Aug 04, 2012 4:55 pm
grandh01 wrote:If y = 2^x+1, what is the value of y - x?
(1) 2^2x+2 = 64
(2) y = 2^2x -1
we need y-x. If we have the value of x, we'll have the answer. We know that
y= 2^x+1

Lets look at the statements:

(1) 2^(2x+2) = 64= 2^6 => x = 2.
We have found a unique value of x from this equation by comparing bases. Sufficient.

(2) y = 2^(2x -1)
Comparin this to given value of y:
2^(x + 1) = 2^(2x-1)
x+ 1 = 2x-1 => x =2. Sufficient again.

D is correct. :)

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by Anurag@Gurome » Sat Aug 04, 2012 9:14 pm
grandh01 wrote:If y = 2^x+1, what is the value of y - x?
(1) 2^2x+2 = 64
(2) y = 2^2x -1
(1) 2^(2x+2) = 64 implies 2^(2x+2) = 2^6
Since bases are the same, so exponents will also be equal, so 2x + 2 = 6 or 2x = 4 or x = 2
Now we can find y and hence the value of y - x; SUFFICIENT.

(2) y = 2^(2x -1)
Also, y = 2^x+1
So, 2^(x + 1) = 2^(2x -1)
Since bases are the same, so exponents will also be equal, so x + 1 = 2x - 1 or x = 2
Again we can find y and hence the value of y - x; SUFFICIENT.

The correct answer is D.
Anurag Mairal, Ph.D., MBA
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