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GMAT Prep-Problem Solving

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by Anurag@Gurome » Mon May 16, 2011 8:02 pm
clinton wrote:If (2^x) (3^y) = 288, where x and y are positive integers, then (2^x-1) (3^y-2) =


-16
-24
-48
-96
-144

Could someone give me a step by step process.

Solution:
288 = 144 *2 = 36*8 = 9*32 = (2^5)*(3^2).
Or x = 5 and y = 2.
Or 2^(x-1)*3^(y-2) = 2^4*3^0 = 16.
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by GMATGuruNY » Mon May 16, 2011 8:05 pm
clinton wrote:If (2^x) (3^y) = 288, where x and y are positive integers, then (2^x-1) (3^y-2) =


-16
-24
-48
-96
-144

Could someone give me a step by step process.
2^(x-1) * 3^(y-2)
= (2^x)/2 * (3^y)/(3^2)
= (2^x)(3^y)/18
= 288/18
= 16.

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by kareem.firoz » Mon May 16, 2011 8:36 pm
Anurag@Gurome wrote:
clinton wrote:If (2^x) (3^y) = 288, where x and y are positive integers, then (2^x-1) (3^y-2) =


-16
-24
-48
-96
-144

Could someone give me a step by step process.

Solution:
288 = 144 *2 = 36*8 = 9*32 = (2^5)*(3^2).
Or x = 5 and y = 2.
Or 2^(x-1)*3^(y-2) = 2^4*3^0 = 16.
Hi,
Sorry if this is a blunder. But I would really like to know why cant (2^x-1) (3^y-2) be read as ((2^x)-1)((3^y)-2). (that's the equation i was working on, until i saw the replies)
Would GMAT be clear enough to put it as 2^(x-1)*3^(y-2)? Or should I be good enough to read it so?

thanks,
FK
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by Anurag@Gurome » Mon May 16, 2011 8:55 pm
kareem.firoz wrote:
Anurag@Gurome wrote:
clinton wrote:If (2^x) (3^y) = 288, where x and y are positive integers, then (2^x-1) (3^y-2) =


-16
-24
-48
-96
-144

Could someone give me a step by step process.

Solution:
288 = 144 *2 = 36*8 = 9*32 = (2^5)*(3^2).
Or x = 5 and y = 2.
Or 2^(x-1)*3^(y-2) = 2^4*3^0 = 16.
Hi,
Sorry if this is a blunder. But I would really like to know why cant (2^x-1) (3^y-2) be read as ((2^x)-1)((3^y)-2). (that's the equation i was working on, until i saw the replies)
Would GMAT be clear enough to put it as 2^(x-1)*3^(y-2)? Or should I be good enough to read it so?

thanks,
FK
GMAT is normally very clear about what it asking. If it is asking for {(2^x) - 1}*{(3^y) - 2}, only x and y will appear above as powers.
If it is asking for {2^(x-1)}*{3^(y-2)}, both (x-1)and (y-2) will appear above as powers.
Here had the question asked for {(2^x) - 1}*{(3^y) - 2}we would have got 2^5 - 1 = 31 as one of the factors of any options.
But it is not there. So, we can assume that the question is asking for {2^(x-1)}*{3^(y-2)}.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
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