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3^X-3^(X-1)=162 ?!?1

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fahadmuhammad86
 Post subject: 3^X-3^(X-1)=162 ?!?1
 Post Posted: Mon Nov 23, 2009 4:55 pm 
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Students


Posts: 11
Im having a hard time figuring this question out:

3^X-3^(X-1)=162 What is x(x-1)=?

Answer is 16.

Can anyone explain how to do this question?
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nitin_prakash_khanna
 Post subject: Re: 3^X-3^(X-1)=162 ?!?1
 Post Posted: Thu Nov 26, 2009 11:24 am 
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Students


Posts: 68
given
3^x-3^(x-1) = 162
lets first simplify the left side.

3^x- {3^x*3^-1}= 3^x-(3^x)/3
3^x {1-(1/3)}
3^x*2/3 = 162= 2*81= 2*3^4

This implies
x-1 = 4
so x=5

x*x-1 = 5*4 =20

Not sure why the answer is 16, can you please re check and post it here.
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rambabu
 Post subject: Re: 3^X-3^(X-1)=162 ?!?1
 Post Posted: Fri Nov 27, 2009 2:31 am 
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Course Students


Posts: 5
For the a given question, answer must be 20.
I guess, either the stated answer or given question would be wrong.
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RonPurewal
 Post subject: Re: 3^X-3^(X-1)=162 ?!?1
 Post Posted: Sat Jan 09, 2010 3:41 am 
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ManhattanGMAT Staff


Posts: 6765
rambabu wrote:
For the a given question, answer must be 20.
I guess, either the stated answer or given question would be wrong.


yeah, 16 is the wrong answer; it should be 20.

by the way, if you are not absolutely amazing at algebra, it's much easier to figure out the value of x by simply throwing in values until 3^x - 3^(x-1) comes out as 162. (shouldn't take too long -- just adjust upward if you get less than 162, and downward if you get more.)
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