algebric equation

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hetavdave: Senior | Next Rank: 100 Posts; Posts: 77; Joined: Sat Dec 27, 2008 10:58 pm; Thanked: 4 times

by hetavdave » Sun Aug 09, 2009 1:03 am

I was able to guess the correct answer but can anyone please explain the answer in detail.

If 2^x - 2^x-2 = 3(2^13) then what is value of x?

a. 9
b. 11
c. 13
d. 15
e. 17

OA
d

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Source: Beat The GMAT — Problem Solving | Sun Aug 09, 2009 1:03 am

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members; Thanked: 712 times; GMAT Score:770

by DanaJ » Sun Aug 09, 2009 4:01 am

It's only a matter of seeing the common factor of 2^x and 2^(x-2). It will be 2^(x-2):

2^x - 2^(x-2) = 2^(x-2)*(2^2 - 1) = 2^(x-2)*3

Since you have 2^(x - 2)*3 = 3*2^13, you get that x - 2 = 13, with x = 15.

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