Exponent Problem

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alicia: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Thu Aug 26, 2010 12:44 pm

by alicia » Sat Sep 17, 2011 9:21 am

This was a problem on my practice test. Please advise on the step by step solution/breakdown for this problem:

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

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

The correct answer is d. 15

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Sat Sep 17, 2011 9:28 am

2^x - 2^x-2 = 3(2^13)
i think the problem is like this : 2^x - 2^(x-2) = 3(2^13)
-> 2^x - 2^x/4 = 3(2^13) (as 2^(a-b) can be written as 2^a / 2^b)
4* 2^x - 2^x = 3(2^13)*4
3*2^x = 3(2^13)*(2^2)
2^x = 2^(13+2) = 2^15
thus x=15

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Cans!!

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alicia: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Thu Aug 26, 2010 12:44 pm

by alicia » Sat Sep 17, 2011 8:03 pm

Thanks!

However, I don't understand how you got from 2^x-2 to 2^x/4

Please explain.

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Sat Sep 17, 2011 9:49 pm

2^(x-2) to (2^x)/4
lhs: (2^x)*(2^(-2)) = (2^x)/4

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Cans!!

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Sep 18, 2011 3:42 am

Can's solution is great. For a less algebraic approach, check here:

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Sun Sep 18, 2011 4:30 am

alicia wrote:This was a problem on my practice test. Please advise on the step by step solution/breakdown for this problem:

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

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

The correct answer is d. 15

2^x - 2^x-2 = 3(2^13)

Or, 2^x - 2^x-2 = {(2^2) - 1}(2^13)

Or , 2^x - 2^x-2 = 2^15 -2^13

Now we can safely claim x = 15...

Abhishek

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leumas: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Sun Aug 21, 2011 1:47 am; Thanked: 3 times

by leumas » Thu Sep 22, 2011 9:31 am

alicia wrote:This was a problem on my practice test. Please advise on the step by step solution/breakdown for this problem:

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

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

The correct answer is d. 15

There can be only two options. 15 or 17 since rhs has 2^13

Now: (2^x - 2^(x-2))/ 2^13 = 3

Substitute 15: Answer will be 4-1 =3 Success!

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