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Power rules question

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Power rules question [#permalink] New post 15 Oct 2011, 11:26
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

89% (01:57) correct 11% (02:19) wrong based on 9 sessions
Hello,

can anybody help me understand this question?

Many thanks!!
Daniele


If 2^x- 2^(x-2) = 3(2^13) then x is equal to ?
a .9
b.11
c.13
d.15
e.17
[Reveal] Spoiler: OA
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Joined: 21 Aug 2010
Posts: 189
Location: United States
GMAT 1: 700 Q49 V35
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Re: Power rules question [#permalink] New post 15 Oct 2011, 12:43
danielezunino wrote:
Hello,

can anybody help me understand this question?

Many thanks!!
Daniele


If 2^x- 2^(x-2) = 3(2^13) then x is equal to ?
a .9
b.11
c.13
d.15
e.17



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


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

So the value of X should be more than 13. Only 2 options which are greater than 13.

15 and 17

If we substitute 15.

2^15 = 3(2^13)+2^13
2^2 * 2^13 = 4(2^13)
4(2^13) = 4 (2^13) so 15 (D )
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Joined: 21 Aug 2010
Posts: 189
Location: United States
GMAT 1: 700 Q49 V35
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GMAT ToolKit User
Re: Power rules question [#permalink] New post 15 Oct 2011, 12:52
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gopu106 wrote:
danielezunino wrote:
Hello,

can anybody help me understand this question?

Many thanks!!
Daniele


If 2^x- 2^(x-2) = 3(2^13) then x is equal to ?
a .9
b.11
c.13
d.15
e.17



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


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

So the value of X should be more than 13. Only 2 options which are greater than 13.

15 and 17

If we substitute 15.

2^15 = 3(2^13)+2^13
2^2 * 2^13 = 4(2^13)
4(2^13) = 4 (2^13) so 15 (D )


Another way

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

==>[2^2 * 2^(x-2)] - 2^(x-2) = 3(2^13)
==>4[2^(x-2)] - 2^(x-2) = 3(2^13)
==>3[2^(x-2)] = 3(2^13)

==>x-2 = 13
x=15 (D)
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Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 178
Location: India
Concentration: Finance, International Business
WE: Information Technology (Investment Banking)
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Re: Power rules question [#permalink] New post 15 Oct 2011, 22:35
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KUDOS
Let us take 2^x =a

now in the equation we replace 2^x by a
=> a-a/4 = 3(2^13)
=>a/4=2^13
=>a=2^15

now a=2^x =>2^x = 2^15

so x=15
Intern
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Re: Power rules question [#permalink] New post 16 Oct 2011, 00:13
Thanks a lot to both of you!!! now it is really clear :-D
Re: Power rules question   [#permalink] 16 Oct 2011, 00:13
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