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If 2^(2p-10) = 2(2^9-2p), then p =

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If 2^(2p-10) = 2(2^9-2p), then p = [#permalink] New post 03 Oct 2013, 23:01
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A
B
C
D
E

Difficulty:

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Question Stats:

89% (01:44) correct 11% (01:45) wrong based on 53 sessions
If 2^(2p-10) = 2*2^(9-2p), then p =

A. 5
B. 3
C. 0
D. -1
E. -2
[Reveal] Spoiler: OA

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Last edited by Bunuel on 03 Oct 2013, 23:15, edited 2 times in total.
Edited the question.
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Re: If 2^2p-10 = 2(2^9-2p), then p = [#permalink] New post 03 Oct 2013, 23:06
avohden wrote:
If 2 ^2^p^-^1^0 = 2(2 ^9^-^2^p), then p =

A. 5
B. 3
C. 0
D. -1
E. -2


2 ^2^p^-^1^0 = 2(2 ^9^-^2^p)
this can be written as
2 ^2^p^-^1^0 = (2 ^10^-^2^p)
now equating the powers
2p-10=10-2p
4p = 20
p = 5

hence A
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Re: If 2^2p-10 = 2(2^9-2p), then p = [#permalink] New post 03 Oct 2013, 23:09
avohden wrote:
If 2 ^2^p^-^1^0 = 2(2 ^9^-^2^p), then p =

A. 5
B. 3
C. 0
D. -1
E. -2


2 ^2^p^-^1^0 = 2(2 ^9^-^2^p)

2(2^(9-2p)) can be written as (2^1)*(2^(9-2p))=>2^(1+9-2p)=>2^(10-2p)

hence 2^(2p-10)=2^(10-2p)
2p-10=10-2p
4p=20
p=5
Ans 'A'
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Re: If 2^2p-10 = 2(2^9-2p), then p = [#permalink] New post 03 Oct 2013, 23:14
avohden wrote:
If 2 ^2^p^-^1^0 = 2(2 ^9^-^2^p), then p =

A. 5
B. 3
C. 0
D. -1
E. -2


2 ^2^p^-^1^0 = 2^1^+^9^-^2^p (adding the powers with same base)
2 ^2^p^-^1^0 = 2^1^0^-^2^p

Comparing the powers, (Since same base), we get

2p - 10 = 10 - 2p

p =5

Hope it helped.
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Re: If 2^(2p-10) = 2(2^9-2p), then p = [#permalink] New post 26 Feb 2014, 02:21
Divide the equation by 2 & equate the powers

2p - 11 = 9 - 2p

4p = 20

p = 5 = Answer = A
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Re: If 2^(2p-10) = 2(2^9-2p), then p =   [#permalink] 26 Feb 2014, 02:21
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