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2^x+2^x+2^x+2^x = 2^n

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Manager
Manager
Joined: 03 Jun 2010
Posts: 185
Location: United States (MI)
Concentration: Marketing, General Management
WE: Business Development (Consumer Products)
Followers: 4

Kudos [?]: 19 [0], given: 40

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Re: 2^x+2^x+2^x+2^x = 2^n [#permalink] New post 12 Jan 2011, 21:59
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

87% (01:19) correct 12% (00:00) wrong based on 8 sessions
it can be rewritten:
4*2^x=2^n
4=2^2
then
2^2*2^x=2^n
we can write 2+x=n
so, x=n-2
(D)
[Reveal] Spoiler: OA
Joined: 31 Dec 1969
Location: United States
Concentration: Marketing, Other
GMAT 1: 710 Q49 V38
GMAT 2: 660 Q V
GPA: 3.64
WE: Accounting (Accounting)
Followers: 0

Kudos [?]: 46 [0], given: 72024

Re: 2^x+2^x+2^x+2^x = 2^n [#permalink] New post 13 Jan 2011, 07:56
ulm wrote:
it can be rewritten:
4*2^x=2^n
4=2^2
then
2^2*2^x=2^n
we can write 2+x=n
so, x=n-2
(D)

D as well with the same reasoning
Manager
Manager
Joined: 27 Jul 2010
Posts: 79
Concentration: Strategy, International Business
GMAT 1: 740 Q50 V40
GPA: 3.65
Followers: 1

Kudos [?]: 8 [0], given: 5

Re: 2^x+2^x+2^x+2^x = 2^n [#permalink] New post 13 Jan 2011, 09:00
2^x + 2^x + 2^x + 2^x = 4 * 2^x = 2^2 * 2^x = 2^(2+x)
so , if 2^(2+x)= 2^n then 2+x=n so x=n-2.

answer d
Intern
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Posts: 20
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Kudos [?]: 0 [0], given: 0

Re: 2^x+2^x+2^x+2^x = 2^n [#permalink] New post 20 Jan 2011, 05:29
Yep D
4(2^x)=2^n
2^2(2^x)=2^n
2^(x+2)=2^n
x+2=n
x=n-2

Posted from my mobile device Image
Intern
Intern
Joined: 16 Mar 2010
Posts: 13
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Kudos [?]: 2 [0], given: 3

Re: 2^x+2^x+2^x+2^x = 2^n [#permalink] New post 20 Jan 2011, 07:21
I to am with the algebraic approach for arriving at the solution.

But if in the heat of things we forget a ^ m * a ^ n = a ^ {(m+n)} we can substitute for x and solve

2^x + 2^x + 2^x + 2^x = 2^n

Substitute x = 1

2^1 + 2^1 + 2^1 + 2^1 = 2^n

8 = 2^n

n = 3

x = 1 & n = 3
x = 1 = n - 2

D
Senior Manager
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Kudos [?]: 28 [0], given: 161

GMAT ToolKit User GMAT Tests User
Re: 2^x+2^x+2^x+2^x = 2^n [#permalink] New post 18 Feb 2011, 14:02
u can also plug x=0 and u get n=2.
than u can c on the answers
n-2 = x

2-2=0. finish...
Re: 2^x+2^x+2^x+2^x = 2^n   [#permalink] 18 Feb 2011, 14:02
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2^x+2^x+2^x+2^x = 2^n

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