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If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 =

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Director
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If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 = [#permalink] New post 22 Oct 2013, 18:40
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

78% (01:40) correct 22% (00:27) wrong based on 58 sessions
If x =\frac{1}{2}, then x^{-1} + x^{-2} + x^{-3} + x^{-4} =

(A) 1/32
(B) 15/16
(C) 1
(D) 30
(E) 32
[Reveal] Spoiler: OA

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Last edited by Bunuel on 23 Oct 2013, 00:19, edited 1 time in total.
Edited the question.
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Re: If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 = [#permalink] New post 23 Oct 2013, 00:20
Expert's post
avohden wrote:
If x =\frac{1}{2}, then x^{-1} + x^{-2} + x^{-3} + x^{-4} =

(A) 1/32
(B) 15/16
(C) 1
(D) 30
(E) 32



x^{-1} + x^{-2} + x^{-3} + x^{-4} =\frac{1}{x}+\frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^4}=2+4+8+16=30.

Answer: D.
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Director
Director
User avatar
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 513
Location: United States (FL)
Schools: UFL (A)
GMAT 1: 600 Q45 V29
GMAT 2: 590 Q35 V35
GMAT 3: 570 Q42 V28
GMAT 4: 610 Q44 V30
GPA: 3.45
WE: Accounting (Accounting)
Followers: 19

Kudos [?]: 252 [0], given: 629

Re: If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 = [#permalink] New post 23 Oct 2013, 06:55
Official Explanation

Answer: D
--- Plug in 1/2 for each of the occurrences of x:

x^-1 + x^-2 + x^-3 + x^-4 =
(1/2)^-1 + (1/2)^-2 + (1/2)^-3 + (1/2)^-4 =
1/(1/2) + 1/(1/2)^2 + 1/(1/2)^3 + 1/(1/2)^4 =
2 + 1/(1/4) + 1/(1/8) + 1/(1/16) =
2 + 4 + 8 + 16 =
30, choice (D).
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Director
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Joined: 27 Dec 2012
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Location: India
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Kudos [?]: 203 [0], given: 165

Re: If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 = [#permalink] New post 26 Feb 2014, 01:46
Did in this way

Given x = 1/2, so 1/x = 2

Placing the values, 2+4+8+16 = 30 = Answer = D
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Re: If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 =   [#permalink] 26 Feb 2014, 01:46
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