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

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Director
Status: 1,750 Q's attempted and counting
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GMAT 1: 600 Q45 V29
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WE: Accounting (Accounting)
If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 = [#permalink]

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22 Oct 2013, 19:40
00:00

Difficulty:

5% (low)

Question Stats:

74% (01:39) correct 26% (00:42) wrong based on 109 sessions

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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

Last edited by Bunuel on 23 Oct 2013, 01:19, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 39709
Re: If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 = [#permalink]

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23 Oct 2013, 01:20
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

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

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Director
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 512
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)
Re: If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 = [#permalink]

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23 Oct 2013, 07:55
Official Explanation

--- 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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Re: If x = 1/2, then x^-1 + x^-2 + x^-3 + x^-4 = [#permalink]

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26 Feb 2014, 02:46
1
KUDOS
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, 02:46
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