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The operation & is defined for all integers a and b by the

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The operation & is defined for all integers a and b by the [#permalink]

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New post 24 Oct 2013, 09:47
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The operation & is defined for all integers a and b by the equation a&b = (a - 1)(b - 1). If x&13 = 96, what is the value of x ?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 12

GH-04.15.13 | OE to follow
[Reveal] Spoiler: OA
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Kudos [?]: 90022 [0], given: 10402

Re: The operation & is defined for all integers a and b by the [#permalink]

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New post 24 Oct 2013, 09:50
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Kudos [?]: 90022 [1] , given: 10402

Re: The operation & is defined for all integers a and b by the [#permalink]

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New post 24 Oct 2013, 09:51
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Bunuel wrote:
avohden wrote:
The operation & is defined for all integers a and b by the equation a&b = (a - 1)(b - 1). If x&13 = 96, what is the value of x ?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 12

GH-04.15.13 | OE to follow


a&b = (a - 1)(b - 1)
x&13 = (x-1)(13-1) = 96 --> x-1=8 --> x=9.

Answer: C.


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Director
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User avatar
Status: 1,750 Q's attempted and counting
Affiliations: University of Florida
Joined: 09 Jul 2013
Posts: 513
Location: United States (FL)
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WE: Accounting (Accounting)
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Kudos [?]: 731 [0], given: 630

Re: The operation & is defined for all integers a and b by the [#permalink]

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New post 29 Oct 2013, 21:00
Official Explanation

Answer: C
If a&b = (a - 1)(b - 1), we can come up with an algebraic representation of x&13:

x&13 = (x - 1)(13 -1), or: (x - 1)(12)

We know that's equal to 96, so we can solve for x: 96 = (x-1)(12) | 8 = x - 1 | x = 9, choice (C).
Re: The operation & is defined for all integers a and b by the   [#permalink] 29 Oct 2013, 21:00
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