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

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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
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WE: Accounting (Accounting)
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Kudos [?]: 828 [0], given: 630

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

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24 Oct 2013, 10:47
00:00

Difficulty:

5% (low)

Question Stats:

81% (01:39) correct 19% (00:53) wrong based on 96 sessions

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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
Math Expert
Joined: 02 Sep 2009
Posts: 39064
Followers: 7757

Kudos [?]: 106584 [0], given: 11630

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

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24 Oct 2013, 10:50
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.

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Math Expert
Joined: 02 Sep 2009
Posts: 39064
Followers: 7757

Kudos [?]: 106584 [1] , given: 11630

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

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24 Oct 2013, 10:51
1
KUDOS
Expert's post
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)
Followers: 26

Kudos [?]: 828 [0], given: 630

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

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29 Oct 2013, 22:00
Official Explanation

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, 22:00
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