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avohden
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The operation & is defined for all integers a and b by the 24 Oct 2013, 10:47
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C
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Question Stats:

87% (00:50) correct 13% (01:17) wrong based on 302 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
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C
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The operation & is defined for all integers a and b by the 24 Oct 2013, 10:50
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avohden
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
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a&b = (a - 1)(b - 1)
x&13 = (x-1)(13-1) = 96 --> x-1=8 --> x=9.

Answer: C.
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The operation & is defined for all integers a and b by the 24 Oct 2013, 10:51
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Bunuel
avohden
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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The operation & is defined for all integers a and b by the 29 Oct 2013, 22:00
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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).
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The operation & is defined for all integers a and b by the 28 Oct 2019, 08:13
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avohden
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
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(x-1)(13-1) = 96 = 8*12
(x-1)*12 = 8*12
x = 9

IMO C
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The operation & is defined for all integers a and b by the 18 May 2023, 11:03
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To find the value of x given the equation x&13 = 96, where the operation & is defined as (a - 1)(b - 1), we can substitute the values into the equation:

x&13 = (x - 1)(13 - 1) = 96

Simplifying this equation:

(x - 1)(12) = 96

Dividing both sides of the equation by 12:

x - 1 = 8

Adding 1 to both sides of the equation:

x = 9

Therefore, the value of x is 9. Hence, the correct option is (C) 9.
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