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The operation @ is defined by the equation a@b = (a – 1)(b –

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The operation @ is defined by the equation a@b = (a – 1)(b – [#permalink] New post 30 Jul 2018, 10:27
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Question Stats:

61% (01:10) correct 38% (01:10) wrong based on 42 sessions
The operation @ is defined by the equation a@b = (a – 1)(b – 2). x@5 = 3@x

Quantity A
Quantity B
x
1


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The operation @ is defined by the equation a@b = (a – 1)(b – [#permalink] New post 01 Aug 2018, 09:12
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x@5 = (x-1)(3)
= 3x - 3

3@x = 2(x-2)
= 2x - 4

From question,
3x - 3 = 2x - 4
or, x= -1
B>A

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Retired Moderator
User avatar
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2914 [0], given: 394

Re: The operation @ is defined by the equation a@b = (a – 1)(b – [#permalink] New post 12 Aug 2018, 05:36
Expert's post
Explanation

This problem defines a function for the made-up symbol @. Use the definition of the new symbol to rewrite the equation x@5 = 3@x without the @ operator:


For x@5, a = x and b = 5: x@5 = (x – 1)(5 – 2) = 3x – 3.
For 3@x, a = 3 and b = x: 3@x = (3 – 1)(x – 2) = 2x – 4.

Equating these two expressions gives you:
\(3x - 3 = 2x - 4\)
\(x = -1\)

Quantity B is greater.
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Re: The operation @ is defined by the equation a@b = (a – 1)(b –   [#permalink] 12 Aug 2018, 05:36
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