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# If a#b = and a@b = 3a – 2b, what is the value of 1@2 – 3#4?

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1783 [1] , given: 397

If a#b = and a@b = 3a – 2b, what is the value of 1@2 – 3#4? [#permalink]  27 Jul 2018, 07:13
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Question Stats:

100% (00:35) correct 0% (00:00) wrong based on 5 sessions
If $$a#b = \frac{1}{2a-3b}$$ and $$a@b = 3a – 2b$$, what is the value of $$1@2 - 3#4$$?

(A) $$\frac{-7}{6}$$
(B) –1
(C) $$\frac{-5}{6}$$
(D) $$\frac{2}{3}$$
(E) $$\frac{7}{6}$$
[Reveal] Spoiler: OA

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Sandy
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1783 [0], given: 397

Re: If a#b = and a@b = 3a – 2b, what is the value of 1@2 – 3#4? [#permalink]  12 Aug 2018, 05:29
Expert's post
Explanation

This problem defines functions for the made-up symbols # and @. Substitute a = 1 and b = 2 into the function for a@b: 3(1) – 2(2) = –1. Substitute a = 3 and b = 4 into the function for a#b: $$\frac{1}{2(3)-3(4)}=\frac{1}{-6}$$.

Now, subtract: $$(-1) - \frac{1}{-6}= -1 + \frac{1}{6}= \frac{-5}{6}$$.
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Sandy
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Re: If a#b = and a@b = 3a – 2b, what is the value of 1@2 – 3#4?   [#permalink] 12 Aug 2018, 05:29
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