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

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If a#b = 1/(2a-3b) and a@b = 3a – 2b, what is the value of 1@2 - 3#4 ?  [#permalink]

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New post 29 Jul 2018, 23:37
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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) \(\frac{7}{6}\)

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If a#b = 1/(2a-3b) and a@b = 3a – 2b, what is the value of 1@2 - 3#4 ?  [#permalink]

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New post 30 Jul 2018, 00:40
a#b = \(\frac{1}{2a-3b}\)

3#4 = \(\frac{1}{2(3)-3(4)}\) = \(\frac{1}{6-12}\) = \(\frac{-1}{6}\)

\(a@b = 3a-2b\)

\(1@2 = 3(1)-2(2) = 3-4 = -1\)

1@2-3#4 = \(-1 - (\frac{-1}{6})\) = \(-1 + \frac{1}{6}\) = \(\frac{-5}{6}\)

Hence option C
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Re: If a#b = 1/(2a-3b) and a@b = 3a – 2b, what is the value of 1@2 - 3#4 ?  [#permalink]

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New post 30 Oct 2018, 22:51
Just for my future knowledge -

I am confused little bit by the '-' sign in between the expression 1@2-3#4 and no usage of parenthesis. Why can this expression also be simplified to 1@-1#4 ?
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Re: If a#b = 1/(2a-3b) and a@b = 3a – 2b, what is the value of 1@2 - 3#4 ?  [#permalink]

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New post 24 Nov 2018, 10:01
anant327 wrote:
Just for my future knowledge -

I am confused little bit by the '-' sign in between the expression 1@2-3#4 and no usage of parenthesis. Why can this expression also be simplified to 1@-1#4 ?


Because 1@2 and 3#4 are two different notations or you can say two different formulas. There is no link between 2 and 3 within themselves unless both notations are solved separately.
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Re: If a#b = 1/(2a-3b) and a@b = 3a – 2b, what is the value of 1@2 - 3#4 ? &nbs [#permalink] 24 Nov 2018, 10:01
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