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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 30 Jul 2018, 00:37
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A
B
C
D
E

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  15% (low)

Question Stats:

76% (01:13) correct 24% (01:36) wrong based on 72 sessions

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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 Jul 2018, 01:40
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, 23:51
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, 11:01
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 ?  [#permalink]

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New post 11 Jul 2019, 00:22
Bunuel wrote:
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) \(\frac{7}{6}\)


This is a flawed question since it does not provide preference of operators.
How can somebody ascertain the priority of @ or # over -.
GMAT will never provide such questions in which priority is not decided.

This is a poor quality question and is flawed.
This may be corrected as

If \(a#b = \frac{1}{2a-3b}\) and \(a@b = 3a – 2b\), what is the value of \((1@2) - (3#4)\)?
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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 12 Jul 2019, 19:01
Bunuel wrote:
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) \(\frac{7}{6}\)


1@2:

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

3#4:

1/(2(3) - 3(4)) = 1/(6 - 12) = -1/6

Therefore,

(1@2) - (3#4) = -1 - (-1/6) = -1 + 1/6 = -5/6

Answer: 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] 12 Jul 2019, 19:01
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