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Math Expert V
Joined: 02 Sep 2009
Posts: 56307
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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Difficulty:   15% (low)

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

### HideShow timer Statistics 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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MBA Section Director V
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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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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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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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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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Senior Manager  G
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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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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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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

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. 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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