Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 21 Jul 2019, 12:18

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
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]

### Show Tags

30 Jul 2018, 00:37
00:00

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) $$\frac{7}{6}$$

_________________
MBA Section Director
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 2561
GPA: 4
WE: Engineering (Computer Software)
Re: If a#b = 1/(2a-3b) and a@b = 3a – 2b, what is the value of 1@2 - 3#4 ?  [#permalink]

### Show Tags

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
_________________
Intern
Joined: 28 Aug 2018
Posts: 27
Location: India
Schools: LBS '21 (A)
GMAT 1: 650 Q49 V31
GPA: 3.16
Re: If a#b = 1/(2a-3b) and a@b = 3a – 2b, what is the value of 1@2 - 3#4 ?  [#permalink]

### Show Tags

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 ?
SVP
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1687
Location: India
GPA: 3.01
WE: Engineering (Real Estate)
Re: If a#b = 1/(2a-3b) and a@b = 3a – 2b, what is the value of 1@2 - 3#4 ?  [#permalink]

### Show Tags

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.
_________________
"Do not watch clock; Do what it does. KEEP GOING."
Senior Manager
Joined: 03 Jun 2019
Posts: 415
Location: India
Re: If a#b = 1/(2a-3b) and a@b = 3a – 2b, what is the value of 1@2 - 3#4 ?  [#permalink]

### Show Tags

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 $$(1@2) - (3#4)$$?
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post.
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6967
Location: United States (CA)
Re: If a#b = 1/(2a-3b) and a@b = 3a – 2b, what is the value of 1@2 - 3#4 ?  [#permalink]

### Show Tags

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

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

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
Display posts from previous: Sort by