Last visit was: 22 Apr 2026, 19:37 It is currently 22 Apr 2026, 19:37
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
Sub 505 (Easy)|   Algebra|   Functions and Custom Characters|                  
User avatar
pete300
User avatar
Joined: 17 Sep 2003
Last visit: 05 Nov 2003
Posts: 3
Own Kudos:
35
 [35]
Location: NY
Posts: 3
Kudos: 35
 [35]
If the operation @ is defined for all a and b by the equatio Updated on: 09 Nov 2025, 09:26
Originally posted by pete300 on 18 Sep 2003, 07:58.
Last edited by Bunuel on 09 Nov 2025, 09:26, edited 4 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
4
Kudos
Add Kudos
31
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

86% (01:10) correct 14% (01:49) wrong based on 1594 sessions

History

Date
Time
Result
Not Attempted Yet
If the operation \(@\) is defined for all a and b by the equation \(a@b =\frac{a^2*b}{3}\), then \(2@(3@-1) =\)

A. 4
B. 2
C. -4/3
D. -2
E. -4
ShowHide Answer
Official Answer
E
Every tricky question should trigger a follow up quiz. Build that habit with GMAT Club Forum Quiz →.
Most Helpful Reply
User avatar
guy123
User avatar
Joined: 15 Sep 2003
Last visit: 02 Dec 2003
Posts: 35
Own Kudos:
59
 [8]
Location: california
Posts: 35
Kudos: 59
 [8]
If the operation @ is defined for all a and b by the equatio 21 Sep 2003, 11:37
5
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Formula: a@b=((a^2)*b)/3
Question: 2@(3@-1)= ?

work within the parenthesis first so solve (3@-1) first


(3@-1)= ((3^2)*-1)/3 = (9*-1)/3= -9/3=-3
now take -3 plug back into equation and solve the rest

2@(-3)=((2^2)*-3)/3 = (4*-3)/3= -12/3= -4

so -4 is the answer....this question is merely testing order of operations

remember PEMDAS
General Discussion
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,754
Own Kudos:
810,672
Given Kudos: 105,823
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,754
Kudos: 810,672
If the operation @ is defined for all a and b by the equatio 12 Aug 2014, 01:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
pete300
If the operation @ is defined for all a and b by the equation a@b =(a^2*b)/3, then 2@(3@-1) =

A. 4
B. 2
C. -4/3
D. -2
E. -4
Show more

Check other Operations/functions defining algebraic/arithmetic expressions probelms in our Special Questions Directory.
avatar
PareshGmat
avatar
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,531
Own Kudos:
8,271
 [2]
Given Kudos: 193
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,531
Kudos: 8,271
 [2]
If the operation @ is defined for all a and b by the equatio 12 Aug 2014, 03:27
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
a@b \(= \frac{ba^2}{3}\)

2@(3@-1)

Solving the bracket first

3@-1\(= \frac{-1*3^2}{3} = -3\)

2@-3\(= \frac{-3*2^2}{3} = -4\)

Answer = E
avatar
kinsho
avatar
Joined: 10 Nov 2014
Last visit: 04 Feb 2025
Posts: 7
Own Kudos:
4
Posts: 7
Kudos: 4
If the operation @ is defined for all a and b by the equatio 16 Mar 2016, 19:07
Kudos
Add Kudos
Bookmarks
Bookmark this Post
anceer
If the operation ◙ is defined for all a and b by the equation a ◙ b = \(a^2b\)/3
then 2 ◙ (3 ◙ – 1) =

A. 4
B. 2
C. -4/3
D. -2
E. -4
Show more

Just plugging numbers into the function and following through.

First, we solve for (3 ◙ – 1).

\(((3^2)(-1)) / 3 = -3\)

Now we solve for 2 ◙ -3

\(((2^2)(-3)) / 3 = -4\)

Answer is -4 (E)
User avatar
sashiim20
User avatar
Joined: 04 Dec 2015
Last visit: 05 Jun 2024
Posts: 608
Own Kudos:
1,972
Given Kudos: 276
Location: India
Concentration: Technology, Strategy
Schools: ISB '19 IIMB IIMA XLRI HEC Sept19 intake Rotman '21 NUS '21 NTU '20 Trinity MBA '20 Bocconi '21 Smurfit "21
WE:Information Technology (Consulting)
Schools: ISB '19 IIMB IIMA XLRI HEC Sept19 intake Rotman '21 NUS '21 NTU '20 Trinity MBA '20 Bocconi '21 Smurfit "21
Posts: 608
Kudos: 1,972
If the operation @ is defined for all a and b by the equatio 22 Dec 2018, 19:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
pete300
If the operation @ is defined for all a and b by the equation a@b =(a^2*b)/3, then 2@(3@-1) =

A. 4
B. 2
C. -4/3
D. -2
E. -4
Show more

\(a@b =\frac{(a^2*b)}{3}\)

\(2@(3@-1)\) ----- \((i)\)

\(3@-1 = \frac{3^2*(-1)}{3} = \frac{-9}{3} = -3\)

Hence \((i)\) becomes \(=> 2@-3\)

\(2@-3 = \frac{2^2*-3}{3} = -4\)

Answer E
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 22 Apr 2026
Posts: 5,985
Own Kudos:
5,858
Given Kudos: 163
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,985
Kudos: 5,858
If the operation @ is defined for all a and b by the equatio 15 Sep 2019, 06:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
pete300
If the operation @ is defined for all a and b by the equation a@b =(a^2*b)/3, then 2@(3@-1) =

A. 4
B. 2
C. -4/3
D. -2
E. -4
Show more

3@-1 = 9(-1)/3 = -3
2@-3= 4(-3)/3 =-4

IMO E

Posted from my mobile device
avatar
monk123
avatar
Joined: 15 Jun 2015
Last visit: 08 May 2022
Posts: 197
Own Kudos:
192
Given Kudos: 140
Location: India
Posts: 197
Kudos: 192
If the operation @ is defined for all a and b by the equatio 27 May 2020, 06:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
\(a@b = (a^2*b)/3\)
lets take
3@-1= (3^2*-1)/3
= (9*-1)/3
= -3
Now, put -3 in \(2@(3@-1)\)
2@-3 = (2^2*-3)/3
= (4*-3)/3
= -4

ANSWER (E)
User avatar
BrushMyQuant
User avatar
Joined: 05 Apr 2011
Last visit: 03 Apr 2026
Posts: 2,286
Own Kudos:
2,678
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert
Expert reply
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,286
Kudos: 2,678
If the operation @ is defined for all a and b by the equatio 28 Sep 2022, 11:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given that a@b =\(\frac{(a^2*b)}{3}\) and we need to find the value of 2@(3@-1)

Lets start by finding the value of 3@-1

To find 3@-1 we need to compare what is before and after in a@b and 3@-1

=> We need to substitute a with 3 and b with -1 in a@b =\(\frac{(a^2*b)}{3}\) to get the value of 3@-1

=> 3@-1 =\(\frac{(3^2*(-1))}{3}\) = \(\frac{9*-1}{3}\) = -3

=> 2@(3@-1) = 2@-3 = \(\frac{(2^2*-3)}{3}\) = 4*-1 = -4

So, Answer will be E
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,964
Own Kudos:
1,117
Posts: 38,964
Kudos: 1,117
If the operation @ is defined for all a and b by the equatio 09 Nov 2025, 09:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109754 posts
Krunaal
Tuck School Moderator
853 posts