Last visit was: 23 Apr 2026, 18:11 It is currently 23 Apr 2026, 18:11
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
Walkabout
User avatar
Joined: 02 Dec 2012
Last visit: 04 Feb 2026
Posts: 172
Own Kudos:
29,264
 [57]
Given Kudos: 51
Products:
GMAT Club Tests
Posts: 172
Kudos: 29,264
 [57]
If the operation @ is defined by x@y=(xy)^1/2 for all 17 Dec 2012, 07:43
10
Kudos
Add Kudos
47
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
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:

90% (01:11) correct 10% (01:51) wrong based on 3105 sessions

History

Date
Time
Result
Not Attempted Yet
If the operation @ is defined by \(x@y=\sqrt{xy}\) for all positive numbers x and y, then (5@45)@60 =

(A) 30
(B) 60
(C) 90
(D) \(30\sqrt{15}\)
(E) \(60\sqrt{15}\)
ShowHide Answer
Official Answer
A
If this question felt shaky, try an adaptive mini quiz of similar problems in GMAT Club Forum Quiz →. Free plan gives 5 questions per day.
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,785
Own Kudos:
810,872
 [6]
Given Kudos: 105,853
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: 109,785
Kudos: 810,872
 [6]
If the operation @ is defined by x@y=(xy)^1/2 for all 17 Dec 2012, 07:46
6
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Walkabout
If the operation @ is defined by \(x@y=\sqrt{xy}\) for all positive numbers x and y, then (5@45)@60 =

(A) 30
(B) 60
(C) 90
(D) \(30\sqrt{15}\)
(E) \(60\sqrt{15}\)
Show more

\((5@45)@60 =(\sqrt{5*45})@60=(\sqrt{225})@60=15@60=\sqrt{15*60}=30\).

Answer: A.
User avatar
Carcass
User avatar
Board of Directors
Joined: 01 Sep 2010
Last visit: 23 Apr 2026
Posts: 4,712
Own Kudos:
37,838
 [5]
Given Kudos: 4,925
Posts: 4,712
Kudos: 37,838
 [5]
If the operation @ is defined by x@y=(xy)^1/2 for all 17 Dec 2012, 07:50
5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I'm writing the answer but Bunuel is too fast to reply, a machine :)
General Discussion
User avatar
avohden
User avatar
Joined: 09 Jul 2013
Last visit: 14 Mar 2015
Posts: 405
Own Kudos:
3,202
 [5]
Given Kudos: 630
Status:1,750 Q's attempted and counting
Affiliations: University of Florida
Location: United States (FL)
Schools: Warrington (A)
GMAT 1: 570 Q42 V28
GMAT 2: 610 Q44 V30
GMAT 3: 600 Q45 V29
GMAT 4: 590 Q35 V35
GPA: 3.45
WE:Accounting (Accounting)
Schools: Warrington (A)
GMAT 4: 590 Q35 V35
Posts: 405
Kudos: 3,202
 [5]
If the operation @ is defined by x@y=(xy)^1/2 for all 24 Oct 2013, 20:11
3
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
I tried to keep the numbers as manageable as possible and use numbers that I knew the perfect squares of.

\((5@45)@60\)= \(\sqrt{5*(5*9)}\) \(=5*3=15\)

\(15@60=\) \(\sqrt{(3*5)*(3*4*5)}\) \(= 3*5*2= 30\)
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 23 Apr 2026
Posts: 22,283
Own Kudos:
26,531
 [2]
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,283
Kudos: 26,531
 [2]
If the operation @ is defined by x@y=(xy)^1/2 for all 21 Jun 2016, 10:29
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Walkabout
If the operation @ is defined by \(x@y=\sqrt{xy}\) for all positive numbers x and y, then (5@45)@60 =

(A) 30
(B) 60
(C) 90
(D) \(30\sqrt{15}\)
(E) \(60\sqrt{15}\)
Show more

We are given that the operation @ is defined by x@y = √(xy) for all positive numbers.

We are next given that (5@45)@60. Following PEMDAS rules, we want to begin with the operation inside the parentheses. According to the operation, x will be replaced with 5, and y will be replaced with 45. Thus, we have:

5@45 = √(5 *45) = √225 = 15

We have determined that (5@45) = 15, so we substitute 15 for (5@45) to obtain 15@60.

According to the operation, x will now be replaced with 15 and y will now be replaced with 60. Thus we have:

15@60 = √(15*60) = √900 = 30

The answer is A.
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,451
 [3]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,451
 [3]
If the operation @ is defined by x@y=(xy)^1/2 for all Updated on: 25 May 2020, 13:28
Originally posted by BrentGMATPrepNow on 28 Aug 2017, 15:39.
Last edited by BrentGMATPrepNow on 25 May 2020, 13:28, edited 1 time in total.
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Walkabout
If the operation @ is defined by \(x@y=\sqrt{xy}\) for all positive numbers x and y, then (5@45)@60 =

(A) 30
(B) 60
(C) 90
(D) \(30\sqrt{15}\)
(E) \(60\sqrt{15}\)
Show more

I call these "Strange Operator" questions.
We want to evaluate: (5 @ 45) @ 60

Start with (5 @ 45)
(5 @ 45) = √[(5)(45)]
= √225
= 15


So, (5 @ 45) @ 60 = 15 @ 60
From here, 15 @ 60 = √[(15)(60)]
= √900
= 30

Answer: A
User avatar
BrushMyQuant
User avatar
Joined: 05 Apr 2011
Last visit: 03 Apr 2026
Posts: 2,286
Own Kudos:
2,680
 [3]
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: 2,680
 [3]
If the operation @ is defined by x@y=(xy)^1/2 for all 17 Jan 2022, 10:17
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Given that \(x@y=\sqrt{xy}\) and we need to find the value of \((5@45)@60\)

Let's start by finding the value of \(5@45\)

To find \(5@45\) we need to compare \(5@45\) with x@y and see what is before the \(@\) what is after
=> x = 5 and y = 45

=> to find the value of \(5@45\) we need to replace x with 5 and y with 45 in \(x@y=\sqrt{xy}\)
=> \(5@45\)=\(\sqrt{5*45}\) = \(\sqrt{5*5*9}\) = \(\sqrt{5^2*3^2}\) = 5*3 = 15

=> \((5@45)@60\) = \(15@60\)

Similarly, \(15@60=\sqrt{15*60}\) = \(\sqrt{15*15*4}\) = \(\sqrt{15^2*2^2}\) = 15*2 = 30

So, Answer will be A
Hope it helps!

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

User avatar
totaltestprepNick
User avatar
Joined: 25 Aug 2014
Last visit: 22 Apr 2026
Posts: 469
Own Kudos:
4
Given Kudos: 2
GMAT 1: 750 Q49 V42
GMAT 1: 750 Q49 V42
Posts: 469
Kudos: 4
If the operation @ is defined by x@y=(xy)^1/2 for all 01 Mar 2026, 18:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Walkabout
If the operation @ is defined by \(x@y=\sqrt{xy}\) for all positive numbers x and y, then (5@45)@60 =

(A) 30
(B) 60
(C) 90
(D) \(30\sqrt{15}\)
(E) \(60\sqrt{15}\)
Show more

Show Spoiler
A




Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience

[email protected]
Moderators:
Bunuel
Math Expert
109785 posts
Krunaal
Tuck School Moderator
853 posts