Last visit was: 19 Nov 2025, 02:39 It is currently 19 Nov 2025, 02:39
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,379
Own Kudos:
778,173
 [3]
Given Kudos: 99,977
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: 105,379
Kudos: 778,173
 [3]
If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib 24 Dec 2020, 01:15
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

62% (02:22) correct 38% (02:27) wrong based on 168 sessions

History

Date
Time
Result
Not Attempted Yet
If A, B, and C are positive integers and \(\sqrt{A*B*C}=504\), is B divisible by 2?

(1) C = 168
(2) A is a perfect square


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
C
User avatar
callmeDP
User avatar
Joined: 25 Oct 2020
Last visit: 12 Dec 2022
Posts: 71
Own Kudos:
111
 [3]
Given Kudos: 274
Status:No one but you matter
Location: India
Schools: Alberta '23 HEC Montreal
Schools: Alberta '23 HEC Montreal
Posts: 71
Kudos: 111
 [3]
If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib 24 Dec 2020, 05:04
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
If A, B, and C are positive integers and \(\sqrt{A*B*C}=504\), is B divisible by 2?

(1) C = 168
(2) A is a perfect square

504=21*3*8


1. C = 168 = 3*7*8

Does not tell us anything about B. >> Not.Sufficient.

2. A is perfect sq.

Ok so this means \(\sqrt{B*C}\) is also perfect square but what their values are we dont know. >> Not.Sufficient.

Togther, C = 168 and A is perfect sq. so yes B should be such that \(\sqrt{B*C}\) is also perfect sq. and we will get definite Yes or No.

Sufficient.

IMO C
User avatar
rocky620
User avatar
Retired Moderator
Joined: 10 Nov 2018
Last visit: 11 May 2023
Posts: 501
Own Kudos:
607
 [1]
Given Kudos: 229
Location: India
Concentration: General Management, Strategy
Schools: IIMA PGPX'22 IIMB EPGP'22 IIMC PGPEX'22 ISB'22
GMAT 1: 590 Q49 V22
WE:Other (Retail: E-commerce)
Schools: IIMA PGPX'22 IIMB EPGP'22 IIMC PGPEX'22 ISB'22
GMAT 1: 590 Q49 V22
Posts: 501
Kudos: 607
 [1]
If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib 24 Dec 2020, 08:07
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
504 = \(2^3\) * \(3^2\) * 7

Statement 1:

C=168 = \(2^3\)*3*7. All 2s are gone, nothing left for B.
So, B is not divisible by 2.
Sufficient.

Statement 2:
A is a perfect square, It can be 4, 9, 36, in every case we have a 2 left (min). It can be a factor of B or C.
Insufficient

IMO Option A
avatar
TarunKumar1234
avatar
Joined: 14 Jul 2020
Last visit: 28 Feb 2024
Posts: 1,107
Own Kudos:
1,348
 [2]
Given Kudos: 351
Location: India
Posts: 1,107
Kudos: 1,348
 [2]
If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib 24 Dec 2020, 08:47
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
given, Sqrt (A∗B∗C)=504= (2^3)*(3^2)*7, so A*B*C = (2^6)*(3^4)*(7^2)

Stat1: C = 168 = (2^3)*3*7
So, A*B = (2^3)*(3^3)*(7^1), now, B can be divisible by 2 or not. Not sufficient.

Stat2: A is a perfect square
So, A*B*C = (2^6)*(3^4)*(7^2), now, B can be divisible by 2 or not. Not sufficient.

Combining Stat 1 and 2,
A*B = (2^3)*(3^3)*(7^1), and A is a perfect square, so for B, we have always one 2 left. Sufficient

So, I think C. :)
avatar
Himanshu930
avatar
Joined: 17 Aug 2014
Last visit: 04 Jan 2021
Posts: 5
Own Kudos:
7
 [1]
Posts: 5
Kudos: 7
 [1]
If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib 24 Dec 2020, 09:54
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
504 = 2*2*2*3*3*7
so A*B*C = 2*2*2*2*2*2*3*3*3*3*7*7

Statement 1: C=168 = 2*2*2*3*7
=> A*B = 2*2*2*3*3*3*7
As we don't know the value of A so this statement is not sufficient.

Statement 2: A is a perfect square
As there are six 2s, four 3s and two 7s so, there are many perfect squares.
So, this statement is also not sufficient.

Combining Statements A and B:
C= 2*2*2*3*7
A*B = 2*2*2*3*3*3*7
If A is a perfect square then it can have maximum of two 2s which means one of the 2 will be left. So, B will always be a multiple of 2.

So, correct answer is C.
User avatar
CEdward
User avatar
Joined: 11 Aug 2020
Last visit: 14 Apr 2022
Posts: 1,203
Own Kudos:
272
Given Kudos: 332
Posts: 1,203
Kudos: 272
If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib 25 Dec 2020, 00:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is the answer E?
Couldn't we just use knowledge of odd/even to figure this one out?
From the stem, we see that the\( \sqrt{ABC}\) gives us 504. This tells us that ABC MUST be an even perfect square.

Statement 1 - C = 168
1. a is even, b is even, c is even YES b is divisible by 2
2. a is odd, b is even, c is even YES
3. a is even, b is odd, c is even NO
Insufficient

Statement 2 - a is a perfect square
This means a could be odd or even, doesn't tell us anything about B

Combined:
Well if b could be even or odd, we don't know.
Insufficient

Answer: E
User avatar
parth2424
User avatar
Joined: 11 Oct 2020
Last visit: 17 Dec 2021
Posts: 35
Own Kudos:
9
Given Kudos: 122
Posts: 35
Kudos: 9
If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib 01 Jan 2021, 22:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If A, B, and C are positive integers and \(\sqrt{A*B*C}=504\), is B divisible by 2?

(1) C = 168
(2) A is a perfect square


Are You Up For the Challenge: 700 Level Questions


Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here
Show more
Q - is b even
(Abc) = 504 * 504 or abc = even
1) c = 168 even insufficient
2) a is a perfect sq
A can end in
1,4,5,9,6 insufficient
1&2 )
Ab = (504*504/168) or even
Even * even = even
Od * even = even
A can be both od/even
So b has to be even. And divisible by 2
Hence ans C

Posted from my mobile device
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,583
Own Kudos:
1,079
Posts: 38,583
Kudos: 1,079
If A, B, and C are positive integers and ABC^(1/2) = 504, is B divisib 29 Aug 2023, 11:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
105379 posts
kingbucky
496 posts