Last visit was: 24 Apr 2026, 01:08 It is currently 24 Apr 2026, 01:08
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
avatar
TheUltimateWinner
avatar
Schools: Harvard '24 Judge '23 LBS '24 McCombs '24 Mendoza Tepper '24 Ross '24 Cox Marshall '24 Fisher Kelley '24 Jones McDonough '24 Owen '24 Terry BU Simon '24 Katz GWU Mason Babson Gabelli Foster '24 Goizueta '24 Scheller Stern '23 CBS '23 Booth '23 Haas '25 Wharton '25 Stanford '26 Johnson'23 Fuqua '23 Kellogg '23 Kenan-Flagler'23 INSEAD Aug 22 intake Olin '23 Said '23 Sloan '23 Carey Arizona "22 Yale '23 UC Davis Madison '23 Anderson '23 Carroll Carlson '23 Darden '23
Posts: 2,465
Kudos: 2,456
 [5]
Is p^2 divisible by 24? p is an integer. 1) p is divisible by 6 2) p^3 19 Apr 2019, 09:15
Kudos
Add Kudos
5
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:

55% (hard)

Question Stats:

61% (01:56) correct 39% (01:52) wrong based on 148 sessions

History

Date
Time
Result
Not Attempted Yet
Is \(p^2\) divisible by 24? p is an integer.

(1) \(p\) is divisible by 6
(2) \(p^3\) is divisible by 24­
ShowHide Answer
Official Answer
E
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 22 Apr 2026
Posts: 11,229
Own Kudos:
45,006
 [1]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,229
Kudos: 45,006
 [1]
Is p^2 divisible by 24? p is an integer. 1) p is divisible by 6 2) p^3 20 Apr 2019, 00:22
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is \(p^2\) divisible by 24? p is an integer.
1) \(p\) is divisible by 6
So \(p^2\) will be divisible by \(6^2\) or 36..
But 36 is not a multiple of 24, so we cannot say anything about 24.
Insufficient

2) \(p^3\) is divisible by 24
So \(p^3=24a=2^3*3*a\).
Thus p will surely be divisible by 2*3 or 6..
But we cannot say anything about 24 as 6 is not a multiple of 24.
If a number is divisible by 24, it is surely divisible by its factors 1,3,4,6,12 etc but the vice versa need not be true.
Insufficient

Combined
Both the choices tell us that p is divisible by 6, but nothing about 24.
Insufficient

E
User avatar
miquelperezn
User avatar
Joined: 03 Jun 2023
Last visit: 21 Oct 2025
Posts: 5
Given Kudos: 21
Posts: 5
Kudos: 0
Is p^2 divisible by 24? p is an integer. 1) p is divisible by 6 2) p^3 02 May 2024, 09:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I do not understand why statement 1) and 2) combined are insufficient... could any expert help here?

Thanks!
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Apr 2026
Posts: 109,802
Own Kudos:
810,909
 [1]
Given Kudos: 105,868
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: 109,802
Kudos: 810,909
 [1]
Is p^2 divisible by 24? p is an integer. 1) p is divisible by 6 2) p^3 02 May 2024, 10:13
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
 
miquelperezn
I do not understand why statement 1) and 2) combined are insufficient... could any expert help here?

Thanks!
Show more
­Is \(p^2\) divisible by 24? p is an integer.

Since p is an integer, for \(p^2\) to be divisible by 24 = 2^3*3, p must be divisible by 2^23.

(1) \(p\) is divisible by 6

This implies that p is divisible by 2*3. Not sufficient.

(2) \(p^3\) is divisible by 24­

This implies the same as above: that p is divisible by 2*3. Not sufficient.

(1)+(2) Both statements give us the same information: p is divisible by 2*3. If p = 6, then the answer is NO: \(p^2 = 36\) is NOT divisible by 24. However, if \(p = 2^2*3 = 12\), then \(p^2 = 144\) IS divisible by 24. Not sufficient.

Answer: E.

P.S. Worth noting though that such type of pure algebraic questions are no longer a part of the DS syllabus of the GMAT.­

­DS questions in GMAT Focus encompass various types of word problems, such as:
  • Word Problems
  • Work Problems
  • Distance Problems
  • Mixture Problems
  • Percent and Interest Problems
  • Overlapping Sets Problems
  • Statistics Problems
  • Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won't encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."­

­Check GMAT Syllabus for Focus Edition­

Hope it helps.­
 ­
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,965
Own Kudos:
1,117
Posts: 38,965
Kudos: 1,117
Is p^2 divisible by 24? p is an integer. 1) p is divisible by 6 2) p^3 15 Jul 2025, 14:34
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
109802 posts
kingbucky
498 posts
Gmat860sanskar
212 posts