Last visit was: Mon Sep 14, 2026 5:05 am It is currently Mon Sep 14, 2026 5:05 am
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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 14 Sep 2026
Posts: 113,494
Own Kudos:
841,173
 [22]
Given Kudos: 111,512
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,494
Kudos: 841,173
 [22]
If a and b are integers, and 240a = b 3 , which of the following must Mon Feb 17, 2020 7:39 am
Kudos
Add Kudos
22
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

57% (02:00) correct 43% (02:25) wrong based on 392 sessions

History

Date
Time
Result
Not Attempted Yet
If \(a\) and \(b\) are integers, and \(240a = b^3\), which of the following must be an integer?

I. \(\frac{a}{300}\)

II. \(\frac{a}{600}\)

III.\(\frac{a}{450}\)

A. None
B. I only
C. III only
D. I and III only
E. I, II, and II


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
D
User avatar
lacktutor
User avatar
Joined: 25 Jul 2018
Last visit: 23 Oct 2023
Posts: 658
Own Kudos:
1,495
 [5]
Given Kudos: 69
Posts: 658
Kudos: 1,495
 [5]
If a and b are integers, and 240a = b 3 , which of the following must Mon Feb 17, 2020 11:39 am
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If a and b are integers, and \(240a=b^{3}\), which of the following must be an integer?

\(240a=2^{4}*3*5*a= b^{3}\\
\)

In order b to be the integer, a must be at least \(2^{2}* 3^{2}*5^{2}= 4*9*25=900\)

I. \(\frac{a}{300}\)--YES

II. \(\frac{a}{600}\)- NO

III. \(\frac{a}{450}\) -YES

The answer is D.
User avatar
jkolachi
User avatar
Joined: 12 Oct 2015
Last visit: 05 Feb 2025
Posts: 237
Own Kudos:
415
 [1]
Given Kudos: 144
Location: Canada
Concentration: Leadership, Accounting
Schools: Ivey '19 (A) Queen's 19 (A) Schulich Jan 18 Intake (A)
GMAT 1: 700 Q47 V39
GPA: 3
WE:Accounting (Accounting)
Products:
My Reviews
Schools: Ivey '19 (A) Queen's 19 (A) Schulich Jan 18 Intake (A)
GMAT 1: 700 Q47 V39
Posts: 237
Kudos: 415
 [1]
If a and b are integers, and 240a = b 3 , which of the following must Mon Feb 17, 2020 2:11 pm
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 13 Sep 2026
Posts: 8,817
Own Kudos:
5,340
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,817
Kudos: 5,340
If a and b are integers, and 240a = b 3 , which of the following must Tue Feb 18, 2020 2:09 am
Kudos
Add Kudos
Bookmarks
Bookmark this Post
240 = 2^4*3*5 and a has to be 2^2*3^2*5^2 for both LHS = RHS
for given option only option 1 & 3 are true and would give an integer value
IMO D


Bunuel
If \(a\) and \(b\) are integers, and \(240a = b^3\), which of the following must be an integer?

I. \(\frac{a}{300}\)

II. \(\frac{a}{600}\)

III.\(\frac{a}{450}\)

A. None
B. I only
C. III only
D. I and III only
E. I, II, and II


Are You Up For the Challenge: 700 Level Questions
Show more
User avatar
exc4libur
User avatar
Joined: 24 Nov 2016
Last visit: 22 Mar 2022
Posts: 1,678
Own Kudos:
1,495
 [1]
Given Kudos: 607
Location: United States
Posts: 1,678
Kudos: 1,495
 [1]
If a and b are integers, and 240a = b 3 , which of the following must Mon Mar 30, 2020 8:13 am
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
If \(a\) and \(b\) are integers, and \(240a = b^3\), which of the following must be an integer?

I. \(\frac{a}{300}\)

II. \(\frac{a}{600}\)

III.\(\frac{a}{450}\)

A. None
B. I only
C. III only
D. I and III only
E. I, II, and II
Show more

\(240a = b^3…24*10a=b^3…2^4*3*5*a=b^3\)
\(2^4*3*5*a=perfect.cube…(powers.primes.must.be.multiples.of.3)\)
\(perfect.cube=min(2^6*3^3*5^3)\)
\(min(a)=2^2*3^2*5^2\)

\(a/pf(300)=3*100=3*2^2*5^2…must.be.div\)
\(a/pf(600)=6*100=3*2^3*5^2…min(a)=2^2≠2^3…may.not.be.div\)
\(a/pf(450)=45*10=3^2*2*5^2…must.be.div\)

Ans (D)
User avatar
riarr
User avatar
Joined: 15 May 2021
Last visit: 20 Mar 2024
Posts: 3
Given Kudos: 114
Location: India
Posts: 3
Kudos: 0
If a and b are integers, and 240a = b 3 , which of the following must Thu Jan 20, 2022 9:45 pm
Kudos
Add Kudos
Bookmarks
Bookmark this Post
why cant we assume a and b to be 0?
In this case 240 (0)= (0)^3 and A,B,C will not be an integer so answer is none
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 14 Sep 2026
Posts: 113,494
Own Kudos:
841,173
Given Kudos: 111,512
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,494
Kudos: 841,173
If a and b are integers, and 240a = b 3 , which of the following must Fri Jan 21, 2022 12:47 am
Kudos
Add Kudos
Bookmarks
Bookmark this Post
riarr
why cant we assume a and b to be 0?
In this case 240 (0)= (0)^3 and A,B,C will not be an integer so answer is none
Show more

I think you are missing that zero is an integer.

ZERO:

1. Zero is an INTEGER.

2. Zero is an EVEN integer.

3. Zero is neither positive nor negative (the only one of this kind)

4. Zero is divisible by EVERY integer except 0 itself (\(\frac{x}{0} = 0\), so 0 is a divisible by every number, x).

5. Zero is a multiple of EVERY integer (\(x*0 = 0\), so 0 is a multiple of any number, x)

6. Zero is NOT a prime number (neither is 1 by the way; the smallest prime number is 2).

7. Division by zero is NOT allowed: anything/0 is undefined.

8. Any non-zero number to the power of 0 equals 1 (\(x^0 = 1\))

9. \(0^0\) case is NOT tested on the GMAT.

10. If the exponent n is positive (n > 0), \(0^n = 0\).

11. If the exponent n is negative (n < 0), \(0^n\) is undefined, because \(0^{negative}=0^n=\frac{1}{0^{(-n)}} = \frac{1}{0}\), which is undefined. You CANNOT take 0 to the negative power.

12. \(0! = 1! = 1\).



2. Properties of Integers



For more check Ultimate GMAT Quantitative Megathread



Hope it helps.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,235
Own Kudos:
1,158
Posts: 39,235
Kudos: 1,158
If a and b are integers, and 240a = b 3 , which of the following must Mon Jul 21, 2025 12:38 am
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.
Moderator:
Bunuel
Math Expert
113494 posts