Last visit was: 10 Jul 2025, 00:41 It is currently 10 Jul 2025, 00:41
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 July 2025
Posts: 102,612
Own Kudos:
Given Kudos: 97,883
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,612
Kudos: 739,967
 [11]
1
Kudos
Add Kudos
10
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
SiffyB
Joined: 23 Jan 2019
Last visit: 10 Dec 2021
Posts: 174
Own Kudos:
323
 [6]
Given Kudos: 80
Location: India
Posts: 174
Kudos: 323
 [6]
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
General Discussion
avatar
Javedkhan740
Joined: 01 Jan 2020
Last visit: 18 Mar 2022
Posts: 4
Own Kudos:
2
 [1]
Given Kudos: 9
Posts: 4
Kudos: 2
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 09 Jul 2025
Posts: 21,066
Own Kudos:
Given Kudos: 296
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: 21,066
Kudos: 26,121
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If a, b, and c are distinct positive integers, and a + b + c = 31, what is the greatest possible value of a*b*c?

A. 1024
B. 1056
C. 1072
D. 1080
E. 1200


The greatest product of any number of positive integers when they are given a fixed sum is when the numbers are closest to one another. Since there are 3 numbers and their sum is 31, each number should be around 10. Therefore, the greatest product would be 10 x 10 x 11 = 1100 if the 3 numbers are not necessarily distinct. However, since they have to be distinct, we can decrease one of the 10s to 9 and increase 11 to 12. Therefore, the greatest product is 9 x 10 x 12 = 1080 given that the 3 numbers are distinct and their sum is 31.

Answer: D
avatar
Onyedelmagnifico
Joined: 25 Feb 2020
Last visit: 08 Jul 2025
Posts: 9
Own Kudos:
Given Kudos: 12
Posts: 9
Kudos: 2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
We try finding three consecutive numbers and sum it to 31.
That let a be the greatest of such positive integer such that
a+a-1+a-2=31
3a=34
a=11.333
Take the ceiling function of a we have 12 and floor function of a-1 and a-2 we have
10 and 9 respectively. Hence the greatest product is
9×10×12=1080. Hence OPTION D.
{The Transformation-Nigeria}

Posted from my mobile device
User avatar
BrushMyQuant
Joined: 05 Apr 2011
Last visit: 07 Jul 2025
Posts: 2,243
Own Kudos:
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
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,243
Kudos: 2,457
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given that a, b, and c are distinct positive integers, and a + b + c = 31, And we need to find the greatest possible value of a*b*c?

Theory: Given the sum of a set of number, their product will be maximum when they are equal or are close by

For a * b * c to be maximum all of them should be close to each other
Now, 31/3 ~ 10
=> Numbers can be 10, 10, 11 to make the sum as 31
But, they need to be distinct
=> we can try with 9, 10, 12 to get the product as 9 * 10 * 12 = 1080

So, Answer will be D
Hope it helps!

Watch the following video to MASTER Sequence problems

User avatar
Jalmagro
Joined: 05 Mar 2024
Last visit: 09 Jul 2025
Posts: 9
Own Kudos:
Given Kudos: 78
Location: United States
Products:
Posts: 9
Kudos: 1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Easy way to start:

Factor the highest number given (1200)

You find the three main factors (12, 10, and 10) are not only not distinct but also equate to 32

Then trickle down to the next option, factor 1080 to get down to (12, 9, 10)

Answer D :)
Moderators:
Math Expert
102612 posts
PS Forum Moderator
683 posts