Last visit was: 05 Sep 2026, 19:50 It is currently 05 Sep 2026, 19:50
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
kevincan
User avatar
GMAT Instructor
Joined: 04 Jul 2006
Last visit: 05 Sep 2026
Posts: 2,478
Own Kudos:
4,918
 [7]
Given Kudos: 451
GMAT 1: 790 Q51 V51
GRE 1: Q170 V170
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GMAT 1: 790 Q51 V51
GRE 1: Q170 V170
Posts: 2,478
Kudos: 4,918
 [7]
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
User avatar
NiharikaRawat
Joined: 18 Jul 2025
Last visit: 04 Sep 2026
Posts: 1
Given Kudos: 251
Posts: 1
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
adconsectetur
Joined: 27 Feb 2026
Last visit: 05 Sep 2026
Posts: 65
Own Kudos:
Given Kudos: 12
GMAT Focus 1: 715 Q90 V85 DI81
Products:
GMAT Focus 1: 715 Q90 V85 DI81
Posts: 65
Kudos: 33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 05 Sep 2026
Posts: 11,288
Own Kudos:
46,097
 [2]
Given Kudos: 339
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,288
Kudos: 46,097
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Add all of them and you have two of each of ab, bc and ab added, that is 2(ab+bc+ac)=152+162+170=484
So ab+bc+ac=242.
Choose any of the given expression and subtract from above..
C(a+b)=ca+bc=170..
So ab =242-170=72
Thus ab*c will be a multiple of 72..
Hit 720..


If there were other multiples of 72 in options..
Subtract the other two expressions in similar manner to get ac and bc as 80 and 90..
Therefore ab*bc*ac =72*80*90
(abc)^2=72*8*10*9*10=72*72*10*10
So abc = 720


NiharikaRawat
kevincan
If a, b, and c are positive real numbers such that a(b + c) = 152, b(c + a) = 162, and c(a + b) = 170, what is the value of abc?

(A) 704
(B) 720
(C) 736
(D) 760
(E) 784
User avatar
shessa
Joined: 26 May 2023
Last visit: 12 Jul 2026
Posts: 6
Given Kudos: 47
Location: Ireland
Concentration: Healthcare, General Management
Posts: 6
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
please provide simplified and quicker solution for this question
User avatar
KarishmaB
Joined: 16 Oct 2010
Last visit: 05 Sep 2026
Posts: 16,643
Own Kudos:
81,184
 [1]
Given Kudos: 491
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,643
Kudos: 81,184
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
kevincan
If a, b, and c are positive real numbers such that a(b + c) = 152, b(c + a) = 162, and c(a + b) = 170, what is the value of abc?

(A) 704
(B) 720
(C) 736
(D) 760
(E) 784
Since all products are integers, I am thinking that likely a, b and c are integers. Also the products are similar, so it seems that a, b and c have values close to each other. All are distinct because the result in all 3 cases is different.

c(a+b) = 170 = 10*17
So a and b could be 8 and 9 to give a+b=17

b(c + a) = 162 = 9*18
a(b + c) = 152 = 8*19

So a = 8, b = 9, c = 10 works.
abc = 8*9*10 =720

This method works when you have a strong sense of numbers.
Moderator:
Math Expert
113155 posts