Last visit was: 10 Aug 2024, 20:29 It is currently 10 Aug 2024, 20:29
Toolkit
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

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.

# If a, b and c are integers, is (a·b) a multiple of 18?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94848
Own Kudos [?]: 648554 [12]
Given Kudos: 86900
Math Expert
Joined: 02 Sep 2009
Posts: 94848
Own Kudos [?]: 648554 [1]
Given Kudos: 86900
General Discussion
VP
Joined: 14 Jul 2020
Posts: 1114
Own Kudos [?]: 1300 [2]
Given Kudos: 351
Location: India
Manager
Joined: 09 Dec 2019
Posts: 123
Own Kudos [?]: 173 [2]
Given Kudos: 5
Re: If a, b and c are integers, is (a·b) a multiple of 18? [#permalink]
2
Kudos
If a, b and c are integers, is (a·b) a multiple of 18?

(1) 2a = 3b
a = 3b/2

Put b = 2, a = 3 and a.b = 6, which is not a multiple of 18

Put b = 6, a = 9 and a.b = 54, multiple of 18
Not sufficient

(2) 2b = 3c
b = 3c/2

Put c = 2, then b = 3 and put a = 1, a.b = 3

Put c = 2, then b = 3 and put a = 6, a.b = 18

Not sufficient

(1) + (2)

2b = 3c
b = 3c/2

2a = 3b
2a = 3(3c/2)
a = 9c/4

Since a, b, and C are integers. Minimum value of c = 4

For c = 4, a = 9, b = 6

a.b = 54

So, For any value of c, a is always a multiple of 9 and b is always a multiple if 6. Thus, a.b is always a multiple of 18

Sufficient

Option C

Posted from my mobile device
Intern
Joined: 09 Mar 2021
Posts: 28
Own Kudos [?]: 30 [1]
Given Kudos: 25
Location: South Africa
Schools: LBS MAM "23
GPA: 3.01
WE:Design (Computer Software)
Re: If a, b and c are integers, is (a·b) a multiple of 18? [#permalink]
1
Kudos
imo C
If a, b and c are integers, is (a·b) a multiple of 18?

(1) 2a = 3b
b= 2a/3
if a = 3 , b = 2 => ab = 6
if a= 18 , b= 12 => ab = 18 (12) .. Multiple of 18 ...
Not sufficient

(2) 2b = 3c
not sufficient ..

no combining 1 and 2 ..

b= 2a/3
c = 2b/3
since minimum of b has to be 6 (in form of 6n , n 1,2,3 ...) to satisfy a b c are integer ..
if b = 6 , c = 4 , a = 9 ... ab = 18 (something) .. multiple of 18 ...
.. Sufficient
Non-Human User
Joined: 09 Sep 2013
Posts: 34358
Own Kudos [?]: 860 [0]
Given Kudos: 0
Re: If a, b and c are integers, is (a·b) a multiple of 18? [#permalink]
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.
Re: If a, b and c are integers, is (a·b) a multiple of 18? [#permalink]
Moderator:
Math Expert
94848 posts