November 20, 2018 November 20, 2018 09:00 AM PST 10:00 AM PST The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat. November 20, 2018 November 20, 2018 06:00 PM EST 07:00 PM EST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50664

If a, b and c are integers, is 3c/2 an integer?
[#permalink]
Show Tags
21 Aug 2017, 20:52
Question Stats:
72% (02:07) correct 28% (02:00) wrong based on 150 sessions
HideShow timer Statistics




Manager
Joined: 12 Feb 2017
Posts: 69

If a, b and c are integers, is 3c/2 an integer?
[#permalink]
Show Tags
Updated on: 23 Aug 2017, 06:56
We are supposed to find whether 3c/2 is an integer or not For 3c/2 to be an integer c must be divisible by 2.Hence we simply need to check whether c is even or odd. 1) ac/2 is an integer means ac is even; for ac to be even we have 3 possibilities : a:even c:even a: even c:odd a: odd c:even As c can be even and odd, stmt 1 is not sufficient 2)bc/3 is even means bc is even For bc to be even we have 3 possibilities b: even c:even b: even c:odd b:odd c: even From stmt 2 we can not predict whether c is even or odd From stmt 1 and 2 We can not firmly predict whether c is even or odd Hence Ans is E Kudos if it helps .. Sent from my MotoG3 using GMAT Club Forum mobile app




Director
Joined: 18 Aug 2016
Posts: 625
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38

Re: If a, b and c are integers, is 3c/2 an integer?
[#permalink]
Show Tags
21 Aug 2017, 21:53
Bunuel wrote: If a, b and c are integers, is 3c/2 an integer?
(1) ac/2 is a multiple of 3
(2) bc/3 is even (1) tells us either a is 3k and c = 2k or c is 3k and a is 2k..in both the cases answer is different Not sufficient (2) tells us either b is 2k and c is 3k or c is 2k and b is 3k..in both the cases answer is different Not sufficient on combining also we have either c=3k or c=2k..different answers.Not sufficient E
_________________
We must try to achieve the best within us
Thanks Luckisnoexcuse



Intern
Joined: 19 Sep 2016
Posts: 35

Re: If a, b and c are integers, is 3c/2 an integer?
[#permalink]
Show Tags
23 Aug 2017, 03:12
is 3c/2 an integer? statement 1 : ac/2 is a multiple of 3, i.e ac/2 can be equal to 3,6,9,12,15,18... and so on. further it can also be seen that ac would be a multiple of 6 ie. ac = 6,12,18,24,30.. and so on. so we know that ac = even but dont know whether c is even or not, hence insufficient. Statement 2 : bc/3 is even which means that bc can be 6,12,18,24... and so on. also bc is also even but still cannot determine whether b is even or c is even, hence, insufficient.
statement 1 + statement 2 : ac=even and bc=even so cannot determine whether c is even or not. hence answer is E as both statements are not sufficient to answer.



Intern
Joined: 24 Jul 2017
Posts: 48
Location: India
WE: Information Technology (Computer Software)

Re: If a, b and c are integers, is 3c/2 an integer?
[#permalink]
Show Tags
23 Aug 2017, 05:53
3c/2 > I ? 1 > ac/2 is a multiple of 3. For this statement to be true, 'ac' must be even. So, odd*even = even or even*even = even. Hence, a or c can either be even or odd. If c is odd, 3c/2 cannot be integer. Hence, not sufficient. 2 > bc/3 is even. For this statement to be true, 'bc' has to be even. Again, b or c can either be odd or even as explained in (1). Hence, not sufficient. (1) + (2) > ac/2 is a multiple of 3 and bc/3 is even. We know that ac and bc must be even. But we do not know if c is even or odd. Hence, we cannot say if 3c/2 is an integer or not. Hence, not sufficient. E. Hope it helps



Intern
Joined: 14 Jul 2013
Posts: 12

If a, b and c are integers, is 3c/2 an integer?
[#permalink]
Show Tags
23 Aug 2017, 12:11
Hi!
a, b, c are integers  condition
3c/2= integer?  Question
Rephrased question  is c even?
Statement 1: ac/2= = multiple of 3; a= even number and c= odd multiple of 3, or c= even number and a= odd multiple of 3. Not sufficient to answer the question
Statement 2: bc/3 = even; b= odd multiple of 3, c= even number and b multiple of 3, or c= odd multiple of 3 and b= even number. Not sufficient to answer the question
1 + 2: Using the same case the statements together are not sufficient to answer the question.
Hence, E.



Intern
Joined: 29 Jul 2012
Posts: 15

Re: If a, b and c are integers, is 3c/2 an integer?
[#permalink]
Show Tags
24 Aug 2017, 11:02
Please confirm if this is a right approach: 1. ac/2=3n ==> ac=6n ==> c=6n/a ==> 3c/2=9n/a. a is not known so A is insufficient. 2. bc/3=2n ==> bc=6n ==> c=6n/b ==>3c/2=9n/b. b is no known so B is insufficient. 3. Combining both, still a & b are unknown so it cannot be answered and answer choice is E



ISB, NUS, NTU Moderator
Joined: 11 Aug 2016
Posts: 312

Re: If a, b and c are integers, is 3c/2 an integer?
[#permalink]
Show Tags
24 Aug 2017, 11:33
Prob: 3C/2 is Int. ? For 3C/2 to be an integer, C should be a multiple of 2. Therefore, our Effective Prob Reduces to is C a multiple of 2 ? Now analyzing the statements. Statement 1: ac/2 = 3k, where K is any factor. This tells us that ac=3x2xk i.e. axc is a multiple of 3 & 2. No information regarding c. Hence Insufficient ! Statement 2: bc/3 = 2u, where u is any factor. This tells us that bc=3x2xu i.e. bxc is a multiple of 3 & 2. No information regarding c. Hence Insufficient ! Now Statement 1 & Statement 2 Combined: ac=3x2xk & bc=3x2xu Again no information regarding C or A&B. Hence Insufficient !Ans.: E
_________________
~R. If my post was of any help to you, You can thank me in the form of Kudos!!



NonHuman User
Joined: 09 Sep 2013
Posts: 8823

Re: If a, b and c are integers, is 3c/2 an integer?
[#permalink]
Show Tags
12 Sep 2018, 04:39
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If a, b and c are integers, is 3c/2 an integer? &nbs
[#permalink]
12 Sep 2018, 04:39






