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# If a, b and c are integers, is 3c/2 an integer?

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If a, b and c are integers, is 3c/2 an integer?  [#permalink]

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21 Aug 2017, 21:52
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72% (02:02) correct 28% (01:58) wrong based on 201 sessions

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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

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If a, b and c are integers, is 3c/2 an integer?  [#permalink]

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Updated on: 23 Aug 2017, 07:56
4
1
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

Originally posted by pushkarajnjadhav on 23 Aug 2017, 06:01.
Last edited by pushkarajnjadhav on 23 Aug 2017, 07:56, edited 2 times in total.
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Re: If a, b and c are integers, is 3c/2 an integer?  [#permalink]

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21 Aug 2017, 22:53
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
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Re: If a, b and c are integers, is 3c/2 an integer?  [#permalink]

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23 Aug 2017, 04:12
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.
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Re: If a, b and c are integers, is 3c/2 an integer?  [#permalink]

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23 Aug 2017, 06:53
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
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If a, b and c are integers, is 3c/2 an integer?  [#permalink]

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23 Aug 2017, 13:11
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.
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Re: If a, b and c are integers, is 3c/2 an integer?  [#permalink]

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24 Aug 2017, 12:02
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
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Re: If a, b and c are integers, is 3c/2 an integer?  [#permalink]

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24 Aug 2017, 12:33
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
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Re: If a, b and c are integers, is 3c/2 an integer?  [#permalink]

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12 Sep 2018, 05:39
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Re: If a, b and c are integers, is 3c/2 an integer?   [#permalink] 12 Sep 2018, 05:39
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