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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

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.

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

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23 Aug 2017, 06:01

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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

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.

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.

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

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 !