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Is 2a/bc an integer? Where a,b,c are positive integers. (1)

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Is 2a/bc an integer? Where a,b,c are positive integers. (1) [#permalink]

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New post 03 Jul 2010, 23:25
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Is 2a/bc an integer? Where a,b,c are positive integers.

(1) \(\frac{b}{2}\) is a factor of \(a\)
(2) All the prime factors of \(c\) are also factors of \(\frac{b}{2}\)
[Reveal] Spoiler: OA

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Re: Is 2a/bc an integer? Where a,b,c are positive integers. (1) [#permalink]

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New post 03 Jul 2010, 23:41
I'd choose E.

I - Dividing a by b/2 is equal to 2a/b and is an integer, but you don't know what the effect is of C on 2a/b - so I is INSUF
II - No info given about A - so II is INSUF

I&II - 2a/b is an integer, and could very well be 1. Dividing by C - even with C's prime factors the same with b/2 would yield a non-integer. (i.e. A = 4, B = 8, C = 4 - 2A/B = 1 & B and C's prime factors are the same. 2A/BC = 1/4, change A to 16, 2A/BC = 1)
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Re: Is 2a/bc an integer? Where a,b,c are positive integers. (1) [#permalink]

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Re: Is 2a/bc an integer? Where a,b,c are positive integers. (1) [#permalink]

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New post 29 Oct 2017, 01:13
I thought of it this way:

st1: b/2 is a factor of A. So, b is a factor of 2a. but what is c? Hence we don't know if 2a/bc is an INT

st2: all PRIME factors of C are factors of b/2. rest of the factors? If deno> numerator then 2a/bc won't be an INT

st 1 + 2: c has all prime factors of b/2 which is factor of 2a. But what about the rest of the factors of c? They can make the deno larger and 2a/bc won't be an integer
Re: Is 2a/bc an integer? Where a,b,c are positive integers. (1)   [#permalink] 29 Oct 2017, 01:13
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