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

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Senior Manager
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 302
Is 2a/bc an integer? Where a,b,c are positive integers. (1)  [#permalink]

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03 Jul 2010, 23:25
1
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:42) correct 40% (01:15) wrong based on 64 sessions

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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 $$\frac{b}{2}$$
Manager
Joined: 04 Feb 2010
Posts: 152
Re: Is 2a/bc an integer? Where a,b,c are positive integers. (1)  [#permalink]

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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)
Senior Manager
Joined: 15 Jan 2017
Posts: 355
Re: Is 2a/bc an integer? Where a,b,c are positive integers. (1)  [#permalink]

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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) &nbs [#permalink] 29 Oct 2017, 01:13
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