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# If a and b are positive integers

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Senior Manager
Joined: 24 Mar 2010
Posts: 349

Kudos [?]: 115 [0], given: 4

If a and b are positive integers [#permalink]

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13 Oct 2012, 18:18
00:00

Difficulty:

35% (medium)

Question Stats:

61% (00:26) correct 39% (00:38) wrong based on 51 sessions

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If a and b are positive integers, is a/b an even integer?

1. ab is an even integer
2. b/a is an even integer
[Reveal] Spoiler: OA

Kudos [?]: 115 [0], given: 4

Senior Manager
Joined: 11 May 2011
Posts: 355

Kudos [?]: 120 [0], given: 46

Location: US
Re: If a and b are positive integers [#permalink]

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13 Oct 2012, 19:12
Shawshank wrote:
If a and b are positive integers, is a/b an even integer?

1. ab is an even integer
2. b/a is an even integer

1. ab is an even integer - we've 3 options -
a = even & b = even
a = odd & b = even
a = even & b = odd
Can't conclude that a/b is an even integer or not. Insuff.

2. b/a is an even integer - this means that B is greater than a and the value is one among 0, 2, 4, 6 etc.
However, the reverse of these numbers are 1/2,1/4,1/6,1/8 etc, and we know that these numbers are not even.
Sufficient.

Cheers!
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Kudos [?]: 120 [0], given: 46

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129114 [0], given: 12194

Re: If a and b are positive integers [#permalink]

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14 Oct 2012, 01:51
Shawshank wrote:
If a and b are positive integers, is a/b an even integer?

1. ab is an even integer
2. b/a is an even integer

m19 q31

If a and b are positive integers, is a/b an even integer?

(1) ab is an even integer. If $$a=b=2$$ then the answer is NO but if $$a=2$$ and $$b=1$$ then the answer is YES. Not sufficient.

(2) b/a is an even integer --> $$\frac{b}{a}=even$$ --> $$\frac{a}{b}=\frac{1}{even}\neq{integer}$$, so $$\frac{a}{b}\neq{even}$$. Sufficient.

Hope it's clear.
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Kudos [?]: 129114 [0], given: 12194

Re: If a and b are positive integers   [#permalink] 14 Oct 2012, 01:51
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