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Even integer

by rahulvsd » Thu Apr 19, 2012 6:36 am
If a > 0 and b > 0 , is a/b an even integer?

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

[spoiler]OA: B[/spoiler]
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Source: — Data Sufficiency |
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by aneesh.kg » Thu Apr 19, 2012 6:42 am
Statement (1) alone is insufficient.
You can understand by taking a =4, b= 2 and a =2 and b = 4. In both cases, ab = 8 (even) but a/b is even in the former case (a/b = 2) but a fraction in the latter case (a/b = 1/2).
So, a/b may or may not be an even integer.

But, Statement (2) is sufficient because if b/a is an even integer, a/b is 1/(even integer) and thus a fraction. As we see, a/b is NOT AN EVEN INTEGER.

So, the answer to the question is a NO using Statement (2) independently.

(B) is the answer.
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by Anurag@Gurome » Thu Apr 19, 2012 5:38 pm
rahulvsd wrote:If a > 0 and b > 0 , is a/b an even integer?

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

[spoiler]OA: B[/spoiler]
(1) ab is an even integer.
If a = 2, b = 3, then ab = 2 * 3 = 6, which is an even integer. Here a/b = 2/3, which is not an even integer.
If a = 4, b = 2, then ab = 4 * 2 = 8, which is an even integer. Here a/b = 4/2 = 2, which is an even integer.
No definite answer; NOT sufficient.

(2) b/a is an even integer.
Now a/b is reciprocal of b/a. Let's take an example to see this:
If a = 5, b = 10, then b/a = 10/5 = 2. Here a/b = 5/10 = 1/2, which is reciprocal of b/a.
It can be seen that since b/a is an even integer, so a/b will always be a fraction and can never be an even integer.
So, the answer to the main question is "no"; SUFFICIENT.

The correct answer is B.
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