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M19-31

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:07
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65% (hard)

Question Stats:

53% (01:01) correct 47% (00:54) wrong based on 168 sessions

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If $$a$$ and $$b$$ are positive integers, is $$\frac{a}{b}$$ an even integer?

(1) $$ab$$ is an even integer

(2) $$\frac{b}{a}$$ is an even integer
[Reveal] Spoiler: OA

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16 Sep 2014, 00:07
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Official Solution:

(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) $$\frac{b}{a}$$ is an even integer. Given: $$\frac{b}{a}=even$$. Hence, $$\frac{a}{b}=\frac{1}{even} \ne integer$$, so $$\frac{a}{b} \ne even$$. Sufficient.

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Joined: 21 Dec 2015
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WE: Account Management (Commercial Banking)

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07 Dec 2016, 07:55
Bunuel :

in the 2nd option :

b/a = even integer.

That means b has to be even and a can be even or odd.

The question : Is a/b = even integer?

a we know is even or odd, b is even.

If a is even and b is even = odd or even integer
If a is odd and b is even = non integer.

Hence insufficient. Am i wrong in this thinking?
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Posts: 43828

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07 Dec 2016, 08:04
Vishvesh88 wrote:
Bunuel :

in the 2nd option :

b/a = even integer.

That means b has to be even and a can be even or odd.

The question : Is a/b = even integer?

a we know is even or odd, b is even.

If a is even and b is even = odd or even integer
If a is odd and b is even = non integer.

Hence insufficient. Am i wrong in this thinking?

If you read the solution you'll see that we can deduce one more thing from b/a = even that b must be greater than a. So, a/b no matter whether a is even or not will not be an integer.
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08 Dec 2016, 06:45
Bunuel : Thanks. Got it.
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04 Sep 2017, 10:34
can someone post the possible answer selections? can't seem to see them on my screen
Math Expert
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04 Sep 2017, 10:36
mak218 wrote:
can someone post the possible answer selections? can't seem to see them on my screen

This is a data sufficiency question. Options for DS questions are always the same.

The data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), you must indicate whether—

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

I suggest you to go through the following posts:
ALL YOU NEED FOR QUANT.

Hope this helps.
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Re: M19-31   [#permalink] 04 Sep 2017, 10:36
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