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# M04-13

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Math Expert
Joined: 02 Sep 2009
Posts: 50711

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15 Sep 2014, 23:22
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Difficulty:

35% (medium)

Question Stats:

69% (00:56) correct 31% (00:51) wrong based on 173 sessions

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If $$a$$, $$b$$ and $$x$$ are positive integers, is $$x$$ even?

(1) $$x = \frac{a}{b}$$ and $$b$$ is odd.

(2) $$x = \frac{a}{b}$$ and $$a$$ is odd.

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Joined: 02 Sep 2009
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15 Sep 2014, 23:22
Official Solution:

(1) $$x=\frac{a}{b}$$ and $$b$$ is odd. $$x$$ can be odd as well as even, consider: $$x=a=b=1$$ and $$x=a=2$$ and $$b=1$$. Not sufficient.

(2) $$x=\frac{a}{b}$$ and $$a$$ is odd. Cross-multiply: $$bx=a=\text{odd}$$. Now, in order for the product of two integers $$b$$ and $$x$$ to be odd, both integers must be odd. So, the answer to the question whether $$x$$ is even is NO. Sufficient.

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Joined: 13 Oct 2013
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13 Jul 2015, 11:51
Hi Bunuel,
I have a question ,
so can we take a and b as same value?
for this type of question , if they have not mentioned explicitly, we can take same value?
My thinking was as question says a and b are positive integers, i thought they should be of different values.

Thank you !!

Bunuel wrote:
Official Solution:

(1) $$x=\frac{a}{b}$$ and $$b$$ is odd. $$x$$ can be odd as well as even, consider: $$x=a=b=1$$ and $$x=a=2$$ and $$b=1$$. Not sufficient.

(2) $$x=\frac{a}{b}$$ and $$a$$ is odd. Cross-multiply: $$bx=a=\text{odd}$$. Now, in order for the product of two integers $$b$$ and $$x$$ to be odd, both integers must be odd. So, the answer to the question whether $$x$$ is even is NO. Sufficient.

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Math Expert
Joined: 02 Sep 2009
Posts: 50711

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13 Jul 2015, 23:43
sunita123 wrote:
Hi Bunuel,
I have a question ,
so can we take a and b as same value?
for this type of question , if they have not mentioned explicitly, we can take same value?
My thinking was as question says a and b are positive integers, i thought they should be of different values.

Thank you !!

Bunuel wrote:
Official Solution:

(1) $$x=\frac{a}{b}$$ and $$b$$ is odd. $$x$$ can be odd as well as even, consider: $$x=a=b=1$$ and $$x=a=2$$ and $$b=1$$. Not sufficient.

(2) $$x=\frac{a}{b}$$ and $$a$$ is odd. Cross-multiply: $$bx=a=\text{odd}$$. Now, in order for the product of two integers $$b$$ and $$x$$ to be odd, both integers must be odd. So, the answer to the question whether $$x$$ is even is NO. Sufficient.

It's the other way around: unless it is explicitly stated otherwise, different variables CAN represent the same number.
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Joined: 12 Jun 2016
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22 May 2017, 01:58
I used the following approach

S1: $$x = \frac{a}{b}$$ and $$b$$ is odd.

This means, b is a factor of a. This also means

$$x = \frac{(n) * b}{b}$$. Here n = some positive integer. =>
$$x = n$$. if n is even, x is even.
If n is odd, x is odd. Two different answer for x. Insufficient.

S2: $$x = \frac{a}{b}$$ and $$a$$ is odd.

By same reasoning, this means, b is a factor of a.

$$x = \frac{(n) * b}{b}$$. Here n = some positive integer. =>
$$x = n$$.
However, n cannot be odd even since a is odd. Hence, x = odd. Sufficient

Not sure if I am able to clearly convey what I intend to say.
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My Best is yet to come!

Intern
Joined: 22 Mar 2016
Posts: 7

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28 Mar 2018, 05:32
Bunuel, I just signed up for Gmat club test and the questions are amazing,I am currently scoring Q42 on a good day and Q35 on a bad one. How should I combine these questions and the OG questions. Can I use just these (how different are they from OG). I am taking the test in a month and my target score is Q45, and I study an hour and half quant every day, thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 50711

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28 Mar 2018, 08:24
AMARAAZUNWIE wrote:
Bunuel, I just signed up for Gmat club test and the questions are amazing,I am currently scoring Q42 on a good day and Q35 on a bad one. How should I combine these questions and the OG questions. Can I use just these (how different are they from OG). I am taking the test in a month and my target score is Q45, and I study an hour and half quant every day, thanks.

GMAT Club Tests' questions are generally significantly harder than that of OG. I'd suggest to do them only after you are comfortably solving most of the questions from OG.
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Re: M04-13 &nbs [#permalink] 28 Mar 2018, 08:24
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# M04-13

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