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# M03-11

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:19
00:00

Difficulty:

5% (low)

Question Stats:

80% (00:30) correct 20% (00:20) wrong based on 167 sessions

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If $$x$$ is an integer, is $$x$$ even?

(1) $$\frac{11}{x}$$ is an integer

(2) $$\frac{22}{x}$$ is an integer

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15 Sep 2014, 23:19
Official Solution:

Statement (1) by itself is sufficient. $$x$$ can be one of the following values, which are all odd: 1, 11, -1, -11.

Statement (2) by itself is insufficient. $$x$$ can be one of the following integers, which are either even or odd: 1, 2, 11, 22, -1, -2, -11, -22.

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20 Oct 2014, 14:44
Bunuel wrote:
Official Solution:

Statement (1) by itself is sufficient. $$x$$ can be one of the following values, which are all odd: 1, 11, -1, -11.

Statement (2) by itself is insufficient. $$x$$ can be one of the following integers, which are either even or odd: 1, 2, 11, 22, -1, -2, -11, -22.

for statement 1, we can take x=0 which will make it even.
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20 Oct 2014, 14:48
awal_786@hotmail.com wrote:
Bunuel wrote:
Official Solution:

Statement (1) by itself is sufficient. $$x$$ can be one of the following values, which are all odd: 1, 11, -1, -11.

Statement (2) by itself is insufficient. $$x$$ can be one of the following integers, which are either even or odd: 1, 2, 11, 22, -1, -2, -11, -22.

for statement 1, we can take x=0 which will make it even.

If x is 0, then 11/x would be undefined and not an integer (division by 0 is not allowed). So, x cannot be 0.
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11 Oct 2015, 03:02
Bunuel, please correct my (mis)understanding of the DS options:

Option A means to say that Statement A is sufficient to answer the question, so although statement A shows that x=uneven number, and albeit the question asks whether x is an even number, we can conclude that x is not even from statement A. Hence this is more a statement of sufficiency rather than the actual answer itself.

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11 Oct 2015, 05:02
TaiwanTaiwan wrote:
Bunuel, please correct my (mis)understanding of the DS options:

Option A means to say that Statement A is sufficient to answer the question, so although statement A shows that x=uneven number, and albeit the question asks whether x is an even number, we can conclude that x is not even from statement A. Hence this is more a statement of sufficiency rather than the actual answer itself.

Yes, a definite NO answer to the question is still considered to be sufficient.
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08 Aug 2018, 09:54
Isn't 0 an integer too?
An even integer. That's why I marked the first statement as insufficient.

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10 Aug 2018, 00:59
bharatwannagmat wrote:
Isn't 0 an integer too?
An even integer. That's why I marked the first statement as insufficient.

x cannot be 0 in (1) because it says that 11/x is an integer. Recall that division by 0 is not allowed, so if x were 0, then 11/x would be undefined and not an integer.
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Re: M03-11 &nbs [#permalink] 10 Aug 2018, 00:59
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# M03-11

Moderators: chetan2u, Bunuel

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