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# M08 #26

Author Message
Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 178
Location: India
WE: Information Technology (Investment Banking)
Followers: 3

Kudos [?]: 68 [0], given: 1

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06 May 2012, 02:31
If XY is divisible by 4, which of the following must be true?

a) If X is even then Y is odd.
b) If X =\sqrt{2}then Y is not a positive integer.
c) If X is 0 then X+Y is not 0.
d) X^Y is even.
e) X/Y is not an integer.

According to me all the options are incorrect but if I have to chose I will chose D

I do not agree to the OA as it is given that Y is not a positive integer, so it can be a negative integer and then it will not hold true.

Can anyone explain this.
Math Expert
Joined: 02 Sep 2009
Posts: 34442
Followers: 6265

Kudos [?]: 79526 [0], given: 10019

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06 May 2012, 03:00
subhajeet wrote:
If XY is divisible by 4, which of the following must be true?

a) If X is even then Y is odd.
b) If X =\sqrt{2}then Y is not a positive integer.
c) If X is 0 then X+Y is not 0.
d) X^Y is even.
e) X/Y is not an integer.

According to me all the options are incorrect but if I have to chose I will chose D

I do not agree to the OA as it is given that Y is not a positive integer, so it can be a negative integer and then it will not hold true.

Can anyone explain this.

D cannot be correct consider: x=1 and y=4.

As for B. The confusing part is the word "positive":
If $$x=\sqrt{2}$$, $$y$$ can be positive as well as negative BUT it can not be a positive INTEGER.

$$y$$ must be of a type of $$y=\sqrt{2}*2n$$ where $$n$$ is an integer, not necessarily positive. So $$y$$ can be $$\sqrt{2}*8$$, when $$n=4$$ OR $$-\sqrt{2}*2$$, when $$n=-1$$ OR $$0$$, when $$n=0$$.

As when $$y=\sqrt{2}*2n$$ and $$x=\sqrt{2}$$, $$xy=4n$$ and the condition that it's divisible by $$4$$ holds true for any value of $$n$$.

Th is question is discussed here: if-xy-is-divisible-by-4-which-of-the-following-must-be-true-73389.html

Hope it helps.
_________________
Manager
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 178
Location: India
WE: Information Technology (Investment Banking)
Followers: 3

Kudos [?]: 68 [0], given: 1

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07 May 2012, 03:24
Hi Bunnel - Thanks for the detailed explanation.
Re: M08 #26   [#permalink] 07 May 2012, 03:24
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# M08 #26

Moderator: Bunuel

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