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M08 #26

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M08 #26 [#permalink] New post 06 May 2012, 01:31
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.
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Re: M08 #26 [#permalink] New post 06 May 2012, 02:00
Expert's post
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.

Answer: B.

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

Hope it helps.
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Manager
Manager
avatar
Status: MBA Aspirant
Joined: 12 Jun 2010
Posts: 178
Location: India
Concentration: Finance, International Business
WE: Information Technology (Investment Banking)
Followers: 3

Kudos [?]: 22 [0], given: 1

Re: M08 #26 [#permalink] New post 07 May 2012, 02:24
Hi Bunnel - Thanks for the detailed explanation. :)
Re: M08 #26   [#permalink] 07 May 2012, 02:24
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M08 #26

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