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# If x and y are positive integer and x/y is an even integer,

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If x and y are positive integer and x/y is an even integer,  [#permalink]

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Updated on: 10 Mar 2014, 10:52
3
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15% (low)

Question Stats:

79% (01:38) correct 21% (01:41) wrong based on 114 sessions

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If x and y are positive integer and x/y is an even integer, which of the following can be an odd integer?

A. x
B. xy
C. x−y
D. x+2y
E. x/3

it is given that C is correct, why not E.

Yes and No conditions exists in both C & E

m10 q07

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Originally posted by honchos on 10 Mar 2014, 10:16.
Last edited by Bunuel on 10 Mar 2014, 10:52, edited 2 times in total.
Edited the question.
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Re: If x and y are positive integer and xy is an even integer, w  [#permalink]

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10 Mar 2014, 10:50
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1
honchos wrote:
If x and y are positive integer and xy is an even integer, which of the following can be an odd integer?

A. x
B. xy
C. x−y
D. x+2y
E. x/3

it is given that C is correct, why not E.

Yes and No conditions exists in both C & E

It should be x/y not xy.

If x and y are positive integer and $$\frac{x}{y}$$ is an even integer, which of the following can be an odd integer?

A. $$x$$
B. $$xy$$
C. $$x-y$$
D. $$x+2y$$
E. $$\frac{x}{3}$$

Number picking:

If $$x=2$$ and $$y=1$$ only option C is odd: $$x-y=2-1=1=odd$$.

Process of elimination (POE):

$$\frac{x}{y}=even$$ --> $$x=y*even=even$$.

A. $$x$$ --> we know that $$x$$ is even. Discard;
B. $$xy$$ --> since $$x$$ is even, then $$xy$$ is also even. Discard;
C. $$x-y$$. Keep;
D. $$x+2y$$ --> $$x+2y=even+even*y=even+even=even$$. Discard;
E. $$\frac{x}{3}$$ --> $$\frac{even}{odd}$$ is either an even integer (6/3=2) or not an integer at all (2/3). Discard.

Only option C is left.

m10 q07
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Re: If x and y are positive integer and x/y is an even integer,  [#permalink]

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10 Mar 2014, 11:47
I am not convinced may be I am wrong.

C X-Y

Let says X =12 Y=3 iT BECOMES X-Y =9 This is odd True
X = 12 Y = 6 THEN X-Y = 2, Which is even hence this is False.

so both Yes and NO situations are exists for this Option. C can't be the correct answer same logic goes for E. I believe this question is incomplete b'coz of Irrelevant Options.
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Re: If x and y are positive integer and x/y is an even integer,  [#permalink]

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10 Mar 2014, 11:51
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honchos wrote:
I am not convinced may be I am wrong.

C X-Y

Let says X =12 Y=3 iT BECOMES X-Y =9 This is odd True
X = 12 Y = 6 THEN X-Y = 2, Which is even hence this is False.

so both Yes and NO situations are exists for this Option. C can't be the correct answer same logic goes for E. I believe this question is incomplete b'coz of Irrelevant Options.

You have to read questions and solutions more carefully.

The question asks: "which of the following CAN be an odd integer?" not MUST be an odd integer. Only option C CAN be an odd integer, all others cannot.
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Re: If x and y are positive integer and x/y is an even integer,  [#permalink]

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10 Mar 2014, 11:55
Yes I got my mistake, E can be either an EVEN or not at all an Integer, But certainly it can't be Odd.
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Re: If x and y are positive integer and x/y is an even integer,  [#permalink]

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10 Mar 2014, 11:57
1
honchos wrote:
Yes I got my mistake, E can be either an EVEN or not at all an Integer, But certainly it can't be Odd.

Yes, that's correct.
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Re: If x and y are positive integer and x/y is an even integer,  [#permalink]

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10 Sep 2018, 13:59
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Re: If x and y are positive integer and x/y is an even integer,   [#permalink] 10 Sep 2018, 13:59
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