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# If x is an integer, is x even?

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Intern
Joined: 04 Oct 2007
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If x is an integer, is x even? [#permalink]

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05 Oct 2007, 00:21
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62% (01:01) correct 38% (01:18) wrong based on 232 sessions

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If x is an integer, is x even?

(1) x^2 - y^2 = 0
(2) x^2 + y^2 = 18
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 May 2013, 05:10, edited 2 times in total.
Edited the question

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VP
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05 Oct 2007, 01:04
If X is an integer, is X even ?

statement I

X^2 - Y^2 = 0

(X+Y)(X-Y) = 0

X + Y = 0

X = -Y

or

X - Y = 0

X = Y

insufficient

statement II

X^2 + Y^2 = 18

X = 3 and Y = 3 or X = 2 and Y = sqrt(14)

insufficient

both statements

X = Y or X = -Y

X^2 + Y^2 = 18

X is an integer

X = 3 and Y = 3 or X = 3 and Y =-3

either way can't be even

sufficient !

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Director
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Schools: University of Chicago, Wharton School

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05 Oct 2007, 01:08
Pla~Yang wrote:
I don't understand this question, please explain me why the answer is C ?

Q : If X is an integer, is X even

I. X2 - Y2 = 0
II. X2 + Y2 = 18

C. should be C.

from i and ii, x has to be + or - 3. since x is an integer and lxl = lyl, y also has to be an integer as x^2 = y^2 from st 1.

from 2, we know that 2x^2 = 18 when we consider st 1 as well. so x = + or -3. so it is C.

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Intern
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05 Oct 2007, 01:29
Thank you your for explanation, but i still don't understand.
Either way can't be even and the answer still C not E

Q : Are V and W integers?
I. sqrt(V+W) is an integer
II. V/W is an integer

How diff. btw these 2 questions??

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VP
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05 Oct 2007, 01:47
Pla~Yang wrote:
Thank you your for explanation, but i still don't understand.
Either way can't be even and the answer still C not E

Q : Are V and W integers?
I. sqrt(V+W) is an integer
II. V/W is an integer

How diff. btw these 2 questions??

You where asked a yes or no question. So the answer is no ! You have enough data to determine the answer (in this case the answer is no).

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Intern
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05 Oct 2007, 02:22
I get it!!
and it's diff from question below because this Q below got integer and decimal in both I & II. So we can't determine yes or no, right??
Q : Are V and W integers?
I. sqrt(V+W) is an integer
II. V/W is an integer

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VP
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05 Oct 2007, 02:27
Pla~Yang wrote:
I get it!!
and it's diff from question below because this Q below got integer and decimal in both I & II. So we can't determine yes or no, right??
Q : Are V and W integers?
I. sqrt(V+W) is an integer
II. V/W is an integer

you are correct !

Are V and W integers?

statement I

sqrt(V+M) is an integer

can be V=M=2 or V=M=1/2

insufficient

statement II

V/W is an integer

V=W=sqrt(2)

sqrt(2)/sqrt(2) = 1 ---> integer

or

V=W=2

2/2 = 1 ---> integer

insufficient

whats the OA ?

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VP
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05 Oct 2007, 07:33
Pla~Yang wrote:
I don't understand this question, please explain me why the answer is C ?
Q : If X is an integer, is X even
I. X2 - Y2 = 0
II. X2 + Y2 = 18
[/code]

should be C...

Irrelevant Question...
Is Pla-Yang = Grill Fish?

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Location: India
Concentration: General Management, Technology
GPA: 3.3
WE: Engineering (Consulting)
Re: If X is an integer, is X even [#permalink]

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13 Mar 2012, 19:52
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1. X^2 - y^2 = 0 ==> x^2 = y^2. not sufficient
2. x^2 + y^2 = 18 not sufficient

1 and 2 ==> x^2 + x^2 = 18 ==> x = +/- 3
in both cases it is not even so sufficient
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Re: If x is an integer, is x even? [#permalink]

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14 Mar 2012, 10:56
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Expert's post
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If x is an integer, is x even?

(1) x^2 - y^2 = 0 --> x^2=y^2 --> |x|=|y| --> x can be odd as well as even. Not sufficient.

(2) x^2 + y^2 = 18 --> clearly insufficient, for example x can 0, so even as well as 1, so odd.

(1)+(2) Add up equations: 2x^2=18 --> x^2=9 --> x=3=odd or x=-3=odd. Sufficient.

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Re: If x is an integer, is x even? [#permalink]

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03 Oct 2014, 22:54
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Re: If x is an integer, is x even? [#permalink]

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01 Aug 2016, 02:28
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x is an integer, is x even? [#permalink]

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01 Jan 2017, 11:43
Additionally if we add " x and y are positive integers to the stem"
Then B would be sufficient

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Re: If x is an integer, is x even?   [#permalink] 01 Jan 2017, 11:43
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