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If x is an integer, is x even?

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If x is an integer, is x even? [#permalink] New post 04 Oct 2007, 23:21
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Question Stats:

58% (01:52) correct 42% (01:13) wrong based on 62 sessions
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, 04:10, edited 2 times in total.
Edited the question
VP
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 [#permalink] New post 05 Oct 2007, 00:04
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 !

the answer is (C)

:(
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Re: DS Question [#permalink] New post 05 Oct 2007, 00:08
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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 [#permalink] New post 05 Oct 2007, 00:29
Thank you your for explanation, but i still don't understand.
Either way can't be even and the answer still C not E

What about this question...
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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 [#permalink] New post 05 Oct 2007, 00:47
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

What about this question...
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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 [#permalink] New post 05 Oct 2007, 01:22
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??
What about this question...
Q : Are V and W integers?
I. sqrt(V+W) is an integer
II. V/W is an integer
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 [#permalink] New post 05 Oct 2007, 01:27
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??
What about this question...
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

the answer is (E)

whats the OA ?

:)
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Re: DS Question [#permalink] New post 05 Oct 2007, 06:33
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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Re: If X is an integer, is X even [#permalink] New post 13 Mar 2012, 18:52
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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] New post 14 Mar 2012, 09:56
Expert's post
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.

Answer: C.
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Re: If x is an integer, is x even?   [#permalink] 14 Mar 2012, 09:56
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