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if xy =/= 0 ( xy is not 0), is x/y=1? (1) x^2=y^2 (2)

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Jasontuyj2012
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if xy =/= 0 ( xy is not 0), is x/y=1? (1) x^2=y^2 (2) [#permalink] New post   20 Aug 2011, 05:08
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A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

57% (01:04) correct 43% (01:44) wrong based on 7 sessions
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if xy =/= 0 ( xy is not 0), is x/y=1?

(1) x^2=y^2
(2) xy>0

I chose A

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C
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kp1811
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Re: if xy =/= 0 ( xy is not 0), is x/y=1? (1) x^2=y^2 (2) [#permalink] New post   20 Aug 2011, 05:19
Jasontuyj2012 wrote:
if xy =/= 0 ( xy is not 0), is x/y=1?

(1) x^2=y^2
(2) xy>0

I chose A



1. x and y can be 1 or -1, 2 or -2 and hence x/y may or may not be =1. hence not suff
2. xy>0 .... x and y can have different values (1,1) (3,2) hence not suff

together both statements we have x and y should be of the same sign ( either -ve or +ve) and hence x/y =1. so C
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Re: if xy =/= 0 ( xy is not 0), is x/y=1? (1) x^2=y^2 (2) [#permalink] New post   20 Aug 2011, 17:15
Rephrase the question: "\(x = y?\)"

Statement 1: \(x^2 = y^2\) implies that \(|x| = |y|\). In the xy-plane this looks like an X (two lines) straight through the origin with slopes of 1 and -1. For \(xy < 0\) (quadrants II and IV), \(y = -x\). For \(xy > 0\) (quadrants I and III), \(y = x\).

If \(|x| = |y|\), x does not have to equal y, it could equal -y. Insufficient.

Statement 2: \(xy > 0\) means that any point occupies either quadrant I or III. x and y could take on any coordinate in these quadrants, such as (4,3), (1000000000000,1), (-452, -2), or (1,1), (-55,-55) etc. We do not know whether x and y are equal. Insufficient.

Combined: |x| = |y| and xy > 0, so x = y. Sufficient.
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Re: if xy =/= 0 ( xy is not 0), is x/y=1? (1) x^2=y^2 (2) [#permalink] New post   20 Aug 2011, 19:01
rephrasing the question we have

is x=y?

1. Not sufficient

x = +y or x = -y

2. Not sufficient

xy>0

x>0 y>0 or x<0 y<0

if x and y both are >0 and equal to 2 then yes
if x and y both are >0 , x=2 y=4 , then no.

Together,

from two we know that x and y are both of same sign hence we will only have one solution x = y

Answer is C.
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Re: if xy =/= 0 ( xy is not 0), is x/y=1? (1) x^2=y^2 (2) [#permalink] New post   22 Aug 2011, 17:00
U cant ignore the sings. So the answer is C.

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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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Re: if xy =/= 0 ( xy is not 0), is x/y=1? (1) x^2=y^2 (2) [#permalink]
22 Aug 2011, 17:00
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