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Does x + y = 0? (1) xy<0 (2) x^2 = y^2 OA to follow

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Does x + y = 0? (1) xy<0 (2) x^2 = y^2 OA to follow [#permalink] New post 03 Sep 2006, 12:55
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Does x + y = 0?

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

OA to follow
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 [#permalink] New post 03 Sep 2006, 13:56
C

1. XY < 0 x is positive and y negative or vice versa INSUFF for x+y =0; x should be the mirror of y

2. x^2 = y^2 this means x and y can be both positive or negative or mixed so INSUFF

Combined : we know x is the opposite sign of y and that their absolute values are equal so SUFF
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 [#permalink] New post 03 Sep 2006, 14:56
C

From 1, xy<0 implies x & y are of opposite sign
INSUFF

From 2, (x^2-y^2) = 0 i.e. (x-y)(x+y) = 0 i.e either x=y or x=-y
INSUFF

Combined, from 1 x&y have to be of opposite sign hence x=-y is the only possibility. SUFF
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Re: DS numbers [#permalink] New post 03 Sep 2006, 15:12
x,y { I,+,-,0, ==, +- 1/2}

(2) x=0, y=0 Yes
x=1, y = -1 Yes
x=1, y = 1 No
ACE

(1) xy< 0
x= 1, y = -1 Yes
x=1, y = -2 No
x& y have opp signs
CE

(1)&(2)
x=1, y = -1 Yes
x= 1/2 , y = -1/2 Yes
x= 1/4, y = -1/4 Yes

Hence C

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 [#permalink] New post 03 Sep 2006, 19:31
The OA is C, however I didn't agree with the OA because it doesn't appear to account for fractions and negative fractions.

For example, if X=1/2 and Y=1/2, then (1) is fine because 1/2 * 1/2 <0; and (2) is fine because X=Y. Back to the main question, 1/2 + 1/2 does NOT equal 0.

However, if X=1/2 and Y=-1/2, then (1) is still fine; and (2) is still fine because (1/2)^2 = (-1/2)^2. Back to the main question 1/2 +(-1/2) DOES equal 0.

In the first case, X+Y does not equal 0, while in the second case X+Y=0.

The problem does not state that X & Y are intergers or whole numbers or anything, so when accounting for negatives and fractions, I think the answer should be E.

Heman, you give examples of where X is positive, and Y is negative, but with if both are positive fractions?

Can someone point out my mistake, I am confused by this question/answer. Thanks.
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 [#permalink] New post 03 Sep 2006, 20:38
Quote:
For example, if X=1/2 and Y=1/2, then (1) is fine because 1/2 * 1/2 <0; and (2) is fine because X=Y. Back to the main question, 1/2 + 1/2 does NOT equal 0.


1/2*1/2=1/4 which is less than 1 but still greater than zero. Hence in your example 0<xy<1. Hence Statement I is not satisfied.
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 [#permalink] New post 03 Sep 2006, 21:55
another way to think without particular numbers in mind.

2) says x^2 = y^2
=> x^2 - y^2 = 0
=> (x-y)(x+y)= 0
=> x = y or x = -y

1) says xy < 1 => x cannot be equal to y

so x = -y or x+y = 0
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 [#permalink] New post 03 Sep 2006, 21:57
hmm..didn't see gmatornot's posting above...who has solved it pretty much the same way as i did..
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 [#permalink] New post 03 Sep 2006, 22:08
gmatornot wrote:
C

From 1, xy<0 implies x & y are of opposite sign
INSUFF

From 2, (x^2-y^2) = 0 i.e. (x-y)(x+y) = 0 i.e either x=y or x=-y
INSUFF

Combined, from 1 x&y have to be of opposite sign hence x=-y is the only possibility. SUFF


The stem says nothing about x or y having to be whole numbers, natural numbers, etc. let alone integers. Even if we considered x={(-sqrt2)} and y=1.414.... ?

The answer should be (C)

Last edited by GMATT73 on 03 Sep 2006, 22:50, edited 1 time in total.
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 [#permalink] New post 03 Sep 2006, 22:39
tricky question
IMHO E it is
1)clearly insuff
x can be -ve and y+ve
and so y can be-ve and x+ve
2)x^2=y^2 no info about the sugn of x or y
1st and 2 combined
we know x is the opposite sign of y and that their absolute values are equal But the solutiion can be -x=y or x=-y
Hence E it is
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 [#permalink] New post 03 Sep 2006, 22:42
Yurik79 wrote:
tricky question
IMHO E it is
1)clearly insuff
x can be -ve and y+ve
and so y can be-ve and x+ve
2)x^2=y^2 no info about the sugn of x or y
1st and 2 combined
we know x is the opposite sign of y and that their absolute values are equal But the solutiion can be -x=y or x=-y
Hence E it is


in both cases, x+y = 0 , hence serves the purpose to answer the question.
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 [#permalink] New post 03 Sep 2006, 22:45
iced_tea wrote:
Yurik79 wrote:
tricky question
IMHO E it is
1)clearly insuff
x can be -ve and y+ve
and so y can be-ve and x+ve
2)x^2=y^2 no info about the sugn of x or y
1st and 2 combined
we know x is the opposite sign of y and that their absolute values are equal But the solutiion can be -x=y or x=-y
Hence E it is


in both cases, x+y = 0 , hence serves the purpose to answer the question.

Oh now I see my mistake :oops: agree C
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 [#permalink] New post 04 Sep 2006, 10:59
First st says x,y are of different signs

St two says the have the same absolute value

meaning on the number line they are at the same distance from zero and at opposite directions

Thus adding them together will result into a zero

answer C
  [#permalink] 04 Sep 2006, 10:59
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