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# If |x| = |y| and xy < 0, which of the following must be true

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Re: If |x| = |y| and xy < 0, which of the following must be true [#permalink]
|x| = |y| this means when they come out of Mod they will be positive----->eq1

xy < 0 this means multiplication of both values is less than zero or better to be read as -ve. Hence either x or y is -ve---->eq2

so combining eq1 and eq 2
we have

x + (-y) = 0 (because of eq 1)
(-x) + y = 0 (again because of eq 1)

Hence C
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Re: If |x| = |y| and xy < 0, which of the following must be true [#permalink]
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If |x| = |y|

then x^2=y^2
=>x^2-y^2=0
=>(x+y)(x-y)=0
(x+y)=0

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Re: If |x| = |y| and xy < 0, which of the following must be true [#permalink]
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Hi All,

This question can be solved by TESTing VALUES. You can gain a nice shortcut if you realize that you can TEST two pairs of VALUES at the same time.

We're told that |X|=|Y| and that XY < 0. This means that one variable is NEGATIVE and the other is POSITIVE, but it doesn't matter which is which. We're asked which of the following answer MUST be true (which is the same as asking "which is ALWAYS TRUE no matter how many different examples you can come up with?")

Let's TEST....
X = 2
Y = -2

and
X = -2
Y = 2

Answer A: X(Y^2) > 0 If X = -2, Y = 2, then this is NOT TRUE.

Answer B: Y(X^2) > 0 If Y = -2, X = 2, then this is NOT TRUE.

Answer C: X + Y = 0 (2) + (-2) = 0 This IS TRUE.

Answer D: X/Y + 1 = 2 2/-2 + 1 is NOT = 2. This is NOT TRUE

Answer E: 1/X + 1/Y = 1/2 1/2 + 1/-2 is NOT = 1/2 This is NOT TRUE

GMAT assassins aren't born, they're made,
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if |x|=|y| and xy < 0, which of the following must be true? [#permalink]
if |x|=|y| and xy < 0, which of the following must be true?

A) xy^2 >0
B) x^2y > 0
C) x + y = 0
D) x/y + 1 = 2
E) 1/x +1/y = 1/2

Originally posted by zatspeed on 11 Mar 2015, 21:09.
Last edited by zatspeed on 11 Mar 2015, 23:02, edited 1 time in total.
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Re: if |x|=|y| and xy < 0, which of the following must be true? [#permalink]
zatspeed
if |x| |y| and xy < 0, which of the following must be true?

A) xy^2 >0
B) x^2y > 0
C) x + y = 0
D) x/y + 1 = 2
E) 1/x +1/y = 1/2

Hi zatspeed,

In the original prompt (and in the title) is there supposed to be an "=" between |X| and |Y|? Karishma's explanation implies that there should be one there, but your post doesn't currently include that information.

GMAT assassins aren't born, they're made,
Rich
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Re: if |x|=|y| and xy < 0, which of the following must be true? [#permalink]
Sorry about that, not sure why the half the data goes missing after I post it. Will update it.
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Re: If |x| = |y| and xy < 0, which of the following must be true [#permalink]
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zatspeed
if |x|=|y| and xy < 0, which of the following must be true?

A) xy^2 >0
B) x^2y > 0
C) x + y = 0
D) x/y + 1 = 2
E) 1/x +1/y = 1/2
___________
Merging similar topics.
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If |x| = |y| and xy < 0, which of the following must be true [#permalink]
hfbamafan
If |x| = |y| and xy < 0, which of the following must be true?

A. xy^2 > 0

B. yx^2 > 0

C. x + y = 0

D. x/y +1=2

E. 1/x + 1/y = 1/2]

|x| = |y| and xy < 0 simultaneously indicates that if x is positive then y is negative. Again, if y is positive then x is negative. And the value of x and y are identical but in opposite way.
So, if x=5 and y=-5 or
if x=-5 and y=5, then C is valid equation.
Thank you...
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Re: If |x| = |y| and xy < 0, which of the following must be true [#permalink]
hfbamafan
If |x| = |y| and xy < 0, which of the following must be true?

A. xy^2 > 0

B. yx^2 > 0

C. x + y = 0

D. x/y +1=2

E. 1/x + 1/y = 1/2]

We see that the values of x and y must have opposite signs since xy < 0. Furthermore, since |x| = |y|, x and y must be opposites and hence the sum of x and y must be zero.

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Re: If |x| = |y| and xy < 0, which of the following must be true [#permalink]
1
Kudos
Top Contributor
Given that |x| = |y| and xy < 0

xy < 0 means that x and y have DIFFERENT signs. So one is positive and other is negative.
(Watch this video to know about the Basics of Inequality)

Now, |x| = |y| means that the Absolute value of x and y is same and we know that x and y have opposite signs
=> x = -y
or , x + y = 0

Example using values

x +ve, y- ve. Ex: x = 2, y = -2. Making |x| = |y| = |2|= |-2| = 2
x -ve, y +ve. Ex: x = -2, y = 2. Making |x| = |y| = |-2| = |2| = 2

In both the cases x + y = 0

Hope it helps!

Watch the following video to learn the Basics of Absolute Values

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Re: If |x| = |y| and xy < 0, which of the following must be true [#permalink]
Re: If |x| = |y| and xy < 0, which of the following must be true
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Re: If |x| = |y| and xy < 0, which of the following must be true [#permalink]
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Re: If |x| = |y| and xy < 0, which of the following must be true [#permalink]