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

I am assuming the question is
"If |x| = |y| and xy < 0, which of the following must be true?"

The absolute values of x and y should be the same. But one of x and y should be negative and the other should be positive so that xy < 0.
Put x = 1, y = -1 and then x = -1, y = 1 in the options to see which holds since the correct option should hold for all appropriate values of x and y.

A) xy^2 >0
Will not hold for x = -1, y = 1

B) x^2y > 0
Will not hold for x = 1, y = -1

C) x + y = 0
Will hold for both. Hold it.

D) x/y + 1 = 2
Will not hold.

E) 1/x +1/y = 1/2
Will not hold.

Answer (C)
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1. x and y have same magnitude, |x| = |y|
2. They have opposite signs xy<0
Implies x = -y or y = -x
So C: x+y =0

|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

If |x| = |y|

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

So answer c

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

Final Answer:

GMAT assassins aren't born, they're made,
Rich

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

Sorry about that, not sure why the half the data goes missing after I post it. Will update it.

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Merging similar topics.
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|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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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.

Answer: C
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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

So, Answer will be C
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

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