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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

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

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.

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.

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

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08 Jun 2016, 01:43

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

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21 Feb 2017, 13:26

hfbamafan wrote:

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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