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

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

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21 Dec 2013, 13:10
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82% (00:46) correct 18% (01:03) wrong based on 875 sessions

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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]
[Reveal] Spoiler: OA

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Last edited by Bunuel on 22 Dec 2013, 04:56, edited 1 time in total.
Edited the question and added the OA.

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

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21 Dec 2013, 13:16
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

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

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25 Mar 2014, 12:49
|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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26 Jan 2015, 19:27
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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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27 Jan 2015, 00:33
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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

[Reveal] Spoiler:
C

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

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11 Mar 2015, 21:09
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

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]

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11 Mar 2015, 22:03
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zatspeed wrote:
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.

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.

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

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11 Mar 2015, 22:45
zatspeed wrote:
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.

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

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11 Mar 2015, 23:01
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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12 Mar 2015, 06:25
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Expert's post
zatspeed wrote:
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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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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If |x| = |y| and xy < 0, which of the following must be true   [#permalink] 21 Feb 2017, 13:26
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