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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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22 Jan 2016, 12:51
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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. $$\frac{x}{(y+1)}=2$$

E. $$\frac{1}{x}+\frac{1}{y}=\frac{1}{2}$$
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Nov 2017, 21:36, edited 5 times in total.
Reformatted the question
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Re: If |x| = |y| and xy = 0, which of the following must be true? [#permalink]

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22 Jan 2016, 13:04
HarveyKlaus wrote:
If lXl = lYl 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. $$1/x+1/y=1/2$$

Follow posting guidelines, including proper formatting of the question.

For the question, confirm that you have transcribed option E correctly.

You are given that |x| = |y| and xy = 0. For a MUST BE TRUE question, make sure to use POE for the options as the only option remaining will be true for ALL possible cases.

xy=0 ---> either x=0 and y $$\neq$$ 0 or y=0 and x $$\neq$$ 0 or both x =y=0. for the sake of simplicity, I will choose the case when x=y=0 and this also satisfies |x|=|y|.

Substitute x=y=0 in the options A-D and see which one remains true.

A $$xy^2>0$$ . Not true. Eliminate
B. $$x^2y>0$$. Not true. Eliminate
C. $$x+y=0$$. True . Keep.
D. $$x/(y+1)=2$$. x/(y+1) = 0 $$\neq$$ 2. Eliminate.
E. $$1/x+1/y=1/2$$. Not true. Eliminate. The only way you are going to get 1/x + 1/y = 1/2 is when you have x=y=1 . Although you will satisfy |x|=|y| , xy $$\neq$$ 0. Thus eliminate this option.

Hence C is the correct answer.

Hope this helps.
Manager
Joined: 21 Jun 2017
Posts: 78
Re: If |x| = |y| and xy = 0, which of the following must be true? [#permalink]

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13 Oct 2017, 08:22
HarveyKlaus 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. $$1/x+1/y=1/2$$

Any number multiplied by zero, gives the product zero. Since the absolute value of 0 is 0, and |x| = |y|, x,y = 0

Therefore, x + y = 0 is the only answer that must be true.
(C)
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Re: If |x| = |y| and xy = 0, which of the following must be true? [#permalink]

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27 Nov 2017, 19:08
HarveyKlaus 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. $$1/x+1/y=1/2$$

Since |x| = |y| and xy = 0, both x and y must be zero.

Thus, we see that A and B are not true, because both answers are equal to zero.

C, however, must be true because 0 + 0 = 0.

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Re: If |x| = |y| and xy = 0, which of the following must be true?   [#permalink] 27 Nov 2017, 19:08
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