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# If x=−|y| , which of the following must be true?

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Math Expert
Joined: 02 Sep 2009
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If x=−|y| , which of the following must be true?  [#permalink]

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30 Nov 2016, 02:57
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If x=−|y|, which of the following must be true?

A. y=−x

B. x=y

C. |x|=−y

D. x^2=y^2

E. x^3=y^3

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

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30 Nov 2016, 09:27
1
Bunuel wrote:
If x=−|y|, which of the following must be true?

A. y=−x

B. x=y

C. |x|=−y

D. x^2=y^2

E. x^3=y^3

x=−|y|

We can have 2 possibilities -

1. x = -y
2. x = y

Check carefully except Squaring the 2 sides , none must be true ( In all possible cases )...

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

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15 Dec 2016, 05:23
hey abhishek can you explain option c plz thanks
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Re: If x=−|y| , which of the following must be true?  [#permalink]

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15 Dec 2016, 06:09
nks2611 wrote:
hey abhishek can you explain option c plz thanks

x = −|y| --> x = y or x = -y or x = y = 0

Option C: |x| = -y --> This can be true only when y is negative or 0. If y is positive this cannot be true.
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Re: If x=−|y| , which of the following must be true?  [#permalink]

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Updated on: 15 Dec 2016, 12:43
thanks abhishek i got it , actually forgot to read the word must be anyway thanks

Originally posted by nks2611 on 15 Dec 2016, 06:27.
Last edited by nks2611 on 15 Dec 2016, 12:43, edited 1 time in total.
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Re: If x=−|y| , which of the following must be true?  [#permalink]

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15 Dec 2016, 07:29
x=-sqrt (y^2)
x^2=(-sqrt(y^2))^2
x^2=y^2

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

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19 Dec 2016, 11:04
4
Bunuel wrote:
If x=−|y|, which of the following must be true?

A. y=−x

B. x=y

C. |x|=−y

D. x^2=y^2

E. x^3=y^3

We are given that x = -|y|, and must determine which answer choice MUST BE TRUE. We can use numerical values for x and y so long they satisfy the equation x = -|y|, and then use them to test each answer choice.

A) y = −x

Answer choice A does not have to be true. For instance, if x = -2 and y = -2, then -2 ≠ 2 and answer choice A is not true.

B) x = y

Answer choice B does not have to be true. For instance, if x = -2 and y = 2, then -2 ≠ 2 and answer choice B is not true.

C) |x| = −y

Answer choice C does not have to be true. For instance, if x = -2 and y = 2, then |-2| ≠ −2 and answer choice C is not true.

D) x^2=y^2

Answer choice D MUST BE TRUE. Using some of the examples for x and y above, we see that in all cases answer choice D must be true.

If x = -2 and y = -2, then (-2)^2 = (-2)^2, and if x = -2 and y = 2, then (-2)^2 = (2)^2.

In fact, no matter what values for x and y we use (which satisfy the equation x = -|y|), x^2 WILL ALWAYS EQUAL y^2.

Since answer choice D must be true, we can stop here.

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

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20 Dec 2016, 11:16
1
I think in inequalities we should start from the option E as most of the time i got either ans D or E.

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

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26 Dec 2016, 17:57
1
Case 1 : x =-y
Case 2 : x = y
I could not solve after this
Can anyone explain option D
Thanks
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Re: If x=−|y| , which of the following must be true?  [#permalink]

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26 Aug 2019, 22:55
Testing values doesn't seem the best for must be true questions. The numbers I used had 3 correct answers and it was only when I got to D that I saw it must be true.
Re: If x=−|y| , which of the following must be true?   [#permalink] 26 Aug 2019, 22:55
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