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Q02-38 Question # 08 Section # 09

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Q02-38 Question # 08 Section # 09 [#permalink]  23 Jun 2016, 12:50
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15% (01:48) correct 84% (01:37) wrong based on 32 sessions
Given $$x$$, $$y<0$$, what is the value of $$\frac{\sqrt{x^2}}{x} - \sqrt{\frac{-y}{|y|}}$$ ?

A. $$1+y$$

B. $$1-y$$

C. $$-1-y$$

D. $$y-1$$

E. $$x-y$$

Hello,

I was looking at the explanation of this question (ID Q02-38, Question2 section 9) and it quite does not make any sense in the very first step (or maybe I am overlooking something). Kindly check (or possibly explain it if possible/and-is-correct).

Thanks
Arsh
[Reveal] Spoiler: OA

Last edited by Carcass on 04 Jul 2019, 23:42, edited 3 times in total.
Editing the post and adding the tags
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Re: Q02-38 Question # 08 Section # 09 [#permalink]  25 Jun 2016, 01:16
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Expert's post
Hi,

well I have to admit that the explanation is not the top-notch but it is not wrong.

Starting from what we do know: X could be positive or negative: we do not know at the moment AND y is negative.

Now look at the first part of the equation $$\sqrt{x^2}$$ is equal to |x|. From this we also know that |x| = -x. Which means that on the left hand side X is positive, always. On the right hand side for X to be always positive X must be negative. This are math rules that is better for you to know as cold during the exam.

As such, actually we do have that X/X is = 1 and is negative. So -1

Going to the second square root |y| = -y so -y * - y = y^2 that under square root becomes |y|.

At this point we have -1 - |y| AND we already know that |y| = -y .

-1 - (-y) = -1 +y

Hope is clear this. Waiting, though, math expert for further clarification.
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Re: Q02-38 Question # 08 Section # 09 [#permalink]  28 Feb 2018, 21:33
Carcass wrote:
Hi,

well I have to admit that the explanation is not the top-notch but it is not wrong.

Starting from what we do know: X could be positive or negative: we do not know at the moment AND y is negative.

Now look at the first part of the equation $$\sqrt{x^2}$$ is equal to |x|. From this we also know that |x| = -x. Which means that on the left hand side X is positive, always. On the right hand side for X to be always positive X must be negative. This are math rules that is better for you to know as cold during the exam.

As such, actually we do have that X/X is = 1 and is negative. So -1

Going to the second square root |y| = -y so -y * - y = y^2 that under square root becomes |y|.

At this point we have -1 - |y| AND we already know that |y| = -y .

-1 - (-y) = -1 +y

Hope is clear this. Waiting, though, math expert for further clarification.

I still don't know why $$\sqrt{\frac{-y}{|y|}}$$ =-y NOT -1?
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Re: Q02-38 Question # 08 Section # 09 [#permalink]  24 May 2018, 11:07
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Peter wrote:
Carcass wrote:
Hi,

well I have to admit that the explanation is not the top-notch but it is not wrong.

Starting from what we do know: X could be positive or negative: we do not know at the moment AND y is negative.

Now look at the first part of the equation $$\sqrt{x^2}$$ is equal to |x|. From this we also know that |x| = -x. Which means that on the left hand side X is positive, always. On the right hand side for X to be always positive X must be negative. This are math rules that is better for you to know as cold during the exam.

As such, actually we do have that X/X is = 1 and is negative. So -1

Going to the second square root |y| = -y so -y * - y = y^2 that under square root becomes |y|.

At this point we have -1 - |y| AND we already know that |y| = -y .

-1 - (-y) = -1 +y

Hope is clear this. Waiting, though, math expert for further clarification.

I still don't know why $$\sqrt{\frac{-y}{|y|}}$$ =-y NOT -1?

Consider y = (-2), as y<0. hence -y = -(-2) = 2.
|y| = |-2| = 2.
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Re: Q02-38 Question # 08 Section # 09 [#permalink]  04 Jul 2019, 15:54
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I was thinking another way. Let me correct if I am horribly wrong! Let x and y both equal -1. from the first, sqrt of (x square)/x we get -1 and also form second part we get -1. So adding, -2. Consider all options!. Option D fits!
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Re: Q02-38 Question # 08 Section # 09 [#permalink]  05 Jul 2019, 04:49
Expert's post
@AlaminMolla is correct. For ALL negative values of x and y, the expression will ALWAYS evaluate to be -2

So, the question is flawed. At the very least, the question should read "Which of the following COULD BE the value of ...", in which case A, D and E COULD equal -2

@arsh are you sure you transcribed the question correctly?

Cheers,
Brent
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Re: Q02-38 Question # 08 Section # 09 [#permalink]  15 Jul 2019, 15:26
this was hard to understand
Re: Q02-38 Question # 08 Section # 09   [#permalink] 15 Jul 2019, 15:26
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