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Intern  Joined: 24 Jul 2012
Posts: 12
Schools: Schulich '16
GMAT 1: 610 Q49 V26 WE: Consulting (Consulting)
For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?  [#permalink]

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Question Stats: 55% (01:33) correct 45% (01:59) wrong based on 626 sessions

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For x < 0. Simplify $$\sqrt{-(x + 1)*|x-1| + 1}$$?

A. x
B. x - 1
C. x + 1
D. – x
E. – x + 1

Originally posted by Vamshi8411 on 26 Jul 2012, 05:35.
Last edited by Bunuel on 26 Jul 2012, 07:49, edited 1 time in total.
Edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 58401
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?  [#permalink]

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6
1
Vamshi8411 wrote:
For x < 0. Simplify $$\sqrt{-(x + 1)*|x-1| + 1}$$?

A. x
B. x - 1
C. x + 1
D. – x
E. – x + 1

One can also use plug-in method for this problem.

Since given that $$x<0$$, then say $$x=-1$$, then $$\sqrt{-(x + 1)*|x-1| + 1}=\sqrt{-(-1 + 1)*|-1-1| + 1}=\sqrt{0+1}=1$$.

Now, plug $$x=-1$$ into the answer choices to see which one yields 1. Only answer choice D works: $$-x=-(-1)=1$$

Note that for plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.

Hope it helps.
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Joined: 29 Mar 2012
Posts: 295
Location: India
GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38 Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2?  [#permalink]

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9
2
Vamshi8411 wrote:
Q) For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2?

A) x

B) x - 1

C) x + 1

D) – x

E) – x + 1

Hi,

for x<0,
|x-1| = 1-x
$$\sqrt{1-(x + 1) |x-1|}$$
=$$\sqrt{1-(x + 1)(1-x)}$$
=$$\sqrt{1-1+x^2}$$
=$$\sqrt{x^2}$$
=|x|, again x<0
= -x

Regards,
General Discussion
Manager  B
Joined: 26 Jul 2011
Posts: 77
Location: India
WE: Marketing (Manufacturing)
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?  [#permalink]

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Bunuel/Karishma

How can this be done using algebra. As explained by cyber we have taken value of !X-1! as negative, However we have only been provided with X<0. May be I am missing something..Plz Help
Intern  Joined: 01 Jun 2012
Posts: 18
Location: United States
Concentration: Nonprofit
GMAT 1: 720 Q48 V43 GPA: 3.83
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2?  [#permalink]

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1
Vamshi8411 wrote:
Q) For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2?

A) x

B) x - 1

C) x + 1

D) – x

E) – x + 1

Hi,

for x<0,
|x-1| = 1-x
$$\sqrt{1-(x + 1) |x-1|}$$
=$$\sqrt{1-(x + 1)(1-x)}$$
=$$\sqrt{1-1+x^2}$$
=$$\sqrt{x^2}$$
=|x|, again x<0
= -x

Regards,

Hi!

I'm confused as why the answer isn't simply x (as opposed to-x). The absolute value of x, when simplified, is positive x, even if it is stated that x<0. Why do you go back and add a negative?

Thanks!
Director  Joined: 22 Mar 2011
Posts: 588
WE: Science (Education)
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2?  [#permalink]

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1
egiles wrote:
Vamshi8411 wrote:
Q) For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2?

A) x

B) x - 1

C) x + 1

D) – x

E) – x + 1

Hi,

for x<0,
|x-1| = 1-x
$$\sqrt{1-(x + 1) |x-1|}$$
=$$\sqrt{1-(x + 1)(1-x)}$$
=$$\sqrt{1-1+x^2}$$
=$$\sqrt{x^2}$$
=|x|, again x<0
= -x

Regards,

Hi!

I'm confused as why the answer isn't simply x (as opposed to-x). The absolute value of x, when simplified, is positive x, even if it is stated that x<0. Why do you go back and add a negative?

Thanks!

What is positive x when x is negative? What do you mean by absolute value of x, when simplified?
Is $$|-7| = -7?$$ NOOOO! $$|-7|=-(-7)=7>0!!!$$
Absolute value is always non-negative.
_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.
Intern  Joined: 01 Jun 2012
Posts: 18
Location: United States
Concentration: Nonprofit
GMAT 1: 720 Q48 V43 GPA: 3.83
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2?  [#permalink]

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Hi,

for x<0,
|x-1| = 1-x
$$\sqrt{1-(x + 1) |x-1|}$$
=$$\sqrt{1-(x + 1)(1-x)}$$
=$$\sqrt{1-1+x^2}$$
=$$\sqrt{x^2}$$
=|x|, again x<0
= -x

Regards,[/quote]

Hi!

I'm confused as why the answer isn't simply x (as opposed to-x). The absolute value of x, when simplified, is positive x, even if it is stated that x<0. Why do you go back and add a negative?

Thanks![/quote]

What is positive x when x is negative? What do you mean by absolute value of x, when simplified?
Is $$|-7| = -7?$$ NOOOO! $$|-7|=-(-7)=7>0!!!$$
Absolute value is always non-negative.[/quote]

Hi EvaJager,

First, many thanks for the help you give me and others on this board. It is much appreciated.

Here is where my answer differed from yours. When I solved it, I reached this point:

= |x|
= x

Here is what you did:

= |x|
= -x

I am confused why you said the absolute value of x is -x. I thought all the absolute value of all numbers is non-negative.

Thanks again!
Eric
Director  Joined: 22 Mar 2011
Posts: 588
WE: Science (Education)
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2?  [#permalink]

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egiles wrote:
Hi,

for x<0,
|x-1| = 1-x
$$\sqrt{1-(x + 1) |x-1|}$$
=$$\sqrt{1-(x + 1)(1-x)}$$
=$$\sqrt{1-1+x^2}$$
=$$\sqrt{x^2}$$
=|x|, again x<0
= -x

Regards,

Hi!

I'm confused as why the answer isn't simply x (as opposed to-x). The absolute value of x, when simplified, is positive x, even if it is stated that x<0. Why do you go back and add a negative?

Thanks![/quote]

--------------------------------
What is positive x when x is negative? What do you mean by absolute value of x, when simplified?
Is $$|-7| = -7?$$ NOOOO! $$|-7|=-(-7)=7>0!!!$$
Absolute value is always non-negative.[/quote]

Hi EvaJager,

First, many thanks for the help you give me and others on this board. It is much appreciated.

Here is where my answer differed from yours. When I solved it, I reached this point:

= |x|
= x

Here is what you did:

= |x|
= -x

I am confused why you said the absolute value of x is -x. I thought all the absolute value of all numbers is non-negative.

Thanks again!
Eric[/quote]

-------------------------
I am asking the same question again: if $$x = -7,$$ is $$|-7|=-7$$??? NO!!!
$$|-7| = 7$$. But $$x$$ is not $$7, \,\,x$$ is $$-7.$$ What is the connection between $$-7$$ and $$7?$$
Simply, $$7 = -(-7).$$
When $$x$$ is negative, multiplying it by $$-1$$ it turns it into a positive number. Therefore, $$|x|=-x$$ for $$x<0.$$
You cannot write $$|-7|=-7.$$ A letter denoting a number if doesn't have a minus sign in front of it, it doesn't mean it cannot be negative. $$x$$ doesn't automatically designate a positive number. You are stating yourself that $$x$$ is negative!

Absolute value of a number expresses the distance on the number line between that number and 0. Distance between $$-7$$ and $$0$$ is $$7$$.
A number $$x$$ can be negative, for example $$x=-7$$. And $$-x$$ can be positive, if $$x=-5$$, because $$-(-5)=5.$$
_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.
Senior Manager  Joined: 13 Aug 2012
Posts: 401
Concentration: Marketing, Finance
GPA: 3.23
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?  [#permalink]

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1
$$\sqrt{-(x + 1)*|x-1| + 1}$$

Since x < 0, what is |x+1|?
So let x = -1, x-1 = -2
let x = -2, x-1 = -3
Since x-1 is always (-), |x-1| = -(x-1).

Transform the equation:
$$\sqrt{-(x+1)*-(x+1)+1}$$
$$\sqrt{x^2-1+1}$$
$$\sqrt{x^2}=|x|$$

Since x<0, what is |x|?
|x| = -(x)

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Intern  Joined: 02 Nov 2012
Posts: 27
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?  [#permalink]

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Can someone please explain why |x-1| = 1-x. I solved the question by filling in -2 and got the answer, but I really want to understand the algebra? Thanks in advance!
Intern  B
Joined: 20 Dec 2014
Posts: 36
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?  [#permalink]

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Bunuel wrote:
Vamshi8411 wrote:
For x < 0. Simplify $$\sqrt{-(x + 1)*|x-1| + 1}$$?

A. x
B. x - 1
C. x + 1
D. – x
E. – x + 1

One can also use plug-in method for this problem.

Since given that $$x<0$$, then say $$x=-1$$, then $$\sqrt{-(x + 1)*|x-1| + 1}=\sqrt{-(-1 + 1)*|-1-1| + 1}=\sqrt{0+1}=1$$.

Now, plug $$x=-1$$ into the answer choices to see which one yields 1. Only answer choice D works: $$-x=-(-1)=1$$

Note that for plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.

Hope it helps.

Hi

Hypothetically if we land up with a solution as $$\sqrt{- 4}$$ what would be the answer.
Trying to understand the concept.

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Joined: 02 Sep 2009
Posts: 58401
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?  [#permalink]

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MT1988 wrote:
Bunuel wrote:
Vamshi8411 wrote:
For x < 0. Simplify $$\sqrt{-(x + 1)*|x-1| + 1}$$?

A. x
B. x - 1
C. x + 1
D. – x
E. – x + 1

One can also use plug-in method for this problem.

Since given that $$x<0$$, then say $$x=-1$$, then $$\sqrt{-(x + 1)*|x-1| + 1}=\sqrt{-(-1 + 1)*|-1-1| + 1}=\sqrt{0+1}=1$$.

Now, plug $$x=-1$$ into the answer choices to see which one yields 1. Only answer choice D works: $$-x=-(-1)=1$$

Note that for plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.

Hope it helps.

Hi

Hypothetically if we land up with a solution as $$\sqrt{- 4}$$ what would be the answer.
Trying to understand the concept.

It would mean that that you've made an error in arithmetic because even roots, such as square roots from negative numbers are not defined on the GMAT. All numbers in the GMAT are by default real numbers.
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Posts: 995
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For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?  [#permalink]

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Vamshi8411 wrote:
For x < 0. Simplify $$\sqrt{-(x + 1)*|x-1| + 1}$$?

A. x
B. x - 1
C. x + 1
D. – x
E. – x + 1

Finally after getting this logic wrong twice, i got it right in this question

Keyword x < 0

$$\sqrt{-(x + 1)*|x-1| + 1}$$

$$\sqrt{-(x + 1) * - (x-1) + 1}$$

$$\sqrt{x^2}$$

$$x^2$$ = |x|

x < 0

Value is -x
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Many of life's failures happen with people who do not realize how close they were to success when they gave up. For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?   [#permalink] 11 Feb 2019, 02:42
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