Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 30 Apr 2016, 21:51

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 24 Jul 2012
Posts: 13
Schools: Schulich '16
GMAT 1: 610 Q49 V26
WE: Consulting (Consulting)
Followers: 0

Kudos [?]: 21 [1] , given: 7

For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2? [#permalink]

### Show Tags

26 Jul 2012, 05:35
1
KUDOS
9
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

56% (02:03) correct 44% (01:40) wrong based on 461 sessions

### HideShow timer Statictics

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

A. x
B. x - 1
C. x + 1
D. – x
E. – x + 1
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Jul 2012, 07:49, edited 1 time in total.
Edited the question.
Senior Manager
Joined: 29 Mar 2012
Posts: 287
Concentration: Entrepreneurship
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 25

Kudos [?]: 317 [8] , given: 23

Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2? [#permalink]

### Show Tags

26 Jul 2012, 07:42
8
KUDOS
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,
Math Expert
Joined: 02 Sep 2009
Posts: 32549
Followers: 5632

Kudos [?]: 68320 [4] , given: 9797

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

### Show Tags

26 Jul 2012, 07:56
4
KUDOS
Expert's post
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.
_________________
Manager
Joined: 26 Jul 2011
Posts: 125
Location: India
WE: Marketing (Manufacturing)
Followers: 1

Kudos [?]: 79 [0], given: 15

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

### Show Tags

11 Sep 2012, 22:41
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
Current Student
Joined: 01 Jun 2012
Posts: 21
Location: United States
Concentration: Nonprofit
GMAT 1: 720 Q48 V43
GPA: 3.83
Followers: 0

Kudos [?]: 8 [0], given: 15

Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2? [#permalink]

### Show Tags

09 Oct 2012, 20:19
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: 612
WE: Science (Education)
Followers: 90

Kudos [?]: 760 [1] , given: 43

Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2? [#permalink]

### Show Tags

09 Oct 2012, 23:56
1
KUDOS
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.

Current Student
Joined: 01 Jun 2012
Posts: 21
Location: United States
Concentration: Nonprofit
GMAT 1: 720 Q48 V43
GPA: 3.83
Followers: 0

Kudos [?]: 8 [0], given: 15

Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2? [#permalink]

### Show Tags

10 Oct 2012, 09:02
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: 612
WE: Science (Education)
Followers: 90

Kudos [?]: 760 [0], given: 43

Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}1/2? [#permalink]

### Show Tags

10 Oct 2012, 09:55
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: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 22

Kudos [?]: 343 [0], given: 11

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

### Show Tags

06 Dec 2012, 22:37
$$\sqrt{-(x + 1)*|x-1| + 1}$$

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)

_________________

Impossible is nothing to God.

Intern
Joined: 02 Nov 2012
Posts: 36
Followers: 0

Kudos [?]: 4 [0], given: 11

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

### Show Tags

07 Jan 2013, 08:18
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!
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 9242
Followers: 454

Kudos [?]: 115 [0], given: 0

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

### Show Tags

14 Apr 2014, 00:04
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 9242
Followers: 454

Kudos [?]: 115 [0], given: 0

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

### Show Tags

25 Apr 2015, 00:43
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?   [#permalink] 25 Apr 2015, 00:43
Similar topics Replies Last post
Similar
Topics:
4 If x is a positive integer such that (x-1)(x-3)(x-5)....(x-93) < 0, ho 2 29 Jan 2016, 03:14
9 If 0 < x ≤ 1, then which one of the following is the maximum 7 21 Nov 2013, 03:22
48 Which values of x are solutions |x + 1| + |x - 1| <= 2 18 21 May 2012, 09:14
1 Simplify x^y - x^(y-1) to x^(y-1) * (x - 1) 3 19 Jun 2010, 04:39
12 If 0 < x < 1, what is the median of the values x, x^-1, x^2, 10 14 Nov 2006, 13:41
Display posts from previous: Sort by