GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2019, 05:19

### 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

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

Author Message
TAGS:

### Hide Tags

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]

### Show Tags

Updated on: 26 Jul 2012, 07:49
4
30
00:00

Difficulty:

55% (hard)

Question Stats:

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

### HideShow timer Statistics

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
Joined: 02 Sep 2009
Posts: 58449
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?  [#permalink]

### Show Tags

26 Jul 2012, 07:56
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.
_________________
Current Student
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]

### Show Tags

26 Jul 2012, 07:42
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
Joined: 26 Jul 2011
Posts: 77
Location: India
WE: Marketing (Manufacturing)
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
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]

### Show Tags

09 Oct 2012, 20:19
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]

### Show Tags

09 Oct 2012, 23:56
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]

### 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: 588
WE: Science (Education)
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: 401
Concentration: Marketing, Finance
GPA: 3.23
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?  [#permalink]

### Show Tags

06 Dec 2012, 22:37
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)

_________________
Impossible is nothing to God.
Intern
Joined: 02 Nov 2012
Posts: 27
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!
Intern
Joined: 20 Dec 2014
Posts: 36
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?  [#permalink]

### Show Tags

26 Mar 2018, 12:17
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.

_________________
Kindly press "+1 Kudos" to appreciate
Math Expert
Joined: 02 Sep 2009
Posts: 58449
Re: For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?  [#permalink]

### Show Tags

26 Mar 2018, 21:31
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.
_________________
Director
Joined: 09 Mar 2018
Posts: 994
Location: India
For x < 0. Simplify {-(x + 1) |x-1| + 1}^1/2?  [#permalink]

### Show Tags

11 Feb 2019, 02:42
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
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
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
Display posts from previous: Sort by