GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 30 May 2020, 07:57 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If x=-|x|, then which one of the following statements

Author Message
TAGS:

### Hide Tags

Retired Moderator P
Joined: 19 Mar 2014
Posts: 906
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

If x = - |x| , then which one of the following statements could be true?

$$x = - |x|$$

The above equation means:

1. x can be ZERO
2. x can be any negative number

Now lets go the options.

I. x = 0 ===> Holds true based on point (1) above =====> TRUE
II. x < 0 ===> Holds true based on point (2) above =====> TRUE
III. x > 0 ===> Not True as value should either be ZERO or Less than ZERO =====> FALSE

_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
Intern  B
Joined: 06 Feb 2017
Posts: 7
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

Bunuel wrote:
If x = ± |x| , then which one of the following statements could be true?
I. x = 0
II. x < 0
III. x > 0

(A) None (B) I only (C) III only (D) I and II (E) II and III

I've never seen real GMAT question using the sign "±". Moreover as the OA believed to be D, then the question should be:

If x=-|x|, then which one of the following statements could be true?

I. x = 0
II. x < 0
III. x > 0

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III

In this case, D would be correct answer as x can be zero as well as any negative number.

Thanx Bunuel very well explained just tell me if it is x=|x| then what the answer should be
TIA
Math Expert V
Joined: 02 Sep 2009
Posts: 64243
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

Bunuel wrote:
If x = ± |x| , then which one of the following statements could be true?
I. x = 0
II. x < 0
III. x > 0

(A) None (B) I only (C) III only (D) I and II (E) II and III

I've never seen real GMAT question using the sign "±". Moreover as the OA believed to be D, then the question should be:

If x=-|x|, then which one of the following statements could be true?

I. x = 0
II. x < 0
III. x > 0

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III

In this case, D would be correct answer as x can be zero as well as any negative number.

Thanx Bunuel very well explained just tell me if it is x=|x| then what the answer should be
TIA

x = |x| means that x >= 0. So, I and III could be true.
_________________
Director  D
Joined: 13 Mar 2017
Posts: 717
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

If x = - |x| , then which one of the following statements could be true?

I. x = 0
II. x < 0
III. x > 0

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III

x = -|x|
Now |x|>=0
-|x|<=0
so x<=0

Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10594
Location: United States (CA)
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

If x = - |x| , then which one of the following statements could be true?

I. x = 0
II. x < 0
III. x > 0

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III

Since x = -|x|, x must be negative or zero. Thus, I and II are true.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Director  G
Joined: 02 Sep 2016
Posts: 625
If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

1) If x<0, then x=-|x|=0

2) If x<0 i.e. negative, then x= -(-x) [Here -x is positive because x is less than 0. -ve*-ve= +ve]

Originally posted by Shiv2016 on 13 Sep 2017, 05:24.
Last edited by Shiv2016 on 01 Oct 2017, 22:10, edited 1 time in total.
Intern  Joined: 25 Jun 2017
Posts: 3
Location: India
Schools: Stern '18
GMAT 1: 360 Q30 V9
GPA: 2.3
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

If x = - |x| , then which one of the following statements could be true?

I. x = 0
II. x < 0
III. x > 0

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III[/quote]

x=-|x|
I. 0=-|0| =0 YES.
II. -1=-|1|
-1=-1 YES.
III. 2=-|2|
2 = -2 NO.
HENCE ANS IS D.
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3855
If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

1
Shiv2016 wrote:
It would be great if for once someone clear this doubt. I am not able to move to something new in absolute values because of this same doubt. Every time I try to clear it, it becomes worse.

1) If x>=0
then |x|= x

2) If x<0
then |x|= -(-x)= x (in this x is negative now or positive?)

Then in this question, how is II correct?

x<0

x=-|x|

Shiv2016 , in case you are still wondering . . .

On a different question, about a week after you posted this (sorry, I didn't see your post until just now), someone asked exactly what I think you are asking.

I answered, because, as I wrote, that rule can feel very counterintuitive to me.

I wrote down a few ways to think about what you asked and I highlighted, above. Bunuel then added another important way to think about it. So . . . three posts that address what I think you are asking.

Please, take a look at Bunuel 's post starting HERE

Then go to my post (same thread) here: WAYS TO THINK ABOUT x = -|x|

Finally, right below mine, Bunuel here: FINISHES THE DISCUSSION

All of them come from this question

I hope they help. _________________
Visit SC Butler, here! Get two SC questions to practice, whose links you can find by date.

Our lives begin to end the day we become silent about things that matter. -- Dr. Martin Luther King, Jr.
Director  G
Joined: 02 Sep 2016
Posts: 625
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

genxer123 wrote:
Shiv2016 wrote:
It would be great if for once someone clear this doubt. I am not able to move to something new in absolute values because of this same doubt. Every time I try to clear it, it becomes worse.

1) If x>=0
then |x|= x

2) If x<0
then |x|= -(-x)= x (in this x is negative now or positive?)

Then in this question, how is II correct?

x<0

x=-|x|

Shiv2016 , in case you are still wondering . . .

On a different question, about a week after you posted this (sorry, I didn't see your post until just now), someone asked exactly what I think you are asking.

I answered, because, as I wrote, that rule can feel very counterintuitive to me.

I wrote down a few ways to think about what you asked and I highlighted, above. Bunuel then added another important way to think about it. So . . . three posts that address what I think you are asking.

Please, take a look at Bunuel 's post starting HERE

Then go to my post (same thread) here: WAYS TO THINK ABOUT x = -|x|

Finally, right below mine, Bunuel here: FINISHES THE DISCUSSION

All of them come from this question

I hope they help. Thank you so much for your reply. Your posts and Bunuel's posts are to the point and cleared all my doubts related to negative sign.
I again solved the question. I hope the reasoning makes sense now Manager  B
Joined: 21 Jun 2017
Posts: 82
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

If x = - |x| , then which one of the following statements could be true?

I. x = 0
II. x < 0
III. x > 0

(A) None
(B) I only
(C) III only
(D) I and II
(E) II and III

|x| is always positive. Putting a negative sign infront of a positive sign makes the value a negative. So, the value of x is negative. X CANNOT be greater than zero, because this would make x a positive, which would make - |x| a negative, which contradicts the given equation. X could be zero, because the absolute value of zero is zero, and the negative sign does not change the value of zero; therefore, 0 = - |0| holds true.

Therefore, the answer is (D) I and II
Non-Human User Joined: 09 Sep 2013
Posts: 15021
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

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: If x=-|x|, then which one of the following statements   [#permalink] 16 Nov 2019, 19:32

Go to page   Previous    1   2   [ 31 posts ]

# If x=-|x|, then which one of the following statements   