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

 It is currently 19 Sep 2018, 00:27

### 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

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

Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 19 Mar 2014
Posts: 962
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

26 Jun 2017, 01:58
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
Joined: 06 Feb 2017
Posts: 7
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

13 Jul 2017, 08:54
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
Joined: 02 Sep 2009
Posts: 49251
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

13 Jul 2017, 10:07
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
Joined: 13 Mar 2017
Posts: 619
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

14 Jul 2017, 00:36
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

_________________

CAT 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3497
Location: United States (CA)
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

16 Jul 2017, 17:38
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

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Director
Joined: 02 Sep 2016
Posts: 724
If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

Updated on: 01 Oct 2017, 23:10

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]
_________________

Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.

Originally posted by Shiv2016 on 13 Sep 2017, 06:24.
Last edited by Shiv2016 on 01 Oct 2017, 23:10, 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

01 Oct 2017, 09:34
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
Joined: 22 May 2016
Posts: 1973
If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

01 Oct 2017, 12:10
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.
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

Director
Joined: 02 Sep 2016
Posts: 724
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

01 Oct 2017, 23:22
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
Joined: 21 Jun 2017
Posts: 85
Re: If x=-|x|, then which one of the following statements  [#permalink]

### Show Tags

13 Oct 2017, 08:32
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
Re: If x=-|x|, then which one of the following statements &nbs [#permalink] 13 Oct 2017, 08:32

Go to page   Previous    1   2   [ 30 posts ]

Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.