Last visit was: 14 Sep 2026, 21:24 It is currently 14 Sep 2026, 21:24
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
HarveyS
User avatar
Joined: 14 Jan 2013
Last visit: 25 Apr 2017
Posts: 112
Own Kudos:
1,796
 [64]
Given Kudos: 30
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE:Consulting (Consulting)
Posts: 112
Kudos: 1,796
 [64]
If |x| = x, which of the following must be true? 22 Mar 2014, 02:31
7
Kudos
Add Kudos
56
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

68% (00:48) correct 32% (01:08) wrong based on 1480 sessions

History

Date
Time
Result
Not Attempted Yet
If |x| = −x, which of the following must be true?

A. x ≥ 0
B. x ≤ 0
C. x^2 > x
D. x^3 < 0
E. 2x < x

Show Spoiler
If |x| = −x, which of the following must be true?
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 14 Sep 2026
Posts: 113,508
Own Kudos:
841,320
 [19]
Given Kudos: 111,516
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,508
Kudos: 841,320
 [19]
If |x| = x, which of the following must be true? 22 Mar 2014, 04:39
3
Kudos
Add Kudos
16
Bookmarks
Bookmark this Post
Mountain14
If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x2>x
D. x3<0
E. 2x<x
Show more

When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\);

Answer: B.

Below posts might help to brush up fundamentals on modulus:
Theory on Abolute Values: math-absolute-value-modulus-86462.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

Hope this helps.
General Discussion
User avatar
QuantVeda
User avatar
Joined: 20 Mar 2014
Last visit: 07 Dec 2020
Posts: 1
Own Kudos:
2
 [2]
Posts: 1
Kudos: 2
 [2]
If |x| = x, which of the following must be true? 22 Mar 2014, 04:24
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
|x| =-x means absolute value of x is equal to negative of x. Since absolute value cannot be negative hence negative of x should result in a non negative number. It means x is a non positive number i.e. x< 0. Answer is B
User avatar
Senthil7
User avatar
Joined: 31 Mar 2016
Last visit: 05 Mar 2017
Posts: 322
Own Kudos:
221
Given Kudos: 197
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE:Operations (Commercial Banking)
GMAT 1: 670 Q48 V34
Posts: 322
Kudos: 221
If |x| = x, which of the following must be true? 15 May 2016, 11:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If x is negative how can x≤0? x<0 is appropriate as 0 is neither negative nor positive.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 14 Sep 2026
Posts: 113,508
Own Kudos:
841,320
 [2]
Given Kudos: 111,516
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,508
Kudos: 841,320
 [2]
If |x| = x, which of the following must be true? 15 May 2016, 11:47
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Senthil7
If x is negative how can x≤0? x<0 is appropriate as 0 is neither negative nor positive.
Show more

x is not negative, it's non-positive. The given equation holds for 0 too. Please check complete solution above.
User avatar
saurabhsavant
User avatar
Joined: 27 Aug 2016
Last visit: 09 Nov 2017
Posts: 70
Own Kudos:
18
Given Kudos: 149
Location: India
Schools: HEC Montreal '21
GMAT 1: 670 Q47 V37
GPA: 3
WE:Engineering (Energy)
Schools: HEC Montreal '21
GMAT 1: 670 Q47 V37
Posts: 70
Kudos: 18
If |x| = x, which of the following must be true? 04 Apr 2017, 07:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Mountain14
If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x2>x
D. x3<0
E. 2x<x

When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\);

Answer: B.

Below posts might help to brush up fundamentals on modulus:

Hope this helps.
Show more

By definition of mudulus:
mod(x) = x if x greater than or equal to zero and
mod (x) = -x if x is less than zero....
so we get solution as x<0....therefore x to the power 3 will always be negative or less than zero
What is wrong with D?....put in any negative value of x such as -5 or -0.5 or -1 we always get less than zero value.

Is there anything wrong in the abive stated definition of modulus that we learned in high school. I agree B also serves the purpose but then what about the definition...i mean wrong fundamentals were taught????
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 14 Sep 2026
Posts: 113,508
Own Kudos:
841,320
 [1]
Given Kudos: 111,516
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,508
Kudos: 841,320
 [1]
If |x| = x, which of the following must be true? 04 Apr 2017, 07:29
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
saurabhsavant
Bunuel
Mountain14
If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x2>x
D. x3<0
E. 2x<x

When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\);

Answer: B.

Below posts might help to brush up fundamentals on modulus:

Hope this helps.

By definition of mudulus:
mod(x) = x if x greater than or equal to zero and
mod (x) = -x if x is less than zero....
so we get solution as x<0....therefore x to the power 3 will always be negative or less than zero
What is wrong with D?....put in any negative value of x such as -5 or -0.5 or -1 we always get less than zero value.

Is there anything wrong in the abive stated definition of modulus that we learned in high school. I agree B also serves the purpose but then what about the definition...i mean wrong fundamentals were taught????
Show more

D is not always true because it implies that x is negative, while |x|=−x stands true for negative numbers as well as for 0.
User avatar
AkshdeepS
User avatar
Joined: 13 Apr 2013
Last visit: 08 Aug 2026
Posts: 1,420
Own Kudos:
1,977
Given Kudos: 1,002
Status:It's near - I can see.
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE:Engineering (Real Estate)
Products:
My Reviews
Posts: 1,420
Kudos: 1,977
If |x| = x, which of the following must be true? 10 Mar 2018, 04:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HarveyS
If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x2>x
D. x3<0
E. 2x<x
Show more


|x|=−x holds true when x <= 0.

Hence (B)
User avatar
Arpitkumar
User avatar
Joined: 30 May 2018
Last visit: 22 Mar 2021
Posts: 51
Own Kudos:
45
Given Kudos: 121
Concentration: General Management, Marketing
Schools: IIMA PGPX"20 INSEAD Jan '19 HBS '21
GMAT 1: 750 Q49 V45
GPA: 3.45
WE:Other (Retail: E-commerce)
Schools: IIMA PGPX"20 INSEAD Jan '19 HBS '21
GMAT 1: 750 Q49 V45
Posts: 51
Kudos: 45
If |x| = x, which of the following must be true? 15 Sep 2018, 03:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Mountain14
If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x2>x
D. x3<0
E. 2x<x

When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\);

Answer: B.

Below posts might help to brush up fundamentals on modulus:

Hope this helps.
Show more
But wont this also make X^3<0 or option D true ?
User avatar
Luca1111111111111
User avatar
Joined: 20 Apr 2019
Last visit: 04 Feb 2020
Posts: 75
Own Kudos:
54
Given Kudos: 20
Posts: 75
Kudos: 54
If |x| = x, which of the following must be true? 19 Oct 2019, 06:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Arpitkumar
Bunuel
Mountain14
If |x|=−x, which of the following must be true?

A. x≥0
B. x≤0
C. x2>x
D. x3<0
E. 2x<x

When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|={-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|={some \ expression}\). For example: \(|5|=5\);

Answer: B.

Below posts might help to brush up fundamentals on modulus:

Hope this helps.
But wont this also make X^3<0 or option D true ?
Show more
At first sight, yes. However, x could also be 0 in the above equation. 0^3 = 0 and NOT 0^3 < 0 (same for C btw). This is why only B is correct
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 14 Sep 2026
Posts: 22,739
Own Kudos:
26,981
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,739
Kudos: 26,981
If |x| = x, which of the following must be true? 21 Apr 2023, 07:29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HarveyS
If |x| = −x, which of the following must be true?

A. x ≥ 0
B. x ≤ 0
C. x^2 > x
D. x^3 < 0
E. 2x < x

Show Spoiler
If |x| = −x, which of the following must be true?
Show more

Since |x| = -x, x must be negative or equal to zero. Of the answer choices, only answer choice B has values that are either equal to zero or negative.

Answer: B
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,236
Own Kudos:
1,158
Posts: 39,236
Kudos: 1,158
If |x| = x, which of the following must be true? 10 Mar 2025, 05:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderator:
Bunuel
Math Expert
113508 posts