Last visit was: 24 Mar 2025, 13:23 It is currently 24 Mar 2025, 13:23
Home
GMAT
Messages
Tests
Schools
Reviews
Rewards
Chat
My Profile
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
avatar
HarveyKlaus
avatar
Joined: 18 Feb 2015
Last visit: 13 May 2017
Posts: 69
Own Kudos:
611
 [19]
Given Kudos: 15
Posts: 69
Kudos: 611
 [19]
If x < 0, which of the following represents a positive number? Updated on: 01 Apr 2018, 21:05
Originally posted by HarveyKlaus on 10 Jul 2016, 02:46.
Last edited by Bunuel on 01 Apr 2018, 21:05, edited 4 times in total.
Renamed the topic and edited the question.
3
Kudos
Add Kudos
16
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

89% (00:35) correct 11% (00:50) wrong based on 1052 sessions

History

Date
Time
Result
Not Attempted Yet
If x < 0, which of the following represents a positive number?

A) x/|x|
B) |x|/x
C) x|x|
D) -x|x|
E) x|-x|


Show Spoiler
Im not able to get the answer. Modular sign always changes the value inside to a positive value. How can the answer be justified?

Thanks
ShowHide Answer
Official Answer
D
User avatar
msk0657
User avatar
Retired Moderator
Joined: 26 Nov 2012
Last visit: 14 Feb 2020
Posts: 468
Own Kudos:
531
 [2]
Given Kudos: 46
Posts: 468
Kudos: 531
 [2]
If x < 0, which of the following represents a positive number? Updated on: 10 Jul 2016, 06:34
Originally posted by msk0657 on 10 Jul 2016, 05:03.
Last edited by msk0657 on 10 Jul 2016, 06:34, edited 1 time in total.
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
HarveyKlaus
If x<0, which of the following represents a positive number?

A) X/lXl
B) lXl/X
C) XlXl
D) -XlXl
E) Xl-Xl

Im not able to get the answer. Modular sign always changes the value inside to a positive value. How can the answer be justified?

Thanks

Given X < 0 , i.e. X has to be -ve value.

When X is +ve or -ve |+X| = |-X| = |X|.

We know that -ve * -ve will lead to +ve.

- ( X ) |X| = +ve as we required this.

Then only option D fits the bill.
avatar
target760gmat
avatar
Joined: 15 Jun 2016
Last visit: 06 Dec 2016
Posts: 42
Own Kudos:
44
Given Kudos: 42
Location: India
Concentration: Technology, Strategy
Schools: ISB '18 SPJ PGPM"17 NUS '18
GMAT 1: 730 Q50 V39
Schools: ISB '18 SPJ PGPM"17 NUS '18
GMAT 1: 730 Q50 V39
Posts: 42
Kudos: 44
If x < 0, which of the following represents a positive number? 10 Jul 2016, 05:04
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If x<0, which of the following represents a positive number?

A) X/lXl
B) lXl/X
C) XlXl
D) -XlXl
E) Xl-Xl


A - -ve / +ve ---> -ve
B - +ve / - ve ---> -ve
C - -ve * +ve ---> -ve
D - -ve * (-ve) * +ve ---> +ve
E- -ve * +ve ---> -ve


Ans : D which is +ve

Hope it helps
avatar
HarveyKlaus
avatar
Joined: 18 Feb 2015
Last visit: 13 May 2017
Posts: 69
Own Kudos:
611
Given Kudos: 15
Posts: 69
Kudos: 611
If x < 0, which of the following represents a positive number? 10 Jul 2016, 05:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi msk0657.

In option D) we have -x which is being multiplied with the lxl. Don't we know that the outcome from the lxl is going to be positive in any case. So in the end we will have negative*positive(from the modular sign) = negative?
What am i missing?

Thanks,

msk0657
HarveyKlaus
If x<0, which of the following represents a positive number?

A) X/lXl
B) lXl/X
C) XlXl
D) -XlXl
E) Xl-Xl

Im not able to get the answer. Modular sign always changes the value inside to a positive value. How can the answer be justified?

Thanks

Given X < 0 , i.e. X has to be -ve value.

When X is +ve or -ve |+X| = |-X| = |X|.

We know that -ve * -ve will lead to +ve.

- ( -X ) |X| = +ve as we required this.

Then only option D fits the bill.
avatar
target760gmat
avatar
Joined: 15 Jun 2016
Last visit: 06 Dec 2016
Posts: 42
Own Kudos:
44
Given Kudos: 42
Location: India
Concentration: Technology, Strategy
Schools: ISB '18 SPJ PGPM"17 NUS '18
GMAT 1: 730 Q50 V39
Schools: ISB '18 SPJ PGPM"17 NUS '18
GMAT 1: 730 Q50 V39
Posts: 42
Kudos: 44
If x < 0, which of the following represents a positive number? 10 Jul 2016, 05:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi HarveyKlaus,


Just to clarify... |x| is positive but -x is as well positive ... so -x|x| is nothing but -1 * x * |x| ----> -ve * -ve * +ve ---> +ve

Thanks
avatar
HarveyKlaus
avatar
Joined: 18 Feb 2015
Last visit: 13 May 2017
Posts: 69
Own Kudos:
611
Given Kudos: 15
Posts: 69
Kudos: 611
If x < 0, which of the following represents a positive number? 10 Jul 2016, 05:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hitarget760gmat,

So If I get you right, the solution lies in separating the -x sign outside the modules into -1 & -x. Then multiply all these variables will give us a positive solution.

Thanks a lot. That helps.
HK


target760gmat
Hi HArvey,


Just to clarify... |x| is positive but -x is as well positive ... so -x|x| is nothing but -1 * x * |x| ----> -ve * -ve * +ve ---> +ve

Thanks
avatar
target760gmat
avatar
Joined: 15 Jun 2016
Last visit: 06 Dec 2016
Posts: 42
Own Kudos:
44
 [1]
Given Kudos: 42
Location: India
Concentration: Technology, Strategy
Schools: ISB '18 SPJ PGPM"17 NUS '18
GMAT 1: 730 Q50 V39
Schools: ISB '18 SPJ PGPM"17 NUS '18
GMAT 1: 730 Q50 V39
Posts: 42
Kudos: 44
 [1]
If x < 0, which of the following represents a positive number? 10 Jul 2016, 05:46
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Yes that's right... At first look we may be deceived to think tat -x is -ve entity... however it is +ve since x is already a negative entity multiplied with -1.
User avatar
msk0657
User avatar
Retired Moderator
Joined: 26 Nov 2012
Last visit: 14 Feb 2020
Posts: 468
Own Kudos:
531
Given Kudos: 46
Posts: 468
Kudos: 531
If x < 0, which of the following represents a positive number? 10 Jul 2016, 06:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HarveyKlaus
Hi msk0657.

In option D) we have -x which is being multiplied with the lxl. Don't we know that the outcome from the lxl is going to be positive in any case. So in the end we will have negative*positive(from the modular sign) = negative?
What am i missing?

Thanks,

msk0657
HarveyKlaus
If x<0, which of the following represents a positive number?

A) X/lXl
B) lXl/X
C) XlXl
D) -XlXl
E) Xl-Xl

Im not able to get the answer. Modular sign always changes the value inside to a positive value. How can the answer be justified?

Thanks

Given X < 0 , i.e. X has to be -ve value.

When X is +ve or -ve |+X| = |-X| = |X|.

We know that -ve * -ve will lead to +ve.

- ( -X ) |X| = +ve as we required this.

Then only option D fits the bill.


Hi Harvey,

Given that X < 0 then X is always negative i.e X can be -1,-2,-3 etc... - infinite. ( + infinite...... 3,2,1 0 -1,-2,-3......... - infinite )

This is how we get X always negative.

For example, take X has -2 ( Given X < 0 ).

Then if we substitute this value in D

it is mentioned that -X * |X|

Then - ( -2 ) * |-2| = 4, which is positive and you if substitute any X < 0 value we always get positive result itself.

Hope this clears..:)
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 March 2025
Posts: 100,064
Own Kudos:
710,502
Given Kudos: 92,683
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 100,064
Kudos: 710,502
If x < 0, which of the following represents a positive number? 10 Jul 2016, 06:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HarveyKlaus
If x<0, which of the following represents a positive number?

A) x/|x|
B) |x|/x
C) x|x|
D) -x|x|
E) x|x|

Im not able to get the answer. Modular sign always changes the value inside to a positive value. How can the answer be justified?

Thanks

1:
The easiest way would be to simply substitute x by some negative number, say by -1, and check which of the options would give positive result.

2:
Or, since |x| would be positive here, we could drop |x| and concentrate on expressions without modulus.

3:
Or, one can notice that all options but D are basically the same x divided or multiplied by |x|. Since we cannot have more than 1 correct answer none will be correct.

4:
Algebraic way: since x is negative, then |x| = -x, thus D -x|x| = (-x)(-x) = x^2 = positive.

Answer: D.

Hope it's clear.
User avatar
CyberStein
User avatar
Joined: 21 Jun 2017
Last visit: 02 Jun 2023
Posts: 60
Own Kudos:
42
Given Kudos: 3
Posts: 60
Kudos: 42
If x < 0, which of the following represents a positive number? 13 Oct 2017, 08:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HarveyKlaus
If x<0, which of the following represents a positive number?

A) x/|x|
B) |x|/x
C) x|x|
D) -x|x|
E) x|x|

Im not able to get the answer. Modular sign always changes the value inside to a positive value. How can the answer be justified?

Thanks


Given x<0, we know that x's value is negative.
If you put a negative sign infant of a negative variable, that variable value is then positive. Absolute value is always positive. Multiplying two positives always yields positive, whereas one positive and one negative, always yields a negative.

Therefore, the answer is D
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 3,009
Own Kudos:
7,577
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 3,009
Kudos: 7,577
If x < 0, which of the following represents a positive number? 16 Oct 2017, 16:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HarveyKlaus
If x<0, which of the following represents a positive number?

A) x/|x|
B) |x|/x
C) x|x|
D) -x|x|
E) x|x|

Let’s say x = -2 and analyze each answer choice:

A) -2/|2| = -2/2 = -1

B) |-2|/-2 = 2/-2 = -1

C) -2|-2| = -2 x 2 = -4

D) -(-2)|-2| = 2 x 2 = 4

Alternate Solution:

We know that |x| is positive. Therefore, we can ignore the |x| part of the answer choices (because that part is already positive). We know that x itself is negative. Scanning the answer choices, we see that the only choice that negates the already negative value of x is choice D, which makes the value of –x|x| positive.

Answer: D
User avatar
AkshdeepS
User avatar
Joined: 13 Apr 2013
Last visit: 24 Mar 2025
Posts: 1,446
Own Kudos:
1,763
Given Kudos: 1,001
Status:It's near - I can see.
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE:Engineering (Real Estate)
Products:
My Reviews
Posts: 1,446
Kudos: 1,763
If x < 0, which of the following represents a positive number? 09 Mar 2018, 06:13
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HarveyKlaus
If x<0, which of the following represents a positive number?

A) x/|x|
B) |x|/x
C) x|x|
D) -x|x|
E) x|x|

Im not able to get the answer. Modular sign always changes the value inside to a positive value. How can the answer be justified?

Thanks

As every option has |x|, which is always positive or non negative, and x is negative (Given x < 0),

only answer choice with -x can yield the positive result (-x*-x) .

Only option D has "- x".

(D)
User avatar
ramlala
User avatar
Joined: 22 Aug 2020
Last visit: 13 Dec 2022
Posts: 471
Own Kudos:
372
Given Kudos: 30
Location: India
Concentration: International Business, Finance
Schools: IIMA PGPX'23 INSEAD Jan'23 intake Sloan (MIT) ISB HEC Said
GPA: 4
WE:Project Management (Energy)
Schools: IIMA PGPX'23 INSEAD Jan'23 intake Sloan (MIT) ISB HEC Said
Posts: 471
Kudos: 372
If x < 0, which of the following represents a positive number? 13 Mar 2021, 19:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Quote:
If x < 0, which of the following represents a positive number?
Possibilities
x = -ve
|x| = +ve
-x = +ve
|-x| = +ve
Quote:
A) x/|x|
Situation -ve devided by +ve. Result is -ve.
Quote:
B) |x|/x
Situation +ve devided by -ve. Result is -ve.
Quote:
C) x|x|
Situation -ve multiplied to +ve. Result is -ve.
Quote:
D) -x|x|
Situation +ve multiplied to +ve. Result is +ve.
Quote:
E) x|-x|
Situation -ve multiplied to +ve. Result is -ve.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 36,684
Own Kudos:
963
Posts: 36,684
Kudos: 963
If x < 0, which of the following represents a positive number? 27 Dec 2023, 21:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
100064 posts
Krunaal
PS Forum Moderator
510 posts