Last visit was: 14 Jun 2024, 03:01 It is currently 14 Jun 2024, 03:01
Toolkit
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 < 0, which of the following represents a positive number?

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 18 Feb 2015
Posts: 71
Own Kudos [?]: 574 [17]
Given Kudos: 15
Retired Moderator
Joined: 26 Nov 2012
Posts: 473
Own Kudos [?]: 494 [2]
Given Kudos: 46
Intern
Joined: 15 Jun 2016
Posts: 42
Own Kudos [?]: 44 [0]
Given Kudos: 42
Location: India
Concentration: Technology, Strategy
GMAT 1: 730 Q50 V39
Manager
Joined: 18 Feb 2015
Posts: 71
Own Kudos [?]: 574 [0]
Given Kudos: 15
Re: If x < 0, which of the following represents a positive number? [#permalink]
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 wrote:
HarveyKlaus wrote:
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.
Intern
Joined: 15 Jun 2016
Posts: 42
Own Kudos [?]: 44 [0]
Given Kudos: 42
Location: India
Concentration: Technology, Strategy
GMAT 1: 730 Q50 V39
Re: If x < 0, which of the following represents a positive number? [#permalink]
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
Manager
Joined: 18 Feb 2015
Posts: 71
Own Kudos [?]: 574 [0]
Given Kudos: 15
Re: If x < 0, which of the following represents a positive number? [#permalink]
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 wrote:
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
Intern
Joined: 15 Jun 2016
Posts: 42
Own Kudos [?]: 44 [1]
Given Kudos: 42
Location: India
Concentration: Technology, Strategy
GMAT 1: 730 Q50 V39
Re: If x < 0, which of the following represents a positive number? [#permalink]
1
Kudos
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.
Retired Moderator
Joined: 26 Nov 2012
Posts: 473
Own Kudos [?]: 494 [0]
Given Kudos: 46
Re: If x < 0, which of the following represents a positive number? [#permalink]
HarveyKlaus wrote:
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 wrote:
HarveyKlaus wrote:
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..
Math Expert
Joined: 02 Sep 2009
Posts: 93707
Own Kudos [?]: 631617 [0]
Given Kudos: 82302
Re: If x < 0, which of the following represents a positive number? [#permalink]
HarveyKlaus wrote:
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.

Hope it's clear.
Manager
Joined: 21 Jun 2017
Posts: 60
Own Kudos [?]: 39 [0]
Given Kudos: 3
Re: If x < 0, which of the following represents a positive number? [#permalink]
HarveyKlaus wrote:
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.

Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3042
Own Kudos [?]: 6449 [0]
Given Kudos: 1646
Re: If x < 0, which of the following represents a positive number? [#permalink]
HarveyKlaus wrote:
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.

VP
Joined: 13 Apr 2013
Status:It's near - I can see.
Posts: 1475
Own Kudos [?]: 1631 [0]
Given Kudos: 1002
Location: India
GPA: 3.01
WE:Engineering (Real Estate)
Re: If x < 0, which of the following represents a positive number? [#permalink]
HarveyKlaus wrote:
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)
Senior Manager
Joined: 22 Aug 2020
Posts: 472
Own Kudos [?]: 353 [0]
Given Kudos: 30
Location: India
GPA: 4
WE:Project Management (Energy and Utilities)
Re: If x < 0, which of the following represents a positive number? [#permalink]
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.
Non-Human User
Joined: 09 Sep 2013
Posts: 33549
Own Kudos [?]: 837 [0]
Given Kudos: 0
Re: If x < 0, which of the following represents a positive number? [#permalink]
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 < 0, which of the following represents a positive number? [#permalink]
Moderator:
Math Expert
93707 posts