Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 29 May 2015, 16:33

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is x < 0 ? (1) -4x < 0 (2) -4x^2 < 0

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Intern
Joined: 26 Jun 2012
Posts: 10
Followers: 1

Kudos [?]: 5 [0], given: 9

Is x < 0 ? (1) -4x < 0 (2) -4x^2 < 0 [#permalink]  03 Jul 2012, 22:30
00:00

Difficulty:

25% (medium)

Question Stats:

83% (01:26) correct 17% (00:59) wrong based on 35 sessions
Is x < 0 ?

(1) -4x < 0
(2) -4x^2 < 0

What I want to know is

1) -4x < 0 ; either 4 is negative or x is negative. Hence cant say if x <0.
But explanation for this is given that
dividing both sides by -4, we get x > 0. Hence we know that x > 0.
Can anyone please help me understand why -4x is not 4 * (-x)? and in case it is 4*(-x) then why cant x<0 ?

2) Is clear to me. Hence no questions
[Reveal] Spoiler: OA
Senior Manager
Joined: 28 Mar 2012
Posts: 287
Concentration: Entrepreneurship
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 17

Kudos [?]: 207 [1] , given: 23

Re: Help clear concept [#permalink]  03 Jul 2012, 22:59
1
This post received
KUDOS
jayoptimist wrote:
Q) Is x < 0 ?
1) -4x < 0
2) -4x^2 < 0

What I want to know is

1) -4x < 0 ; either 4 is negative or x is negative. Hence cant say if x <0.
But explanation for this is given that
dividing both sides by -4, we get x > 0. Hence we know that x > 0.
Can anyone please help me understand why -4x is not 4 * (-x)? and in case it is 4*(-x) then why cant x<0 ?

2) Is clear to me. Hence no questions

Hi,

-4x<0,
if x < 0, let say, x=-1, then (-4)(-1)>0
which contrary to the given inequality.

again, if x>0, let say, x=2, then (-4)(2)<0
Thus, we can say x>0

Let me know if you need any further clarification,

Regards,
_________________

My posts: Solving Inequalities, Solving Simultaneous equations, Divisibility Rules

My story: 640 What a blunder!

Vocabulary resource: EdPrep

Facebook page: fb.com/EdPrep

Math Expert
Joined: 02 Sep 2009
Posts: 27535
Followers: 4328

Kudos [?]: 42617 [1] , given: 6050

Re: Is x < 0 ? (1) -4x < 0 (2) -4x^2 < 0 [#permalink]  04 Jul 2012, 00:32
1
This post received
KUDOS
Expert's post
jayoptimist wrote:
Is x < 0 ?

(1) -4x < 0
(2) -4x^2 < 0

What I want to know is

1) -4x < 0 ; either 4 is negative or x is negative. Hence cant say if x <0.
But explanation for this is given that
dividing both sides by -4, we get x > 0. Hence we know that x > 0.
Can anyone please help me understand why -4x is not 4 * (-x)? and in case it is 4*(-x) then why cant x<0 ?

2) Is clear to me. Hence no questions

Is x < 0 ?

(1) -4x < 0. Divide both parts by -4 and flip the sign of the inequality since we are dividing by negative number: $$x>0$$. Sufficient. (Or just rewrite as $$4x>0$$, which also leads to $$x>0$$)

(2) -4x^2 < 0 --> $$x^2>0$$. This inequality holds true for positive as well as negative values of $$x$$. Not sufficient.

Answer: A.

As for your question: we CAN write $$-4x < 0$$ as $$4*(-x) < 0$$. Now, from $$4*(-x) < 0$$ we have that the product of the positive number 4 and $$-x$$ is negative, so $$-x$$ must be negative: $$-x<0$$ --> $$x>0$$.

Hope it's clear.

P.S. Please read and follow: rules-for-posting-please-read-this-before-posting-133935.html
_________________
Intern
Joined: 26 Jun 2012
Posts: 10
Followers: 1

Kudos [?]: 5 [0], given: 9

Re: Is x < 0 ? (1) -4x < 0 (2) -4x^2 < 0 [#permalink]  04 Jul 2012, 00:55
Thanks Bunuel. I got it!
Re: Is x < 0 ? (1) -4x < 0 (2) -4x^2 < 0   [#permalink] 04 Jul 2012, 00:55
Similar topics Replies Last post
Similar
Topics:
1 Is xy < 0 ? (1) 4|x| + 2|y| = 0 (2) 7|x| + 5|y| = 0 4 28 Apr 2013, 14:10
If x < 0, what is sqrt(-x|x|) ? 1) -x 2)-1 3) 1 4) x 5) 2 11 Sep 2006, 09:16
0<|x|-4x<5 = ? A. x<0 B. 0<x<1 C. 9 27 Jul 2006, 22:04
is x<0, then sqrt(-x * |x|) 1. -x 2. -1 3. 1 4. x 5. 5 05 May 2006, 22:02
if x<0 then sqrt(-x|x|) is 1. -x 2. -1 3. 1 4. x 5. 6 27 Jan 2006, 22:50
Display posts from previous: Sort by

# Is x < 0 ? (1) -4x < 0 (2) -4x^2 < 0

 Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO 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®.