Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 22 May 2017, 09:31

### 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

# Events & Promotions

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

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 26 Jun 2012
Posts: 9
Followers: 1

Kudos [?]: 14 [0], given: 9

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

### Show Tags

03 Jul 2012, 23:30
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:33) correct 21% (01:08) wrong based on 43 sessions

### HideShow timer Statistics

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
Joined: 29 Mar 2012
Posts: 324
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 30

Kudos [?]: 439 [1] , given: 23

Re: Help clear concept [#permalink]

### Show Tags

03 Jul 2012, 23:59
1
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,
Math Expert
Joined: 02 Sep 2009
Posts: 38796
Followers: 7712

Kudos [?]: 105736 [1] , given: 11578

Re: Is x < 0 ? (1) -4x < 0 (2) -4x^2 < 0 [#permalink]

### Show Tags

04 Jul 2012, 01:32
1
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.

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.

_________________
Intern
Joined: 26 Jun 2012
Posts: 9
Followers: 1

Kudos [?]: 14 [0], given: 9

Re: Is x < 0 ? (1) -4x < 0 (2) -4x^2 < 0 [#permalink]

### Show Tags

04 Jul 2012, 01:55
Thanks Bunuel. I got it!
Re: Is x < 0 ? (1) -4x < 0 (2) -4x^2 < 0   [#permalink] 04 Jul 2012, 01:55
Similar topics Replies Last post
Similar
Topics:
If x is an integer, and 0 < x < 4, is x prime? 4 15 Dec 2015, 04:34
3 Is xy < 0 ? (1) 4|x| + 2|y| = 0 (2) 7|x| + 5|y| = 0 5 24 Mar 2016, 05:33
6 x+y)/Z>0 is x<0? (1) x<y (2) z<0 4 13 Jan 2016, 08:36
15 If x 0, is x^2/|x| < 1? 8 13 Mar 2016, 06:05
5 If x 0, is x^2 / |x| < 1? 12 09 Jun 2015, 23:13
Display posts from previous: Sort by

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

 new topic post reply 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®.