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

It is currently 22 May 2017, 09:31

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.

Close

Request Expert Reply

Confirm Cancel

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
Intern
avatar
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

New post 03 Jul 2012, 23:30
00:00
A
B
C
D
E

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
1 KUDOS received
Kellogg MMM ThreadMaster
User avatar
B
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

GMAT ToolKit User
Re: Help clear concept [#permalink]

Show Tags

New post 03 Jul 2012, 23:59
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,
Expert Post
1 KUDOS received
Math Expert
User avatar
P
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

New post 04 Jul 2012, 01:32
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
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
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

New post 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 Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic If x is an integer, and 0 < x < 4, is x prime? Bunuel 4 15 Dec 2015, 04:34
3 Experts publish their posts in the topic Is xy < 0 ? (1) 4|x| + 2|y| = 0 (2) 7|x| + 5|y| = 0 Rock750 5 24 Mar 2016, 05:33
6 Experts publish their posts in the topic x+y)/Z>0 is x<0? (1) x<y (2) z<0 Baten80 4 13 Jan 2016, 08:36
15 Experts publish their posts in the topic If x 0, is x^2/|x| < 1? msand 8 13 Mar 2016, 06:05
5 Experts publish their posts in the topic If x 0, is x^2 / |x| < 1? zaarathelab 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  


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.