GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Sep 2018, 20:03

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

If x < 0, which of the following must be true?

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49303
If x < 0, which of the following must be true?  [#permalink]

Show Tags

New post 03 Dec 2014, 08:19
2
7
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

65% (01:01) correct 35% (00:54) wrong based on 503 sessions

HideShow timer Statistics

Tough and Tricky questions: Must or Could be True Questions.



If x < 0, which of the following must be true?

I. x^2 > 0
II. x − 2x > 0
III. x^3 + x^2 < 0

A) I only
B) I & II
C) II & III
D) All of the above
E) None of the above

Kudos for a correct solution.

Source: Chili Hot GMAT

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Manager
Manager
avatar
Joined: 12 Sep 2014
Posts: 157
Concentration: Strategy, Leadership
GMAT 1: 740 Q49 V41
GPA: 3.94
Re: If x < 0, which of the following must be true?  [#permalink]

Show Tags

New post 03 Dec 2014, 10:28
3
1
We're told that x is negative and that is all. Let's evaluate.

Since x is negative, x^2 is always positive (>0). True.
Since x is negative then x-2x>0. True as we're essentially adding a negative number to a larger (effectively positive number). For example, if x=-.5, then -0.5 + 1>0 or if x = -1, then -1+2>0.
However, the third doesn't have to be true. If x is a negative fraction, then x^2 is positive and larger than x^3. If x=-1/2, then x^3+x^2 = -1/8 + 1/4>0. However, if x=-1, then -1+1=0. Insufficient, not always true.

Choice B
Intern
Intern
avatar
Joined: 10 Mar 2014
Posts: 37
Concentration: General Management, Technology
GMAT 1: 650 Q47 V32
GPA: 4
Reviews Badge
Re: If x < 0, which of the following must be true?  [#permalink]

Show Tags

New post 03 Dec 2014, 20:35
1
I. x^2 > 0 -TRUE- Irrespective of x sign, it will always be positive because of even power and since x is less than 0 x^2 can't be 0.
II. x − 2x > 0 -TRUE- Since x<0 , -x will be positive
III. x^3 + x^2 < 0 -Can not say-
x^2(x+1)<0 , since x^2 will always be positive => x+1 < 0 => x < -1. But we know that x<0, so x could be -1/2 etc.

Answer is B.
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8288
Location: Pune, India
Re: If x < 0, which of the following must be true?  [#permalink]

Show Tags

New post 03 Dec 2014, 20:44
1
Bunuel wrote:

Tough and Tricky questions: Must or Could be True Questions.



If x < 0, which of the following must be true?

I. x^2 > 0
II. x − 2x > 0
III. x^3 + x^2 < 0

A) I only
B) I & II
C) II & III
D) All of the above
E) None of the above

Kudos for a correct solution.

Source: Chili Hot GMAT


Given: x is negative.
Which of the following must be true?

I. \(x^2 > 0\)
This is always true for real numbers except if x is 0. Since x is negative, this must be true.

II. \(x - 2x > 0\)
\(-x > 0\)
\(x < 0\) (multiplied both sides by -1). This is given so it must be true.

III. \(x^3 + x^2 < 0\)
\(x^2*(x + 1) < 0\)
x^2 is positive so for x^2 * (x+1) to be negative, x+1 should be negative i.e. x < -1. We know that x < 0 but it could very well lie between 0 and -1 and hence this needn't be true. It may or may not be.

So only (I) and (II) must be true.

Answer (B)
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1834
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If x < 0, which of the following must be true?  [#permalink]

Show Tags

New post 03 Dec 2014, 20:53
1
Answer = B) I & II

I. x^2 > 0

Square of any number is always positive. Always true

II. x - 2x > 0

-x > 0
x < 0 (This is the given condition in the problem, which has to be obviously true)

III. x^3 + x^2 < 0

\(For x = \frac{-1}{2}\)

\(\frac{1}{4} - \frac{1}{8} > 0\) (Not necessarily true)

Answer = B
_________________

Kindly press "+1 Kudos" to appreciate :)

Intern
Intern
User avatar
Joined: 08 Jul 2012
Posts: 49
Re: If x < 0, which of the following must be true?  [#permalink]

Show Tags

New post 04 Dec 2014, 00:04
1
Given: x < 0,

I. x^2 > 0 --> squaring is never negative --> so always true
II. x − 2x > 0 --> -x>0, since x is given as -ve no. so -ve of -ve no. is always +ve --> so always true
III. x^3 + x^2 < 0 -->x^2(x+1)<0 and given is x<0 so it can be -1, in that case (-1)^2(-1+1)<0 = 0<0 --> so not always true

Ans. B) I & II
_________________

Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time. - Thomas A. Edison

Senior Manager
Senior Manager
User avatar
B
Joined: 23 Feb 2015
Posts: 419
GMAT ToolKit User
Re: If x < 0, which of the following must be true?  [#permalink]

Show Tags

New post 21 Feb 2017, 13:03
Bunuel wrote:

Tough and Tricky questions: Must or Could be True Questions.



If x < 0, which of the following must be true?

I. x^2 > 0
II. x − 2x > 0
III. x^3 + x^2 < 0

A) I only
B) I & II
C) II & III
D) All of the above
E) None of the above

Kudos for a correct solution.

Source: Chili Hot GMAT


We can invalid III by putting the fraction value of x. So, the correct choice is B.
_________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”
― Henry Wadsworth Longfellow

SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2334
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: If x < 0, which of the following must be true?  [#permalink]

Show Tags

New post 21 Feb 2017, 22:54
Bunuel wrote:

Tough and Tricky questions: Must or Could be True Questions.



If x < 0, which of the following must be true?

I. x^2 > 0
II. x − 2x > 0
III. x^3 + x^2 < 0

A) I only
B) I & II
C) II & III
D) All of the above
E) None of the above

Kudos for a correct solution.

Source: Chili Hot GMAT


Given: x<0
I. x^2 > 0 Since x is Non-Zero so x^2 is bound to be Positive hence CORRECT

II. x − 2x > 0
i.e. -x > 0
i.e. x <0 hence CORRECT

III. x^3 + x^2 < 0
i.e. x^2(x+1) < 0
x^2 is always positive but (x+1) may or may not be negative for values of x less than or greater than -1 hence this is not always True


Answer: Option B
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Intern
Intern
avatar
B
Joined: 29 Jul 2018
Posts: 44
Concentration: Finance, Statistics
Re: If x < 0, which of the following must be true?  [#permalink]

Show Tags

New post 30 Aug 2018, 13:57
x^2> 0 always
x-2x>0
take x = -2
-2+4>0
take x = -1/2
-1/2 + 1>0
so second statement is true
x^3 + x^2<0
x = -2
-8 + 4<0 true
x = -1/2
-1/8 + 1/4<0 false


is my approach correct?
GMAT Club Bot
Re: If x < 0, which of the following must be true? &nbs [#permalink] 30 Aug 2018, 13:57
Display posts from previous: Sort by

If x < 0, which of the following must be true?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


Copyright

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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.