It is currently 19 Feb 2018, 19:45

### 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 a < 0 ? (1) a^3 < a^2 + 2a (2) a^2 > a^3

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

### Hide Tags

Director
Joined: 26 Oct 2016
Posts: 682
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GMAT 1: 770 Q51 V44
GPA: 4
WE: Education (Education)
Is a < 0 ? (1) a^3 < a^2 + 2a (2) a^2 > a^3 [#permalink]

### Show Tags

23 Feb 2017, 18:04
1
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

59% (01:52) correct 41% (01:32) wrong based on 34 sessions

### HideShow timer Statistics

Is a < 0 ?
(1) a^3 < a^2 + 2a
(2) a^2 > a^3
[Reveal] Spoiler: OA

_________________

Thanks & Regards,
Anaira Mitch

SVP
Joined: 11 Sep 2015
Posts: 2051
Is a < 0 ? (1) a^3 < a^2 + 2a (2) a^2 > a^3 [#permalink]

### Show Tags

23 Feb 2017, 18:40
2
KUDOS
Expert's post
Top Contributor
anairamitch1804 wrote:
Is a < 0 ?
(1) a³ < a² + 2a
(2) a² > a³

Target question: Is a < 0 ?

Statement 1: a³ < a² + 2a
Subtract a² and 2a from both sides to get: a³ - a² - 2a < 0
Factor: a(a² - a - 2) < 0
Factor more: a(a - 2)(a + 1) < 0
There are several values of a that satisfy this inequality. Here are two:
Case a: a = 0.5. In this case, a > 0
Case b: a = -10. In this case, a < 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: a² > a³
There are several values of a that satisfy this inequality. Here are two:
Case a: a = 0.5. In this case, a > 0
Case b: a = -10. In this case, a < 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several values of a that satisfy BOTH statements Here are two:
Case a: a = 0.5. In this case, a > 0
Case b: a = -10. In this case, a < 0
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Last edited by GMATPrepNow on 23 Feb 2017, 22:15, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 5655
Re: Is a < 0 ? (1) a^3 < a^2 + 2a (2) a^2 > a^3 [#permalink]

### Show Tags

23 Feb 2017, 18:48
1
KUDOS
Expert's post
Is a < 0 ?
(1) a^3 < a^2 + 2a
$$a^3-a^2-2a<0......a( a^2-a-2)<0......a(a-2)(a+1)<0$$
So a <-1 will give ans as YES..
a=0 or 1 will also be true and ans will be NO
Insufficient

(2) a^2 > a^3
a^2-a^3>0......$$a^2(1-a)>0$$..
So 1-a>0..a<1...
So a can be -1 or 0 or 0.5
Insuff..

Combined
Again a as 0, 0.5 or -3 etc still remains..
Insufficient

E
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

Intern
Joined: 11 Feb 2017
Posts: 2
Location: United States (GA)
Re: Is a < 0 ? (1) a^3 < a^2 + 2a (2) a^2 > a^3 [#permalink]

### Show Tags

23 Feb 2017, 19:57
Is a < 0?

Statement 1: a^3 < a^2 +2a --> a(a+1)(a-2) < 0 Therefore, if this equals zero, then a can be -1, 0, or 2.
Try a = 1, the expression is negative. We can fill in the number line with signs because signs will switch back and forth.
Therefore <----(-1)++++(0)-----(2)+++++>. Statement 1 is correct when a is less than -1 or between 0 and 2. Insufficient.

Statement 2: a^2 > a^3 --> a(a)(a-1) > 0 Therefore, if this equals zero, then a can be 0 or 1.
Try a = 2, the expression is positive. We can fill in the number line with signs because signs will switch back and forth.
Therefore <++++(0)------(1)+++++>. Statement 2 is correct when a is less than 0 or greater than 1. Insufficient.

Combined:
From statement 1, a can be less than -1 or between 0 and 2.
From statement 2, a can be less than 0 or greater than 1.
Therefore, a must be less than -1 or between 1 and 2.
Is a < 0? Yes and no. Insufficient.
Re: Is a < 0 ? (1) a^3 < a^2 + 2a (2) a^2 > a^3   [#permalink] 23 Feb 2017, 19:57
Display posts from previous: Sort by

# Is a < 0 ? (1) a^3 < a^2 + 2a (2) a^2 > a^3

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

 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®.