GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 02 Apr 2020, 21:36

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

Is –1 < a < 0 ? (1) a^3 > a​ (2) a^2 > a^3​

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

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
avatar
P
Joined: 27 Feb 2014
Posts: 330
Location: India
Concentration: General Management, International Business
GMAT 1: 570 Q49 V20
GPA: 3.97
WE: Engineering (Education)
Is –1 < a < 0 ? (1) a^3 > a​ (2) a^2 > a^3​  [#permalink]

Show Tags

New post Updated on: 15 Feb 2020, 00:54
1
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

37% (02:07) correct 63% (01:53) wrong based on 35 sessions

HideShow timer Statistics

Is –1 < a < 0 ?


(1) a^3 > a​

(2) a^2 > a^3​

_________________
When To Use Permutation?

https://youtu.be/oRyquKBDSH0

When To Use Combination?

https://youtu.be/OnqHOLkCqSE

Originally posted by kapil1 on 14 Feb 2020, 23:15.
Last edited by Bunuel on 15 Feb 2020, 00:54, edited 1 time in total.
Renamed the topic and edited the question.
Manager
Manager
avatar
B
Joined: 22 Sep 2014
Posts: 157
Location: United States (CA)
GMAT ToolKit User
Is –1 < a < 0 ? (1) a^3 > a​ (2) a^2 > a^3​  [#permalink]

Show Tags

New post 16 Feb 2020, 16:55
1)+2):

a^2 > a^3​ > a
For any positive number .. this can’t be true ...a^2 has to be the middle number (except when a=1,all equal)

So a must be negative

If a<-1 ..then a2>a>a^3 ...wrong

When -1<a<0... a^2 > a^3​ > a ....... perfect

Hence C

Posted from my mobile device
Senior Manager
Senior Manager
avatar
P
Joined: 27 Feb 2014
Posts: 330
Location: India
Concentration: General Management, International Business
GMAT 1: 570 Q49 V20
GPA: 3.97
WE: Engineering (Education)
Is –1 < a < 0 ? (1) a^3 > a​ (2) a^2 > a^3​  [#permalink]

Show Tags

New post 18 Feb 2020, 23:39
1
1) \(a^3\) > a​

Step 1:
Finding critical points \(a^3\) – a >0 -> a (\(a^2\)-1) >0 -> a (a+1)(a-1)>0​
Critical points are a = -1, 0 , 1​

Step 2: Validating the regions​ on the number line
i) -∞ to –1: when a=-2, inequlaity is invalid​
ii) -1 to 0; when a=-1/2, inequlaity is valid​
iii) 0 to –1; when a=½, it is invalid​
iv) 1 to ∞, when a =2, it is valid​

Step 3: Solution set is –1<a<0 and a>1
No concrete answer to the question

2) \(a^2\) > \(a^3\)​

Step 1:
Finding critical points
\(a^3 – a^2\) < 0​
\(a^2\) (a-1) <0​
Critical points are a = 0, 1​

Step 2:
Validating the regions​
-∞ to 0, when a=-1, valid ​
i) 0 to 1, when a = ½ , valid​
ii)1 to ∞, when a =2, invalid​

Step 3: Solution set -∞ <a<1
No concrete answer to the question​

Combining statements (1) and (2)​
Common solution set is –1<a<0
C is correct​
_________________
When To Use Permutation?

https://youtu.be/oRyquKBDSH0

When To Use Combination?

https://youtu.be/OnqHOLkCqSE
Intern
Intern
avatar
B
Joined: 02 Dec 2018
Posts: 17
Re: Is –1 < a < 0 ? (1) a^3 > a​ (2) a^2 > a^3​  [#permalink]

Show Tags

New post 19 Feb 2020, 07:57
kapil1 wrote:
Is –1 < a < 0 ?

The answer should be D. because using the two statements we are able to give a "Yes" or "No".

Based on statement 1, since the range asked in the question is a subset of valid range, answer is Yes.
Similarly in statement 2, the range asked is in the question(-1 to 0) is a subset of the valid range(-∞ to 1), answer is YES.
Thus, answer should be D



(1) a^3 > a​

(2) a^2 > a^3​
Senior Manager
Senior Manager
avatar
P
Joined: 27 Feb 2014
Posts: 330
Location: India
Concentration: General Management, International Business
GMAT 1: 570 Q49 V20
GPA: 3.97
WE: Engineering (Education)
Re: Is –1 < a < 0 ? (1) a^3 > a​ (2) a^2 > a^3​  [#permalink]

Show Tags

New post 19 Feb 2020, 19:21
shanks2020 wrote:
kapil1 wrote:
The answer should be D. because using the two statements we are able to give a "Yes" or "No".

Based on statement 1, since the range asked in the question is a subset of valid range, answer is Yes.
Similarly in statement 2, the range asked is in the question(-1 to 0) is a subset of the valid range(-∞ to 1), answer is YES.
Thus, answer should be D

shanks2020 Are you getting a definite answer (YES/NO) to the question stem from statement (1) and statement (2) alone?
Lets see:

(1) When a = -1/2, answer to the question stem is yes
when a = 2, answer to the question stem is no

Same reasoning is valid for statement (2) alone.
_________________
When To Use Permutation?

https://youtu.be/oRyquKBDSH0

When To Use Combination?

https://youtu.be/OnqHOLkCqSE
GMAT Club Bot
Re: Is –1 < a < 0 ? (1) a^3 > a​ (2) a^2 > a^3​   [#permalink] 19 Feb 2020, 19:21
Display posts from previous: Sort by

Is –1 < a < 0 ? (1) a^3 > a​ (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