Is n negative?
1. (1  n^2) < 0
2. n^2  n  2 < 0
OAlater
Inequality
This topic has expert replies

 Master  Next Rank: 500 Posts
 Posts: 468
 Joined: 25 Jul 2011
 Thanked: 29 times
 Followed by:4 members
 ganeshrkamath
 Master  Next Rank: 500 Posts
 Posts: 283
 Joined: 23 Jun 2013
 Location: Bangalore, India
 Thanked: 97 times
 Followed by:26 members
 GMAT Score:750
1. (1n)(1+n) < 0vipulgoyal wrote:Is n negative?
1. (1  n^2) < 0
2. n^2  n  2 < 0
OAlater
Case 1: (1+n) < 0 and (1n) > 0 => n < 1 and n < 1
Case 2: (1n) < 0 and (1+n) > 0 => n > 1 and n > 1
Not sufficient.
2. n^2  n 2 < 0
(n+1)(n2) < 0
Case 1: (n+1) < 0 and (n2) > 0 => n < 1 and n > 2 (not possible)
Case 2: (n2) < 0 and (n+1) > 0 => 1 < n < 2
Not sufficient.
Combined:
1 < n < 2
So n is positive.
Choose C
Cheers
Every job is a selfportrait of the person who did it. Autograph your work with excellence.
Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/firstattemp ... tml#688494
Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/firstattemp ... tml#688494

 Master  Next Rank: 500 Posts
 Posts: 269
 Joined: 19 Sep 2013
 Thanked: 94 times
 Followed by:7 members
Q: Is n negative ? OR n < 0 ?
St1:
(1  nÂ²) < 0
nÂ² > 1
n > 1
n > 1 or n < 1
n could be either negative or positive, thus INSUFFICIENT
St2:
nÂ²  n  2 < 0
(n + 1)(n  2) < 0
Case1: (n + 1) < 0 & (n  2) > 0
OR
Case2: (n + 1) > 0 & (n  2) < 0
Case1: n < 1 & n > 2 (This is not possible as a number cannot be greater than 2 and less than 1 at the same time; this case is Invalid)
Case2: n > 1 & n < 2
1 < n < 2 is the only valid case.
1 < n < 2 but n could be either positive or negative, thus INSUFFICIENT
St1+St2:
Combined we know that n has to fall between 1 and 2 and thus is positive, SUFFICIENT
Answer C
St1:
(1  nÂ²) < 0
nÂ² > 1
n > 1
n > 1 or n < 1
n could be either negative or positive, thus INSUFFICIENT
St2:
nÂ²  n  2 < 0
(n + 1)(n  2) < 0
Case1: (n + 1) < 0 & (n  2) > 0
OR
Case2: (n + 1) > 0 & (n  2) < 0
Case1: n < 1 & n > 2 (This is not possible as a number cannot be greater than 2 and less than 1 at the same time; this case is Invalid)
Case2: n > 1 & n < 2
1 < n < 2 is the only valid case.
1 < n < 2 but n could be either positive or negative, thus INSUFFICIENT
St1+St2:
Combined we know that n has to fall between 1 and 2 and thus is positive, SUFFICIENT
Answer C