Inequality

vipulgoyal wrote:Is n negative?
1. (1 – n^2) < 0
2. n^2 – n – 2 < 0

OAlater

1. (1-n)(1+n) < 0
Case 1: (1+n) < 0 and (1-n) > 0 => n < -1 and n < 1
Case 2: (1-n) < 0 and (1+n) > 0 => n > 1 and n > -1
Not sufficient.

2. n^2 - n -2 < 0
(n+1)(n-2) < 0
Case 1: (n+1) < 0 and (n-2) > 0 => n < -1 and n > 2 (not possible)
Case 2: (n-2) < 0 and (n+1) > 0 => -1 < n < 2
Not sufficient.

Combined:
1 < n < 2
So n is positive.

Choose C

Cheers

Q: Is n negative ? OR n < 0 ?

St1:
(1 - n²) < 0
n² > 1
|n| > 1

n > 1 or n < -1

n could be either negative or positive, thus INSUFFICIENT

St2:
n² - 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