Please post in DS section.
Here we need to know the sign of x^n, to figure out whether the expression would be negative or not.
Should be C

-3x^n +ve?

stmt1,

x is -ve.

n is even.-3x^n is negative

n is odd.-3x^n is positive.

Insuff

stmt2,

n is odd.

x is positive.-3x^n is negative

x is negative.-3x^n is positive.

Insuff

Combining 1 and 2,

x is -ve and n is odd

x^n is negative.

(-3)*negative=positive

Suff

Pick C

if n is an integer, is -3x^n positive?
1. x is negative.
Let x = -1, n = 0
-3x^n = -3.. Negative
Let x = -1, n = 1
-3x^n = 9 .. Positive
INSUFF
2. n is odd.
Let n = 1, x = 1
-3x^n = -3.. Negative
Let n=1, x=-1
-3x^n=3.. Positive
INSUFF

Combining:
x<0
When x is less than 0, all odd powers of x are negative.
hence x^n <0
-3(negative) = always positive
HENCE SUFF

pick C

if n is an integer, is -3x^n positive?
1. x is negative.
2. n is odd.


1. x is negative.
n=1,then -3x^n will be positive
n=2,then -3x^n will be -ve

insuff


2. n is odd.
no idea abt sign of n
x can be +ve or -ve
insuff


combined
suff

C