x^n - x^-n = 0

The domain of x here is R-{0}. now if x= 1, it satisfies the equation.
x= -1 also satisfies the equation so the first statement doesn give any single value. moreover if n is zero, then again the equation gets satisfied.

The second statement says n is not zero, then this gives us x=+/-1,

combining the above two will also not give us a single value which is either 1 or -1. so the ans is cant be determined.

I am assuming that the question is actually x^n-x^(-n)=0. Which can be further resolved to x^n - 1/(x^n) = 0 ==> x^(2n) - 1 = 0 ==> x^(2n) = 1.

Stmt 1: This statement is saying that x is an integer. Well, it can be any integer as long as n is 0 (remember o is an even integer). The above equation can be written as x^(2n) = x^0. Hence this statement is not sufficient.

Stmt 2: This statement says that n is not equal to 0. In this case, x can equal to 1 or -1. This statement is not sufficient.

Both the statements together will also not give us the value of x.

Hence, answer should be E

Vemuri, x can be -1 also, hence even in that case, it is not sufficient!

I am assuming the question is

x^n - x^( - n) = 0

Rephrase x^n = x^ (-n)
x^n = 1/ x^n

Stmt I
x is an integer

x=2 n=0
x=1 n=0

INSUFF

Stmt II

n is not 0

x=1 n=2
x= -1 n=2

INSUFF

Together:

x can still be 1 or -1

ISNUFF

Choose E

RockyRambo wrote:Vemuri, x can be -1 also, hence even in that case, it is not sufficient!

Thanks for correcting me

basically,

the q can be simplified as x^2n =1

for no fractional x which is possible.

but possible for +/- 1 hence E.

cramya wrote:I am assuming the question is

x^n - x^( - n) = 0

Rephrase x^n = x^ (-n)
x^n = 1/ x^n

Stmt I
x is an integer

x=2 n=0
x=1 n=0

INSUFF

Stmt II

n is not 0

x=1 n=2
x= -1 n=2

INSUFF

Together:

x can still be 1 or -1

ISNUFF

Choose E

Thanks everyone.OA is E.
And the question was properly written by you.