nahid078 wrote:If n is a positive number

Solution:

We need to determine the value of (x^n)/(y^n). Since the exponents are the same, we can rewrite the expression as (x/y)^n.

Statement One Alone:

-x = y

Since -x = y and y ≠ 0, x/y = x/(-x) = -1. Therefore, to evaluate (x/y)^n is same as evaluating (-1)^n. However, since we don't know the value of n, we can't determine a unique value of (-1)^n.

If n is odd, (-1)^n = -1; however if n is even, (-1)^n = 1.

Statement one is not sufficient to answer the question. Eliminate choices A and D.

Statement Two Alone:

n is a prime number

Since we don't know either the value of x or y, we cannot determine the value of (x/y)^n.

Statement two is not sufficient to answer the question. Eliminate choice B.

Statements One and Two Together:

From statement one we know x/y = -1 and from statement two we know n is a prime number. Recall that in statement one, we have mentioned (-1)^n is either -1 or 1 depending whether n is odd or even, respectively. That is, if we know n is odd, then (-1)^n = -1 and if we know n is even, then (-1)^n = 1.

However, even we are given that n is a prime number, we can't determine whether n is odd or even. Recall that all prime numbers are odd except 2.

So if n = 2, then (-1)^2 = 1; however when n is 3, 5, 7, 11, etc., (-1)^n = -1

Statements one and two together are still not sufficient to answer the question.

Answer: E

We want (x/y)�.

S1:

-x = y, so

(x/y) => (x/-x) => -1

and (x/y)� becomes (-1)�. So if n is odd, the value is -1, and if n is even, the value is 1. Close, but NOT sufficient.

S2:

Useless by itself.

S1+S2:

if n = 2, we get 1, if n = 3, we get -1. Still NOT sufficient.