Data Sufficiency

Hi nahid078,

This question can be solved by TESTing VALUES. We're told N is a POSITIVE INTEGER and the Y cannot be 0. We're asked for the value of (X^N)/(Y^N).

1) -X = Y

IF....
X = 1
Y = -1
N = 2
(1^2)/(-1^(2)) = 1

IF....
X = 1
Y = -1
N = 3
(1^3)/(-1^(3)) = -1
Fact 1 is INSUFFICIENT

2) N is a PRIME number

The same two TESTs that we used in Fact 1 also 'fit' Fact 2 and provide 2 different answers.
Fact 2 is INSUFFICIENT

Combined, we have two sets of values that fit BOTH Facts and provide 2 different answers.
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

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