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
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If n is a positive number
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Solution:nahid078 wrote:If n is a positive number
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
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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.
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.
