If n is a positive integer and y ≠ 0, what is the value of

Question

If n is a positive integer and y ≠ 0, what is the value of  \frac{x^n}{y^n}

(1) -x = y

(2) n is a prime number

mvictor · Answer

my question is, why it is not A but E?

this is how I thought:

-x = y

we can rewrite 
 \frac{x^n}{y^n} 
or -1*( \frac{x^n}{x^n} )
according to PEMDAS, we have Exponents before division, therefore  \frac{x^n}{y^n}  = 1, and since we multiply with -1 then the answer is -1.

I know that  \frac{x^n}{y^n}  = ( \frac{x}{y})^n 
and in this case, the result depends solely on whether n is odd or even.
but why my method is not a good one to use? maybe someone can explain?

Bunuel · Answer

If n is a positive integer and y ≠ 0, what is the value of \(\frac{x^n}{y^n}\)

\(\frac{x^n}{y^n}=(\frac{x}{y})^n\)

(1) -x = y --> x/y = -1. So, the question asks to find the value of \((-1)^n\). If n is even the result will be 1 but of n is odd the result will be -1. Not sufficient.

(2) n is a prime number. Not sufficient.

(1)+(2) n still can be even (2) or odd (3, 5, 7, ...). Not sufficient.

Answer: E,

P.S. Operations involving the same exponents:
Keep the exponent, multiply or divide the bases
\(a^n*b^n=(ab)^n\)

\(\frac{a^n}{b^n}=(\frac{a}{b})^n\)

Theory on Exponents: math-number-theory-88376.html
Tips: exponents-and-roots-on-the-gmat-tips-and-hints-174993.html

All DS Exponents questions to practice: search.php?search_id=tag&tag_id=39
All PS Exponents questions to practice: search.php?search_id=tag&tag_id=60

Tough and tricky DS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125967.html
Tough and tricky PS exponents and roots questions with detailed solutions: tough-and-tricky-exponents-and-roots-questions-125956.html

sanket1991 · Answer

remember, remember 2 is a prime number :wink:

veergmat · Answer

1) x^n/y^n, If x=-y
 then, x^n/y^n = (-1)^n ................. two possible answers depending upon whether n is odd or even.

2) n is prime ................... Insufficient.

Combining 1 & 2 also not helps because 2 is even prime and others are odd primes so insufficient data

EMPOWERgmatRichC · Answer

Hi All,

This DS question can be solved by TESTing Values:

We're told that N is a POSITIVE INTEGER and Y cannot be 0. We're asked for the value of (X^N)/(Y^N)

Fact 1: -X = Y

This tells us that X and Y will be OPPOSITE values

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

X = -2
Y = 2
N = 2
(-2)^2/(2)^2 = 4/4 = 1
Fact 1 is INSUFFICIENT

Fact 2: N is prime

This tells us nothing about the values of X and Y.
Fact 2 is INSUFFICIENT

Combined, we know that...
X and Y are OPPOSITE values
N is a prime

IF...
X = -2
Y = 2
N = 2
(-2)^2/(2)^2 = 4/4 = 1

X = -2
Y = 2
N = 3
(-2)^3/(2)^3 = -8/8 = -1
Combined, INSUFFICIENT

Final Answer:  E

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

lalania1 · Answer

stmt1 is interesting. i found a way to conclude that stmt1 is not sufficient. see attachment.

(-1)^n  = where the result depends on whether n is even or odd.

stmt2 is not sufficient because it can be any prime number: 2,3,5,7,11...

combined is not sufficient because 2(even) and 3(odd) give me different solutions.

bumpbot · Answer

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If n is a positive integer and y ≠ 0, what is the value of

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