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07 Oct 2014, 14:51
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
70% (01:22) correct
30%
(01:19)
wrong
based on 257
sessions
History
Date
Time
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Not Attempted Yet
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
(1) -x = y
(2) n is a prime number
07 Oct 2014, 16:07
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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
\(\frac{x^n}{y^n}=(\frac{x}{y})^n\)
(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
General Discussion
07 Oct 2014, 14:56
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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?
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?
