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Updated on: 06 Apr 2023, 06:19
Originally posted by ChandlerBong on 06 Apr 2023, 04:33.
Last edited by gmatophobia on 06 Apr 2023, 06:19, edited 1 time in total.
Last edited by gmatophobia on 06 Apr 2023, 06:19, edited 1 time in total.
Formatted the question
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
41% (02:20) correct
59%
(02:05)
wrong
based on 59
sessions
History
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Result
Not Attempted Yet
If p and q are distinct positive integers, is \(p^\frac{p}{q} * q^\frac{q}{p}\) an integer?
(A) p is a factor of q.
(B) p is a prime number.
(A) p is a factor of q.
(B) p is a prime number.
06 Apr 2023, 06:31
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ChandlerBong
Statement 1
(A) p is a factor of q.
Case 1: q = 2; p = 1
\(1^\frac{1}{2} * 2^\frac{2}{1}\)
\(1*4\) → Integer
Case 2: q = 6; p = 3
\(3^\frac{3}{6} * 6^\frac{6}{3}\)
\(\sqrt{3}*36\) → Not an Integer
Statement 1 alone is not sufficient. We can eliminate A and D.
Statement 2
(B) p is a prime number.
Case 1: q = 1; p = 2
\(2^\frac{2}{1} * 1^\frac{1}{2}\)
\(1*4\) → Integer
Case 2: q = 6; p = 3
\(3^\frac{3}{6} * 6^\frac{6}{3}\)
\(\sqrt{3}*36\) → Not an Integer
Statement 2 alone is not sufficient. We can eliminate B.
Combined
The statements combined give us the following
p is prime and p is a factor of q.
As p & q are distinct integers we can conclude that, \(\frac{p}{q}\) will always be a fraction less than 1 and \(\frac{q}{p}\) will be an integer greater than 1
\(\text{prime}^{({\text{fraction}})} * \text{integer}^{({\text{integer})}}\)
Hence, we can conclude that \(p^\frac{p}{q} * q^\frac{q}{p}\) will not be an integer.
The statements combined are sufficient.
Option C
13 Aug 2024, 13:43
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