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26 Feb 2018, 03:33
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C
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Difficulty:
15%
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Question Stats:
76% (01:17) correct
24%
(01:38)
wrong
based on 263
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GMAT CLUB'S FRESH QUESTION.
What is the value of the positive integer n?
(1) 11 is a factor of n^2.
(2) \(\sqrt{n}\) is a prime number
M36-15
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28 Sep 2021, 03:12
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Bunuel
Official Solution:
What is the value of the positive integer n?
(1) 11 is a factor of \(n^2\).
Exponentiation does not "produce" primes. So, if 11 is a factor of \(n^2\), then 11 must also be a factor of \(n\). Basically this question says that \(n\) is a multiple of 11. Not sufficient.
(2) \(\sqrt{n}\) is a prime number.
\(n=prime^2\). Also, clearly insufficient.
(1)+(2) \(n\) is a multiple of 11 and \(n=prime^2\), thus \(n=11^2=121.\) Sufficient.
Answer: C
General Discussion
26 Feb 2018, 04:07
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Bunuel
a) if 11 is a factor of n^2
n can be 11/21/1331
insufficient
b) \(\sqrt{n}\) is prime
there are many values of this i.e squares of all prime
insufficient
combining a and b
11 is a factor of n^2 and \(\sqrt{n}\) is prime means n is a square of prime
so n has to be 121
(C) imo
