What is the value of the positive integer n?

Question

GMAT CLUB'S FRESH QUESTION.

(1) 11 is a factor of n^2.
(2)  \sqrt{n}  is a prime number

M36-15

Hatakekakashi · Answer

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

GMATinsight · Answer

Question  : Value of x = ?

Statement 1 : 11 is a factor of n^2.

n may be 11 or 22 or 33 etc. hence
NOT SUFFICIENT

Statement 2 : \sqrt{n}  is a prime number

i.e. n is square if any prime number i.e. n may be 4, 9, 25, 121 etc

NOT SUFFICIENT

Combining the two statements

n is a perfect square of a prime number and also n is divisible by 11 hence

n must be the square of 11 only

SUFFICIENT

ANSWER: OPTION C

Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

Bunuel · Answer

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

What is the value of the positive integer n?

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