What is the value of the positive integer N? (1) N^2 has 3 positive

Question

What is the value of the positive integer N?

(1) N^2 has 3 positive factors

(2) N is a multiple of 3

stne · Answer

(1)  N^2  has  3   positive factors

Square of any prime always has  3  factors e.g.

2^2= 4 -> 1, 2, 4  
3 ^2=9 ->1,3,9  
etc.

Hence N can be  2,3  or any other prime.

Hence  INSUFF.

(2) N is a multiple of  3

N can be  3, 6, 9   etc.

INSUFF.

1+2

clearly N can only be  3

SUFF

Ans C

Hope it's clear.

lucasd14 · Answer

Statement 1 
N^2 has 3 positive factors: N has to be 2 or 3. Other value won't have 3 factors.
Not sufficient.

Statement 2 
N is divisible by 3. 
Not sufficient.

Statement 1 & 2 Combined 
Sufficient: N must be 3.

Harsha_VS · Answer

Number of factors for a number N that can be factored into prime factors and written as N = p^a *q^b*c^r..., is (a+1)*(b+1)*(c+1)..

Here, from 1) we know that number of factors for N^2 is 3. This leads to the inference that N is already a prime number as (a+1)*(b+1)... can result into 3 only when a is 2 and there are no other multiples.

Now, we know that N is a prime number, but it is insufficient to find particular N.

From 2) we know that N is a multiple of 3 
But this alone cannot give a particular N, as N = 3*x, x can be any integer.

Combining 1 & 2, we can associate N as 3. So, C.

divyaansh1337 · Answer

1 we know N^2 has 3 factors , it doesn't help much. NOT A or D
2 n multiple of 3 so could be 3,6 9 also doesn't help NOT B
using both we can say that N^2 using N = 6 = 36 which has 4 factors so N not equal to 6
for N=9 N^2=81 which has 3 factors 3,9 and 27 thus N=9 and Answer is C

TDTGiang · Answer

IMO, n^2 has 3 positive factors => n^2 is a perfect square of a prime number 
=> n can be 2, 3, 5, 7, 11 (not sufficient) 
n is a multiple of 3 => n can be 0, 3, 6, 9, 12, 15 .... (Not sufficient)

(1)+(2): n is a prime and is also a multiple of 3 => n = 3 (Sufficient) => C

What is the value of the positive integer N? (1) N^2 has 3 positive

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