If n is an integer, then n is divisible by how many positive integers?

Question

(1) n and 3^4 are divisible by the same number of positive numbers.
(2) n is the product of 2 and an odd prime number.

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av1901 · Answer

Given information: 'n' is an integer
To determine: Number of factors of 'n'
Pre-think: Number of factors of any number 'n' represented as  a^x b^y  (Where a & b are prime numbers) =  (x+1)(y+1)

(1) n and 3^4 are divisible by the same number of positive numbers.

Number of factors of  3^4 = (4+1) = 5 
=> 'n' also has 5 factors
SUFFICIENT

(2) n is the product of 2 and an odd prime number.

n = 2^1 * Odd^1 
=> Number of factors of 'n' =  (1+1)(1+1) = 4 
SUFFICIENT

Answer - D

p.s.  carcass  , Maybe there is a typo in the question? Because mostly the 2 statements in DS are consistent with the answer as in they give the same answer, but here, although each statement is sufficient, they are giving different answers.
Is something wrong in my thinking or do DS statements sometimes give different answers?
Your thoughts are also appreciated  Bunuel

Thanks

Carcass · Answer

No sir. No typo.

I agree, though. The question is not consistent. It should deliver to us or 4 or 5. However, the same value in both cases.

If n is an integer, then n is divisible by how many positive integers?

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