If x is a positive integer, what is the number of different positive

IMO C

Statement 1 alone insufficient

Statement 2 shows X prime
X can be 2 or 3
Hence Statement 2 not sufficient.

However, if Statement 1 + 2
X is prime different from 2 or 3.
Hence can determine number of positive factors.

If x is a positive integer, what is the number of different positive factors of 24x ?
(1) x is a two-digit number
(2) x^2 has 3 positive factors

Question: 24x =2^3 . 3 . x

statement 1: insufficient
statement 2: x^2 has 3 positive factors
We have to realize that here the questions is talking about factors and Not Prime Factors
This means that two of these 3 factors is 1 and the x^2 itself.
---> x must be a prime number because the square of prime is the only integer that has only 3 factors

24x = 2^3.3.P where P is any prime number
This is not sufficient because the answer is going to be different depending on wether P= 2 or 3 or some other P numbers

Statement 1 + Statement 2
Sufficient because now we now that the Prime number is different from 2 and 3, and now we can use the formulas for finding the number of
of factors of 2^3 . 3 . P = (3+1)(2)(2)

Answer C

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