You could get at the same answer a little faster by thinking about what m could be IF it is not prime (because if it is prime, the answer is always 1):

Statement 1:
The smallest m could be if it is odd, not prime, and not divisible by 3 is 5*7 = 35.
Too Big. M must be prime.

Statement 2
The smallest m could be if it is odd, not prime, and not divisible by 5 is 3*7 = 21.
In range. M may or may not be prime.

Anurag@Gurome wrote:

prateek_guy2004 wrote:If m is a positive odd integer between 2 and 30, then m is divisible by how many different positive prime numbers?
(1) m is not divisible by 3.
(2) m is not divisible by 5.

Note that m is a odd integer between 2 and 30.

Statement 1: Possible values of m are 5, 7, 11, 13, 17, 19, 23, 25 and 29. All of them have only one unique prime factor. Hence, whatever is the value of m, m is divisible by only one prime number.

Sufficient

Statement 2: Possible values of m are 3, 7, 9, 11, 13, 17, 19, 21 etc. For m = 21, m is divisible by two different prime numbers, 3 and 7. But for m = 3, 7, 9 etc, m is divisible by only one prime number.

Not sufficient

The correct answer is A.

how come 23 and 25 have the same number of unique prime factors?
23=23*1
25=25*1
25=5*5

gmatboost wrote:You could get at the same answer a little faster by thinking about what m could be IF it is not prime (because if it is prime, the answer is always 1):

Statement 1:
The smallest m could be if it is odd, not prime, and not divisible by 3 is 5*7 = 35.
Too Big. M must be prime.

Statement 2
The smallest m could be if it is odd, not prime, and not divisible by 5 is 3*7 = 21.
In range. M may or may not be prime.

what about 25, is also prime number?

To reply to the last 2 comments:

23 has only one UNIQUE prime factor: 23 (1 is not prime)
25 has only one UNIQUE prime factor: 5 (it does not count twice, because it says UNIQUE/DIFFERENT)

You are right that 25 is odd, not prime, and not divisible by 3.
Similarly, for Statement 2, 9 is odd, not prime, and not divisible by 5.

What I should have said but did not say was that I was looking for numbers that had MORE THAN 1 different prime factors, which was what the question was really asking for.

It is true that M could be 25 in statement 1, but then, it is still only divisible by 1 prime number (5). I was looking to see if there were any numbers divisible by more than one.