On the GMAT, the question stem would make it clear that only DISTINCT prime factors of m should be considered.
The problem should read as follows:
vipulgoyal wrote:If m is divisible by 3, how many distinct prime factors does m have?
(1) m/3 is divisible by 3
(2) m/3 has two different prime factors
Statement 1: m/3 is divisible by 3
Case 1: m/3 = 3, implying that m=9.
In this case, m=3*3, with the result that m has 1 distinct prime factor.
Case 2: m/3 = 6, implying that m=18.
In this case, m=2*3*3, with the result that m has 2 distinct prime factors.
INSUFFICIENT.
Statement 2: m/3 has two different prime factors
Case 2: m/3 = 2*3, implying that m=2*3*3.
In this case, m has 2 distinct prime factors.
Case 3: m/3 = 2*5, implying that m=2*3*5
In this case, m has 3 distinct prime factors.
INSUFFICIENT.
Statements combined:
m/3 = (3^x)(p^y), where p is a prime number other than 3, and x and y are positive integers.
Since m = [ 3^(x+1) ](p^y), m has 2 distinct prime factors (3 and p).
SUFFICIENT.
The correct answer is
C.
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