How many different prime factors does x have?

Hi Harley1980,

If you're comfortable with the math 'rules' involved, you might be able to answer this question with a 'conceptual' approach. However, TESTing VALUES will help you to get the necessary PROOF of the correct answer.

We're asked for the number of DIFFERENT prime factors of X.

Fact 1: 5X^2 has 2 DIFFERENT prime factors

IF....
X = 2
5X^2 = 20, which has 2 different prime factors (2 and 5)
X = 2, so X has ONE prime factor

IF.....
X = 10
5X^2 = 500, which has 2 different prime factors (2 and 5)
X = 10, so X has TWO different prime factors
Fact 1 is INSUFFICIENT

Fact 2: X > 1

We already have all the work we need to deal with THIS Fact too. The two examples that we used for Fact 1 will 'fit' here....

IF....
X = 2
5X^2 = 20, which has 2 different prime factors (2 and 5)
X = 2, so X has ONE prime factor

IF.....
X = 10
5X^2 = 500, which has 2 different prime factors (2 and 5)
X = 10, so X has TWO different prime factors
Fact 2 is INSUFFICIENT

Combined, we have two different results that already 'fit' BOTH Facts (and provide different results: 1 YES and 1 NO)
Combined, INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich