Data Sufficiency

pavand wrote:What is the GCF and LCM of x, x^2 + 1, 2x+3

a) 6 is a factor of x
b) 5 is not a factor of x

Where is this question from? There are a dozen things wrong with it. First, a real GMAT DS question will never ask for the value of two different quantities; it would ask for the GCD or for the LCM, but not for both. Second, the question should tell you that x is a positive integer. Third, if a DS question asks for the value of some quantity, you only have enough information if you can get one single *numerical* value for that quantity. Here, if x = 6, you'll clearly get a different LCM than when x = 6,000,000,006, so the answer is certainly E; you don't need to do any work. I'm sure that's not the answer the question designer intends, but it's a badly designed question.

I'd add that the GCD here must be 1. Assuming x is a positive integer, x^2 and x^2 + 1 are consecutive integers, so their GCD must be 1, so x^2 and x^2 + 1 share no proper divisors. It follows that x and x^2 + 1 must also share no proper divisors, and thus have a GCD of 1. But you can't get a value for the LCM here.