It's a badly worded question. If this were a real GMAT question, it would say "What is the value of positive integer x?", and Statement 1 would say "x has exactly two positive factors." You won't need to worry about the factors of -2 on a real GMAT question (though -2 does have four factors, -2, -1, 1 and 2), nor will you need to worry about the negative factors of 2 (2 has two negative factors, -1 and -2).

If the word 'positive' is left out, the question in the original post doesn't make sense, mathematically. The only numbers with precisely two factors are 1 and -1 (both have the factors 1 and -1) if we permit negative factors. This contradicts Statement 2. Some prep books claim that 'factor' means 'positive divisor', which simply isn't true in mathematics, but at least on the GMAT, it doesn't matter, since you will never see a question dealing with negative factors.