goelmohit2002 wrote:
Thanks a lot Ian....actually I was stumped by one question that I came across.
How many positive factors does X has ?
1) X^2 has four positive factors.
2) 2X has three positive factors.
OA = A. Can you please tell how can it be A...here I think A can only be correct answer if X is non integer real number......
That cannot be a real GMAT question - where is it from? If a number has exactly four positive divisors, then its prime factorization must either be in the form p^3, or pq, where p and q are different primes. If x^2 is equal to either p^3 or pq, then x is not an integer. So, if Statement 1 is true, the question doesn't make any sense; does that make Statement 1 sufficient? Impossible to say; it's a meaningless question.
With Statement 2, if a number has three positive factors, its prime factorization must be in the form p^2, where p is prime. If we knew x was a positive integer (and in any real GMAT question about divisibility, you would be told this, since otherwise the question 'how many factors does x have?' is meaningless), then we would be certain that x = 2, and the Statement would be sufficient. If x doesn't need to be an integer - well, then again we're looking at a question that does not test divisibility in the way the GMAT does. There isn't anything to gain from studying this question.
