If x, y, and z are positive integers such that x is less than y and y is less than z, is x a factor of the odd integer z?

(1) x and y are prime numbers, whose sum is a factor of 57
(2) z is a factor of 57


(1) states x+y is a factor of 57.The factors of 57 are 1,3 and 19. Since x and y are positive integers and both are prime, x+y cannot be 1, 3 because if its 1 or 3, one of x or y has to be 0 or 1 which is not a prime number.Thus x+y must be 19. Number 2 cannot be the factor of z as z is an odd number.Now x cannot be 17 as it is less than y, still even if it is, it does not tell us whether it is a factor of z or not.Thus option 1 is insufficient to answer the ques.

(2) states z is a factor of 57. Thus z is either 3 or 19. Since x is less than z, and z has factors z itself and 1, so x cannot be the factor of z, but if x = 1 it can be the factor of z, thus statement 2 alone is not sufficient to answer the question.

Now combine both 1 and 2.In this case numbers x and y are 2 and 17 as x is less than y and both x and y are prime numbers, now according to option 2, z is either 1,3, 19 or 57.

Nowhere it is stated that x+y=z, since z is greater than y it can be either 19 or 57, in both the cases x is not the factor of z.

Thus (1) and (2) together are sufficient to answer the question.

Hence answer is C.

Note:- You will notice that 1 and the number itself are always factors of a given number.

Mohit Gupta, one of the Gmat aspirants corrected the above explanation so correct answer is A.

But no where it has been told that X has to be odd number or cannot be even number. As X has to be a PRIME NUMBER, we can assume it to be 2. So X can be 2 and Y can be 17 and thus statement 1 if true, proves that X is not the factor of Z.Now Statement 2 in itself is not sufficient as it tells us about the possible values of Z which can be 1, 3, 19, 57 but does not tell us about the possible values of X and Y.So answer should be A.

Answer is A.