GMATinsight wrote:Is the positive integer x an even number?

(1) If x is divided by 3, the remainder is 2.
(2) If x is divided by 5, the remainder is 2.

We need to determine whether x is an even number.

Statement One Alone:

If x is divided by 3, the remainder is 2.

Statement one alone is not sufficient to answer the question. For example, x could be 5, which is an odd number, or x could be 8, which is an even number.

Statement Two Alone:

If x is divided by 5, the remainder is 2.

Statement two alone is not sufficient to answer the question. For example, x could be 7, which is an odd number, or x could be 12, which is an even number.

Statements One and Two Together:

Using the statements together, we see that the first number that fulfills both statements is n = 2, which is an even number.

To determine the next value in the list, we can use the least common multiple of 3 and 5, which is 3 x 5 = 15. Thus, the next number that could be x is 2 + (5 x 3) = 17, which is an odd number. Thus, the two statements together are still not sufficient to answer the question.

Answer: E