GMAT question - Is the positive integer x even? - Review

Is the positive integer x even?

1. x divided by 3 has a remainder of 1
2. x divided by 6 has a remainder of 1

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
4. EACH statement ALONE is sufficient
5. Statements (1) and (2) TOGETHER are NOT sufficient

Explanation

Is statement (1) sufficient

If x divided by 3 has a remainder of 1 then x could be odd or even.

For example x could be 4 (even) or 7 (odd) and it would have a remainder of 1 when divided by 3.

Therefore statement (1) is not sufficient to answer the question.

Is statement (2) sufficient?

If x divided by 6 has a remainder of 1 then x must be in the set {1, 7, 13, 19, 25...} and therefore x is odd.

If we know that x is odd then we can answer the question "is x even?" with no.

Therefore statement (2) is sufficient to answer the question.

Select an answer

Statement (1) is not sufficient and statement (2) is sufficient so the correct answer is B (2 only).