Question

Is the positive integer \(n\) divisible by 6? Statement I: \(n\) is divisible by 3. Statement II: \(n\) is divisible by 4.

• A. Statement I alone is sufficient, but Statement II alone is not sufficient.
• B. Statement II alone is sufficient, but Statement I alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.

Hint:

Try plugging in two different concrete numbers that satisfy each statement separately and see if they give different yes/no answers to the divisibility-by-6 question.

Answer 1

The Correct Option is C

Divisibility by 6 needs divisibility by both 2 and 3. Statement I gives divisibility by 3 only (not necessarily by 2). Statement II gives divisibility by 4, hence by 2, but not necessarily by 3. Together, \(n\) is divisible by 3 and by 4, so by \(\text{lcm}(3,4)=12\), which is divisible by 6. Neither alone is enough; both together suffice. Correct option: Both statements together are sufficient, but neither statement alone is sufficient.