Question

A, B and C are positive integers. Is their product an even number?
(I) A is an even number.
(II) The product of A and B is an even number and that of A and C is also an even number.

• 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.

Answer 1

The correct option is D Each statement alone is sufficient.

Since the product of any numbers is an even number if and only if at least one of them is an even number. Now,
(I) $\Rightarrow A$ is an even number $\Rightarrow$ Product of A, B, C is even.
(II) $\Rightarrow A\times B$ is an even number and $A\times C$ is also an even number.
$\Rightarrow$ at least one of them (A, B, C) is even.
$\Rightarrow$ their product is an even number.
$\therefore$ Each statement alone is sufficient to answer the question.