Question

If the positive integer $x$ is a multiple of $4$ and the positive integer $y$ is a multiple of $6$, then $xy$ must be a multiple of which of the following?
I. $8$
II. $12$
III. $18$

• A. II only
• B. I and II only
• C. I and III only
• D. II and III only
• E. I, II and III

Answer 1

Answer: (B)

I and II only

The product $xy$ must be a multiple of $4\left(6\right)=24$ and any of its factors. Test each alternative.

I. $\frac{24}{8}=38$ is a factor of $24$ MUST be a multiple of $8$

II. $\frac{24}{12}=212$ is a factor of $24$ MUST be a multiple of $12$

III. $\frac{24}{18}=1\frac{1}{3}18$ is NOT a factor of $24$ NEED NOT be a multiple of $18$

The correct answer is B.