Question

Let $a$, $b$, $c$, and $d$ be integers such that $a = 6b$, $a = 12c$, and $2b = 9d = 12e$. Then which of the following pairs contains a number that is not an integer?

• A. $\left(\frac{a}{27}, \frac{b}{e}\right)$
• B. $\left(\frac{a}{36}, \frac{c}{e}\right)$
• C. $\left(\frac{a}{12}, \frac{b}{18}\right)$
• D. $\left(\frac{a}{6}, \frac{c}{d}\right)$

Hint:

When working with ratios of integers, carefully examine each term to determine if it can simplify to an integer.

Answer 1

The Correct Option is A

From the given relations, we can deduce that: - $a = 6b$ - $a = 12c$ - $2b = 9d = 12e$ Checking each option, we find that $\frac{a}{27}$ and $\frac{b}{e}$ contain non-integer values, making option (1) the Correct Answer.