Question

Let $x$ and $y$ be two natural numbers such that $xy = 12(x + y)$ and $x \le y$. Then the total number of pairs $(x, y)$ is

• A. 8
• B. 6
• C. 4
• D. 16

Answer 1

Answer: (A)

8

Answer 2

$xy - 12x - 12y = 0$ $\Rightarrow (x - 12) (y - 12) = 144$. Now $144$ can be factorised into two factors $x$ and $y$ where $x \le y$ and the factors are $(1, 144), (2, 72), (3, 48), (4, 36), (6, 24), (8, 18), (9, 16), (12, 12)$. Thus there are eight solutions.