Q42 / 125 · BITSAT 2012 · Mathematics

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

  • Correct answer
    A
    8
  • B
    6
  • C
    4
  • D
    16

Solution

$x y-12 x-12 y=0 \Rightarrow(x-12)(y-12)=144$ Now 144 can be factorised into two factors $x$ and $y$ where $x \leq y$ 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.

Hence, the correct answer is option: 'A'.

More Basic of Mathematics Questions