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BITSAT 2012
Exam
BITSAT
Year
2012
Subject
Mathematics
Chapter
Basics of Mathematics

BITSAT 2012 · Mathematics · Basics of Mathematics

Let x and y be two natural numbers such that x y=12(x+y) and x ≤ y...

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

Options

  1. A8
  2. B6
  3. C4
  4. D16

Correct answer

A. 8

Step-by-step solution

xy−12x−12y=0⇒(x−12)(y−12)=144x y-12 x-12 y=0 \Rightarrow(x-12)(y-12)=144 Now 144 can be factorised into two factors xx and yy where x≤yx \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.
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