Numbers-10 (CAT-2004)

The total number of integer pairs (x,y) satisfying the equation x+y=xy is:

(1) 0      (2) 1     (3) 2       (4) none of these

For Answer Click on "Read more" below:

Solution:

x+y=xy => x(1-y) = -y => x = y/(y-1)

In order to x and y be integers, y should be divisible by (y-1) => two consecutive integers being non-co-prime, which is possible only when y = 0 (or) 2  

For y = 0, x = 0/(-1) = 0

 For y = 2, x = 2/1 = 2

(0,0) and (2,2) are the only possible pairs.

Answer (3)