TheCATExam
Sign in

CAT 1993 — QA Question 11

FactorsEasy

Suppose one wishes to find distinct positive integers x, y such that (x + y)/xy is also a positive integer. Identify the correct alternative.

Answer & solution

  • This is never possible.

  • B

    This is possible and the pair (x,y) satisfying the stated condition is unique.

  • C

    This is possible and there exist more than one but a finite number of ways of choosing the pair (x,y).

  • D

    This is possible and the pair (x,y) can be chosen in infinite ways.

Solution

It can be very easy to figure out that (x + y) will always be greater than xy, only if one of them is 1. For eg. If x = 1 and y =2, then (x + y) = 3 and xy = 2.

Hence, (x + y) > xy.

Other than this, for all other values of x & y, (x + y) will always be less than xy, and hence, the ratio of (x+y)xy<1, and hence, cannot be an integer. Also, even if one of the values is 1, (x+y)xy will never be an integer. 

Hence, option (a).

CAT 1993 QA Q11: Suppose one wishes to find distinct positive integers x, y such that (x + y)/xy is also a positive integer. Id — Solution | TheCATExam