TheCATExam
Sign in

CAT 1995 — QA Question 31

Solving Quadratic EquationsEasy
Passage / Data

Direction: Answer the questions based on the following information.
Four sisters — Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs.32.

Two positive integers differ by 4 and sum of their reciprocals is 1021. Then one of the numbers is

Answer & solution

  • 3

  • B

    1

  • C

    5

  • D

    21

Solution

Let one of the numbers be x. So the other number would be (x + 4).

According to the question, we have 1x+1(x+4)=21 or x = 3.

Hint:

​​​​​​​Please note that the sum of reciprocals is basically =(Sum of the int egers)(Product of the int egers). 

So we have to find two integers whose sum is 10 and whose product is 21.

So x + (x + 4) = 10 or x = 3.

Hence, option (a).

CAT 1995 QA Q31: Two positive integers differ by 4 and sum of their reciprocals is 10 21 . Then one of the numbers is — Solution | TheCATExam