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Question

A boss decides to distribute Rs. 2000 between 2 employees. He knows X deserves more that Y, but does not know how much more. So he decides to arbitrarily break Rs. 2000 into two parts and give X the bigger part. What is the chance that X gets twice as much as Y or more?

CAT 2021

A
2/5
CORRECT ANSWER WRONG ANSWER
B
1/2
CORRECT ANSWER WRONG ANSWER
C
1/3
CORRECT ANSWER WRONG ANSWER
D
2/3
CORRECT ANSWER WRONG ANSWER
Solution

Correct option is

(D)

Explanatory Answer :

The bigger part could be any number from 1000 to 2000.

Now, if the bigger part is to be at least twice as much as the smaller part, we have

X ≥ 2Y or X ≥ 2(2000 – X)

Or X ≥ 4000/3

Given that X lies between 1000 and 2000, then the the probability that X lies between 4000/3 and 2000

This probability is equal to 2000−(4000/3)/2000−1000 = 2/3

Hence the answer is "2/3"