## Saturday, 19 November 2011

### Puzzle-23 (CAT-2008)

Directions for Questions 1 and 2:
Five horses, Red, White, Grey, Black and Spotted participated in a race. As per the rules of the race, the persons betting on the winning horse get four times the bet amount and those betting on the horse that came in second get thrice the bet amount. Moreover, the bet amount is returned to those betting on the horse that came in third, and the rest lose the bet amount. Raju bets Rs. 3000, Rs. 2000 Rs. 1000 on Red, White and Black horses respectively and ends up with no profit and no loss.
1. Which of the following cannot be true?
(1) At least two horses finished before Spotted
(2) Red finished last
(3) There were three horses between Black and Spotted
(4) There were three horses between White and Red
(5) Grey came in second

2.  Suppose, in addition, it is known that Grey came in fourth. Then which of the following cannot be true?
(1) Spotted came in first
(2) Red finished last
(3) White came in second
(4) Black came in second
(5) There was one horse between Black and White
Solution follows here:

Solution:
Raju bets Rs. 3000, Rs. 2000 Rs. 1000 on Red, White and Black horses respectively and ends up with no profit and no loss
The possibilities to suite this condition:

 Possibility Red White Black Gray Spotted 1 4 or 5 3 1 2 or 4 or 5 2 or 4 or 5 2 4 or 5 2 4 or 5 1 or 3 1 or 3 3 3 4 or 5 2 1 or 4 or 5 1 or 4 or 5

Q1) we check the answer options one by one:
(1)    At least two horses finished before Spotted
This may be true for all the three possibilities
(2)    Red finished last
This may be true for possibilities 1 and 2
(3)    There were three horses between Black and Spotted
This may be true for all the three possibilities
(4)    There were three horses between White and Red
This is not true for all possibilities
(5)    Grey came in second
This may be true for possibility-1

Q2) we check the answer options one by one:
In addition, it is known that Grey came in fourth. By applying this condition to the above table, possibility-2 is ruled out and the remaining two possibilities are depicted here:

 Possibility Red White Black Gray Spotted 1 5 3 1 4 2 3 3 5 2 4 1

(1)    Spotted came in first
This is true for possibility-3
(2)    Red finished last
This is true for possibility-1
(3)    White came in second
This is not true for all possibilities
(4)    Black came in second
This is true for possibility-3
(5)    There was one horse between Black and White
This is true for possibility-1