Need for Speed – DI Set

Huey , Dewey and Louie are the three grandnephews of millionaire Scrooge McDuck. For their 18^th birthday, they want a sports car each. Being the stingy uncle that Scrooge is, he has asked them to solve a puzzle, the right answer to which would get them a car each. The puzzle is as follows:

I raced all the 25 cars that I have (C1, C2, C3…C25), 5 at a time, and the results were as shown in the table.

Assuming that you cannot use a stop watch to note down the finish time and can only race 5 cars at a time, answer the questions below, which are independent of each other.

Q)How many more races are required to identify the fastest Car?

a)0

b)1

c)2

d)4

Sol. b)1

A race between winners of all races, C1, C6, C11, C16 & C21 would determine the fastest car.

Q)Based on the data, how many more races are required to identify the three fastest Cars?

a) 2

b)3

c)4

d)5

Sol. a) 2

A race (race VI) between winners of all races, C1, C6, C11, C16 & C21 would determine the fastest car.

Let us suppose that C1 was the winner, C6 finished second and C11 finished third.

Now, we know that C1 is the fastest car. Since C16 and C21 are not among the fastest 3 cars, none of the other cars that participated in races IV and V could be in the fastest 3.

Since C1 came first and C6 came second race VI , the second fastest car would either be C2 or C6.

Similarly, the third fastest car can be one among C2, C3, C6, C7 & C16.

Thus if we race C2, C3, C6, C7 & C16 in the 7^th race, we can determine the top three fastest cars.

Q)Given that, in a race between the winners of all 5 races, C6 came first, C1 came second and C11 came third, which of the following cannot be the fastest three cars?

a)C1,C6,C11

b)C6,C2,C3

c)C6, C7, C1

d)C6, C1, C2

Sol. b) C6,C2,C3

Given that in the 6^th race, the result was C6 came first, C1 came second and C11 came third.

Now, if C6 came first, the second fastest car would be either C7 or C1.

The third fastest car would be one of C7, C1, C2, C8 or C11.

Thus,  since C3 cannot be among the top 3, option b is not possible.