XAT 2011 — QA & DI Question 26
Answer the following question based on the information given below.
From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.
In the country of Twenty, there are exactly twenty cities, and there is exactly one direct road between any two cities. No two direct roads have an overlapping road segment. After the election dates are announced, candidates from their respective cities start visiting the other cities. Following are the rules that the election commission has laid down for the candidates:
- Each candidate must visit each of the other cities exactly once.
- Each candidate must use only the direct roads between two cities for going from one city to another.
- The candidate must return to his own city at the end of the campaign.
- No direct road between two cities would be used by more than one candidate.
The maximum possible number of candidates is
Answer & solution
- A
5
- B
6
- C
7
- D
8
9
There are 20 cities connected to each other by roads.
Hence there will be = 190 roads.
Let the maximum number of candidates be n.
Hence the number of roads used by these n candidates will be 20n
Now,
20n ≤ 190
∴ greatest n = 9
Hence, option (e).