XAT 2011 — QA & DI Question 24
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.
One of the contending politicians, Mr. Chanaya, was quite proficient in calculations and could correctly figure out the exact position. He was the last person remaining in the circle. Sensing foul play the politicians decided to repeat the game. However, this time, instead of removing every alternate person, they agreed on removing every 300th person from the circle. All other rules were kept intact. Mr. Chanaya did some quick calculations and found that for a group of 542 people the right position to become a leader would be 437. What is the right position for the whole group of 545 as per the modified rule?
Answer & solution
- A
3
- B
194
249
- D
437
- E
543
Let f (n, k) represent the position of a winner when there are n people out of which every kth person is eliminated.
We have,
f (n, k) = (f (n – 1, k) + k)mod n
Now f (542, 300) = 437
Hence,
f (543, 300) = (437 + 300) mod 543 = 194
f (544, 300) = (194 + 300) mod 544 = 494
f (545, 300) = (494 + 300) mod 545 = 249
∴ A contender at 249th position will win the election.
Hence, option (c).