XAT 2011 — QA & DI Question 23
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.
Which position should a contender choose if he has to be the leader?
Answer & solution
- A
3
67
- C
195
- D
323
- E
451
Let, f(n)represent the position of winner when n persons are standing in a circle.
f (n) = 2l + 1
where, n = 2m + l and 0 ≤ l < 2m
Now, n = 545
∴ n = 512 + 33
∴ n = 29 + 33
l = 33
∴ f (545) = 2 × 33 + 1 = 67
Hence, option (b).