IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Logical Reasoning · Question 11

IIM B UG (B.Sc-Hons.)- Sample Paper 2026 question on Quant Based Puzzles and Optimisation, with the answer and a step-by-step solution.

Quant Based Puzzles and OptimisationLOGICAL REASONING - High LevelMultiple choiceHard
One hundred people stand in a circle, numbered 1 to 100 clockwise. Starting with person 1, they count off round the circle and every second person leaves: person 2 goes first, then person 4, and so on. The counting continues round after round with those who remain, until one person remains. Which position is the survivor standing in?
  1. A
    61
  2. B
    73
  3. C
    65
  4. D
    69
Pick an option, then check.
Answer & solution

Answer: Option B

Start with the simple case. If the number of people is an exact power of 2, the first full round removes every even position and brings the count back to person 1, so person 1 survives.

For 100 people, write 100 as the largest power of 2 below it plus a remainder: 100 = 64 + 36.

Remove people until exactly 64 remain. That takes 36 removals, and those removals are the even positions 2, 4, 6, … , 72.

The next person to count is number 73, and 64 people are left.

Since 64 is a power of 2, whoever counts first at this point survives.

So the survivor is in position 73.

The same result comes from the standard formula: write n = 2ᵐ + L and the survivor is 2L + 1 = 2(36) + 1 = 73.

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