IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Logical Reasoning · Question 6

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 choiceMedium

Set 1: Rubbing out numbers on a board (Q10–Q13) — this question belongs to a set. Read the full set with all 4 questions →

Directions: Study the following information carefully and answer the questions that follow.

The numbers 1, 2, 3, and so on up to 20 are written on a board. A move is made as follows: choose any two of the numbers currently on the board, rub out both of them, and then write down one new number equal to the larger of the two minus the smaller.

Every move therefore leaves the board with one number fewer than before. Moves continue in this way until only a single number is left.

Suppose instead of 1 to 20 the numbers 1 to 21 are written on the board at the start, and the same moves are made until one number is left. Which one of the following could be the number finally left?
  1. A
    10
  2. B
    21
  3. C
    4
  4. D
    0
Pick an option, then check.
Answer & solution

Answer: Option B

The same rule applies: each move changes the total by an even amount, so the total keeps its odd-or-even character.

The starting total is now 1 + 2 + … + 21 = 231, which is odd.

So the number finally left must be odd, which rules out 10, 4 and 0.

That leaves 21, and 21 really is reachable.

Set 21 aside and work on 1 to 20 alone: pair them as (1, 2), (3, 4), … , (19, 20), and each pair leaves 1, giving ten 1s.

Pair those ten 1s to leave five 0s, then combine the 0s to leave a single 0.

Finally take 21 and 0, whose difference is 21.

So 21 is the only option that could be the number left.

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