IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Logical Reasoning · Question 7

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.

As the moves are carried out, which one of the following never changes?
  1. A
    Whether the count of odd numbers is even or odd
  2. B
    The largest number on the board
  3. C
    How many different numbers appear on the board at once
  4. D
    The total of the numbers on the board
Pick an option, then check.
Answer & solution

Answer: Option A

Test each option against a single move, which replaces two numbers by their difference.

Take the count of odd numbers and check the three possible cases.

Two odd numbers: their difference is even, so two odds leave and none arrives — the count drops by 2 and its odd-or-even character is unchanged.

Two even numbers: their difference is even, so the count of odds does not move at all.

One odd and one even: their difference is odd, so one odd leaves and one odd arrives — again no change.

In every case the count of odd numbers keeps the same odd-or-even character, so option (1) never changes.

The largest number can fall, for example 20 and 19 leave 1, so (2) is wrong.

The board shrinks by one number each move and repeats appear, so (3) changes.

The total falls with almost every move, so (4) changes.

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