IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Logical Reasoning · Question 5

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.

Which one of the following CANNOT be the number finally left?

A
7
B
2
C
20
D
0

Pick an option, then check.

Answer & solution

Answer: Option A

Watch what a move does to the total of all the numbers on the board.

Two numbers a and b are replaced by their difference, so the total falls by a + b − |a − b|, which equals twice the smaller of the two.

That change is always even, so the total keeps the same odd-or-even character from start to finish.

The starting total is 1 + 2 + … + 20 = 210, which is even.

So the single number left at the end must be even.

Of the options, 7 is the only odd one, so 7 cannot be the final number.

IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Logical Reasoning · Question 5

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