IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Logical Reasoning · Question 8

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 that the numbers written on the board at the start are 3, 6, 9, and so on up to 60, that is the first twenty multiples of 3. The same moves as in the passage are then made until one number is left. Which one of the following CANNOT be the number finally left?

A
0
B
45
C
6
D
30

Pick an option, then check.

Answer & solution

Answer: Option B

Two things are preserved here, and both must hold for the final number.

First, every number on the board starts as a multiple of 3, and the difference of two multiples of 3 is again a multiple of 3. So the final number is a multiple of 3.

Second, the total keeps its odd-or-even character, as before. The starting total is 3 + 6 + … + 60 = 3 × 210 = 630, which is even, so the final number must be even.

Being both a multiple of 3 and even means the final number must be a multiple of 6.

Checking the options: 0, 6 and 30 are all multiples of 6, but 45 is odd.

So 45 cannot be the number finally left.

IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Logical Reasoning · Question 8

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