IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Logical Reasoning · Question 10

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
A drawer holds 12 black socks, 10 blue socks and 8 grey socks, all mixed together. Socks are taken out one at a time in the dark. What is the least number of socks that must be taken out to be certain of holding at least two socks of each of the three colours?
  1. A
    24
  2. B
    28
  3. C
    30
  4. D
    26
Pick an option, then check.
Answer & solution

Answer: Option A

Think of the worst possible luck: the draw keeps avoiding a second sock of some colour for as long as it can.

The longest such run takes every sock of two colours and only one of the third.

Taking all 12 black and all 10 blue and 1 grey gives 23 socks, still without two grey.

The other combinations are shorter: all black and all grey and 1 blue is 21, and all blue and all grey and 1 black is 19.

So 23 socks can still leave a colour short, and the worst case is 23.

One more sock must then be grey, so 24 socks guarantee two of every colour.

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