IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Logical Reasoning · Question 3

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
Postage stamps are sold in only two denominations, 5 rupees and 8 rupees, and any number of each may be used. In the options below, what is the largest amount of postage that CANNOT be made up exactly using these two denominations?
  1. A
    27
  2. B
    35
  3. C
    31
  4. D
    23
Pick an option, then check.
Answer & solution

Answer: Option A

Check each option to see whether it can be formed as 5a + 8b with a and b whole numbers.

23 = 8 + 5 + 5 + 5, so 23 can be made.

31 = 8 + 8 + 5 + 5 + 5, so 31 can be made.

35 = 5 × 7, so 35 can be made.

27: the multiples of 8 below 27 are 0, 8, 16 and 24, leaving 27, 19, 11 and 3, and none of these is a multiple of 5. So 27 cannot be made.

27 is therefore the largest amount among the options that cannot be made.

This also matches the standard result for two coprime denominations a and b, where the largest unmakeable amount is ab − a − b = 40 − 5 − 8 = 27.

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