Pigeonhole Principle with Orange Boxes

CAT 2001 Slot 1 · QA · Medium · Discrete Mathematics

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Of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges. The number of boxes containing the same number of oranges is at least:

  1. A.

    5

  2. B.

    103

  3. C.

    6

  4. D.

    Cannot be determined

Answer

C

Explanation

Number of possible orange counts per box = 144−120+1=25144 - 120 + 1 = 25. Total boxes = 128. By Pigeonhole Principle, ⌈128/25⌉=6\lceil 128 / 25 \rceil = 6. So at least 6 boxes contain the exact same number of oranges.

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