Pigeonhole Principle with Orange Boxes

CAT 2001 Slot 1 · Quantitative Ability · Medium · Discrete Mathematics

This is a medium Quantitative Ability question from the CAT 2001 Slot 1 paper. It tests Discrete Mathematics. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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 = 144120+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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