CAT 2025 Slot 2 · DILR · Question 12

CAT 2025 Slot 2 previous year question on Games and Tournaments, with the answer and a step-by-step solution.

Games and TournamentsLOGICAL REASONING - High LevelMultiple choiceMedium

Set 3: Balls and Hoops — this question belongs to a set. Read the full set with all 4 questions →

There are six spherical balls, B1, B2, B3, B4, B5, and B6, and four circular hoops H1, H2, H3, and H4.

Each ball was tested on each hoop once, by attempting to pass the ball through the hoop. If the diameter of a ball is not larger than the diameter of the hoop, the ball passes through the hoop and makes a “ping”. Any ball having a diameter larger than that of the hoop gets stuck on that hoop and does not make a ping.

The following additional information is known:

1. B1 and B6 each made a ping on H4, but B5 did not.

2. B4 made a ping on H3, but B1 did not.

3. All balls, except B3, made pings on H1.

4. None of the balls, except B2, made a ping on H2.

Which of the following statements about the relative sizes of the hoops is true?

  1. A

    H2 < H3 < H4 < H1

  2. B

    H1 < H3 < H4 < H2

  3. C

    H1 < H4 < H3 < H2

  4. D

    H2 < H4 < H3 < H1

Pick an option, then check.
Answer & solution

Answer: Option A

B4 pings H3 but not H2, so H2 < B4 ≤ H3, giving H2 < H3.

B1 pings H4 but not H3, so H3 < B1 ≤ H4, giving H3 < H4.

B5 pings H1 but not H4, so H4 < B5 ≤ H1, giving H4 < H1.

Together: H2 < H3 < H4 < H1.

Shortcut: each 'pings hoop X but not hoop Y' clue tells you Y < X. Three such clues order all four hoops.

Hence, the answer is option 1.

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