CAT 2025 Slot 2 · DILR · Question 13

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.

What BEST can be said about the total number of pings from all the tests undertaken?

  1. A

    12 or 13

  2. B

    13 or 14

  3. C

    12 or 13 or 14

  4. D

    At least 9

Pick an option, then check.
Answer & solution

Answer: Option A

Hoops in increasing size: H2 < H3 < H4 < H1, with B2 ≤ H2 < B4 ≤ H3 < B1 ≤ H4 < B5 ≤ H1 < B3.

B2 fits all four hoops: 4 pings.

B4 fails H2, fits H3, H4, H1: 3 pings.

B1 fits only H4 and H1: 2 pings.

B5 fits only H1: 1 ping.

B3 fits none: 0 pings.

B6 fails H2 and fits H4 and H1; whether it fits H3 is unknown: 2 or 3 pings.

Total = 4 + 3 + 2 + 1 + 0 + (2 or 3) = 12 or 13.

Shortcut: five balls are fixed at 4, 3, 2, 1 and 0 pings (sum 10); only B6 varies, between 2 and 3.

Hence, the answer is option 1.

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