CAT 2025 Slot 2 · DILR · Question 10

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 LevelType in the answer (TITA)Medium

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 was the total number of pings made by B1, B2, and B3?

Answer & solution

Answer: 6

A ping on a hoop means ball ≤ hoop; no ping means ball > hoop.

Fact 4: B2 ≤ H2, and every other ball > H2.

Fact 2: B4 ≤ H3 < B1.

Fact 1: B1 ≤ H4 < B5 (and B6 ≤ H4).

Fact 3: B5 ≤ H1 < B3.

Chaining: B2 ≤ H2 < B4 ≤ H3 < B1 ≤ H4 < B5 ≤ H1 < B3.

B3 is larger than H1, the largest hoop, so it makes 0 pings. B2 fits H2, the smallest hoop, so it pings all 4. B1 is larger than H2 and H3 but fits H4 and H1, so it makes 2 pings.

Total = 2 + 4 + 0 = 6.

Shortcut: B3 is the biggest ball (no pings) and B2 the smallest (four pings). B1 is blocked at H3 but passes H4, so only the two largest hoops.

Hence, the answer is 6.

CAT 2025 Slot 2 · DILR · Question 10

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