CAT 2025 Slot 2 · DILR · Question 11

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 balls is NOT NECESSARILY true?

A
B4 < B5 < B3
B
B2 < B1 < B5
C
B1 < B6 < B3
D
B1 < B5 < B3

Pick an option, then check.

Answer & solution

Answer: Option C

The facts chain into B2 ≤ H2 < B4 ≤ H3 < B1 ≤ H4 < B5 ≤ H1 < B3.

B6 is placed only loosely: it pings H4 (B6 ≤ H4) and does not ping H2 (B6 > H2). It is never compared with H3, B4 or B1.

Options 1, 2 and 4 follow directly from the chain.

Option 3 needs B1 < B6. But B6 could be small enough to pass H3, making it smaller than B1. So it is not necessarily true.

Shortcut: find the ball the clues leave loose (B6, pinned only between H2 and H4). Any option that compares it with B1 or B4 cannot be forced.

Hence, the answer is option 3.

CAT 2025 Slot 2 · DILR · Question 11

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