CAT 2025 Slot 3 · DILR · Set 3: Puzzle Solving Competition

The full set and all 4 questions (Q10–Q13) from CAT 2025 Slot 3, with answers and solutions.

Anirbid, Chandranath, Koushik, and Suranjan participated in a puzzle solving competition. The competition comprised 10 puzzles that had to be solved in the same sequence, i.e., a competitor got access to a puzzle as soon as they solved the previous puzzle. Some of the puzzles were visual puzzles and the others were number-based puzzles. The winner of the competition was the one who solved all puzzles in the least time.

The following charts describe their progress in the competition. The chart on the left shows the number of puzzles solved by each competitor at a given time (in minutes) after the start of the competition. The chart on the right shows the number of visual puzzles solved by each competitor at a given time (in minutes) after the start of the competition.

Question 10 · Mixed DI (Radar, Triangular, Stock etc)

Who had solved the largest number of puzzles by the 20-th minute from the start of the competition?

  1. A

    Chandranath

  2. B

    Koushik

  3. C

    Suranjan

  4. D

    Anirbid

Pick an option, then check.
Answer & solution

Answer: Option B

Read each line in the 'All puzzles' chart at time = 20.

Koushik (green) reaches 7 puzzles at minute 19.

Chandranath (yellow) and Anirbid (red) are at 5, and Suranjan (blue) is at 4.

So Koushik had solved the most by the 20th minute.

Shortcut: at minute 20 the green line is clearly highest; no other line has passed 5.

Hence, the answer is option 2.

Question 11 · Mixed DI (Radar, Triangular, Stock etc)

How many minutes did Suranjan take to solve the third visual puzzle in the competition?

Answer & solution

Answer: 2

First identify which puzzles are visual. Koushik's visual count rises at minutes 2, 12, 25 and 29, exactly when he solves puzzles 1, 4, 8 and 9. So the visual puzzles are 1, 4, 8 and 9, and the third visual puzzle is puzzle 8.

Suranjan (blue) solves puzzle 7 at minute 26 and puzzle 8 at minute 28. (His visual count rises to 3 at minute 28, confirming this.)

Time for puzzle 8 = 28 − 26 = 2 minutes.

Shortcut: match the jumps in the visual chart to the jumps in the all-puzzles chart to find the puzzle numbers, then read the time between consecutive steps.

Hence, the answer is 2.

Question 12 · Mixed DI (Radar, Triangular, Stock etc)

At what number in the sequence was the fourth number-based puzzle?

Answer & solution

Answer: 6

The visual puzzles are 1, 4, 8 and 9 (from matching the two charts). The number-based puzzles are therefore 2, 3, 5, 6, 7 and 10.

The fourth number-based puzzle is puzzle 6.

Shortcut: find the visual positions once; every other position is number-based.

Hence, the answer is 6.

Question 13 · Mixed DI (Radar, Triangular, Stock etc)

Which of the following is the closest to the average time taken by Anirbid to solve the number-based puzzles in the competition?

  1. A

    3.3 minutes

  2. B

    2.5 minutes

  3. C

    3.8 minutes

  4. D

    4.0 minutes

Pick an option, then check.
Answer & solution

Answer: Option D

Anirbid (red) solves puzzles 1 to 10 at minutes 4, 9, 11, 14, 19, 22, 27, 29, 33 and 37.

Number-based puzzles are 2, 3, 5, 6, 7 and 10. Their solving times:

Puzzle 2: 9 − 4 = 5; puzzle 3: 11 − 9 = 2; puzzle 5: 19 − 14 = 5; puzzle 6: 22 − 19 = 3; puzzle 7: 27 − 22 = 5; puzzle 10: 37 − 33 = 4.

Total = 24 minutes over 6 puzzles, so the average is 4.0 minutes.

Check against the visual chart: Anirbid's visual count rises at 4, 14, 29 and 33 – puzzles 1, 4, 8 and 9 – and these take 4 + 3 + 2 + 4 = 13 minutes; 13 + 24 = 37, his finishing time.

Shortcut: total time 37 minus time on visual puzzles 13 gives 24 minutes for 6 number-based puzzles.

Hence, the answer is option 4.

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