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CAT 2025Slot 3DILRQues & Sol

Data InterpretationMedium

Data Set

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.

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Question 1

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

Solution

Setup: This question requires reading the left staircase chart (total puzzles solved vs. time) at exactly t = 20 minutes for each of the four competitors and comparing their heights at that point.

Steps:

  1. The left chart is a step (staircase) graph where the height of each colored curve at any time t represents the cumulative number of puzzles solved by that competitor up to minute t. Draw a mental vertical line at t = 20 and read off the height for each curve.
  2. Reading the four staircase curves at t = 20: Koushik (green) sits at the highest step — approximately 6 puzzles solved. Chandranath (yellow) and Anirbid (red) are both at lower steps than Koushik at this time. Suranjan (blue) is at the lowest step among the four at t = 20.
  3. Since Koushik's staircase is at the highest level at t = 20, he has solved the greatest number of puzzles by the 20th minute.

Final Answer: Koushik

Question 2

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

Solution

Setup: To answer this, we must first identify WHICH puzzle number (1 through 10) is the third visual puzzle, and then use the left chart to find the time Suranjan (blue) spent on it. The key technique is cross-referencing both charts using Koushik (green), who provides the clearest data points.

Steps:

  1. From the right chart (visual puzzles solved vs. time), the maximum height reached by any competitor is 4, so there are exactly 4 visual puzzles in the competition (and 6 number-based puzzles).
  2. Cross-reference Koushik (green) across both charts to identify which puzzle numbers are visual:
    • Koushik solves his 1st visual puzzle at t = 2 min (right chart). At t = 2 on the left chart, he has solved 1 total puzzle → Puzzle 1 is visual.
    • Koushik solves his 2nd visual puzzle at t = 12 min. At t = 12 on the left chart, he has solved 4 total puzzles → Puzzle 4 is visual.
    • Koushik solves his 3rd visual puzzle at t = 25 min. At t = 25 on the left chart, he has solved 8 total puzzles → Puzzle 8 is visual.
    • Koushik solves his 4th visual puzzle at t = 29 min. At t = 29 on the left chart, he has solved 9 total puzzles → Puzzle 9 is visual.
  3. The third visual puzzle is Puzzle 8. Now find Suranjan's (blue) time for Puzzle 8 from the left chart: Suranjan completes 8 puzzles at t = 28 min and completes 7 puzzles at t = 26 min. Time taken = 28 − 26 = 2 minutes.

Final Answer: 2

Question 3

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

Solution

Setup: We need to first identify all visual puzzle positions (using cross-referencing of both charts via Koushik's data), then list number-based puzzle positions and find the 4th one in sequence.

Steps:

  1. From the right chart, there are 4 visual puzzles in total (maximum visual count = 4), meaning 6 puzzles are number-based.
  2. Cross-reference Koushik (green) across both charts to identify visual puzzle positions:
    • 1st visual puzzle completed at t = 2 min → total puzzles at t = 2 is 1 → Puzzle 1 is visual.
    • 2nd visual puzzle completed at t = 12 min → total puzzles at t = 12 is 4 → Puzzle 4 is visual.
    • 3rd visual puzzle completed at t = 25 min → total puzzles at t = 25 is 8 → Puzzle 8 is visual.
    • 4th visual puzzle completed at t = 29 min → total puzzles at t = 29 is 9 → Puzzle 9 is visual.
  3. Visual puzzles are at positions: 1, 4, 8, 9. Therefore, number-based puzzles are at positions: 2, 3, 5, 6, 7, 10. Listing them in order: 1st NB = Puzzle 2, 2nd NB = Puzzle 3, 3rd NB = Puzzle 5, 4th NB = Puzzle 6.

Final Answer: 6

Question 4

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

Solution

Setup: First establish which puzzles are number-based using the cross-referencing method (already derived: puzzles 2, 3, 5, 6, 7, 10). Then, read Anirbid's (red) staircase on the left chart to find the time he spent on each of those 6 puzzles, and compute the average.

Steps:

  1. Visual puzzles are at positions 1, 4, 8, 9 (derived by cross-referencing Koushik's data across both charts). Number-based puzzles are at positions: 2, 3, 5, 6, 7, 10.
  2. Read Anirbid's (red) left-chart staircase to find completion times for each puzzle. The time for any individual puzzle = (time he completes that puzzle) − (time he completed the previous puzzle):
    • Puzzle 2 (NB): completed at t = 9, previous puzzle (Puzzle 1) done at t = 4 → 9 − 4 = 5 min
    • Puzzle 3 (NB): completed at t = 11, Puzzle 2 done at t = 9 → 11 − 9 = 2 min
    • Puzzle 5 (NB): completed at t = 19, Puzzle 4 done at t = 14 → 19 − 14 = 5 min
    • Puzzle 6 (NB): completed at t = 22, Puzzle 5 done at t = 19 → 22 − 19 = 3 min
    • Puzzle 7 (NB): completed at t = 27, Puzzle 6 done at t = 22 → 27 − 22 = 5 min
    • Puzzle 10 (NB): completed at t = 37, Puzzle 9 done at t = 33 → 37 − 33 = 4 min
  3. Average = (5 + 2 + 5 + 3 + 5 + 4) / 6 = 24 / 6 = 4.0 minutes.

Final Answer: 4.0 minutes