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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.

Figure for CAT 2025 2025 Slot 3 DILR question 7 (Data Interpretation)

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

Entered answer:

Solution

✅ Correct Answer: 2
Slide 1/6

The ten puzzles are attempted in one fixed sequence that is common to all four competitors, so puzzle nn is the same type (visual or number-based) for everyone.

Left chart (puzzles solved vs time): the instant a competitor's count steps up to nn is the time at which that competitor finished puzzle nn. These give the cumulative completion times.

Right chart (visual puzzles solved vs time): comparing how the visual count rises against how the total count rises identifies each puzzle as visual (VV) or number-based (NN).

The table records the type of each puzzle and each competitor's cumulative completion time (in minutes). From it we can read how many puzzles anyone had finished at any instant, and the time spent on a single puzzle as the gap between consecutive completion times.

PuzzleTypeAnirbidChandranathKoushikSuranjan
1
2
3
4
5
6
7
8
9
10
PuzzleTypeAnirbidChandranathKoushikSuranjan
12
24
36
48
510
612
714
816
919
1022

Koushik's completion times are read from the left chart.

His line steps up by one puzzle about every 22 minutes early on and slows near the end, reaching:

2, 4, 6, 8, 10, 12, 14, 16, 19, 222,\,4,\,6,\,8,\,10,\,12,\,14,\,16,\,19,\,22

His steady, clean steps make him the most reliable line to read first.

PuzzleTypeAnirbidChandranathKoushikSuranjan
1V2
2N4
3V6
4N8
5N10
6N12
7V14
8V16
9V19
10V22

The Type column is filled using the right chart for Koushik.

His visual-puzzle count at each completion instant is:

after P1: 11

after P2: 11

after P3: 22

after P4: 22

after P5: 22

after P6: 22

after P7: 33

after P8: 44

after P9: 55

after P10: 66


The visual count increases exactly at puzzles 1,3,7,8,9,101,3,7,8,9,10, so these are visual (VV).

It stays unchanged at puzzles 2,4,5,62,4,5,6, so these are number-based (NN).

This gives total visual =6=6 and total number-based =4=4. The other three competitors' charts reproduce the same pattern, confirming the common sequence.

PuzzleTypeAnirbidChandranathKoushikSuranjan
1V32
2N74
3V106
4N138
5N1810
6N2212
7V2414
8V2616
9V2819
10V3122

Anirbid's completion times are read from the left chart:

3, 7, 10, 13, 18, 22, 24, 26, 28, 313,\,7,\,10,\,13,\,18,\,22,\,24,\,26,\,28,\,31

He finishes last overall, with all ten done at minute 3131.

PuzzleTypeAnirbidChandranathKoushikSuranjan
1V342
2N774
3V10106
4N13138
5N181610
6N221912
7V242214
8V262416
9V282619
10V312822

Chandranath's completion times are read from the left chart:

4, 7, 10, 13, 16, 19, 22, 24, 26, 284,\,7,\,10,\,13,\,16,\,19,\,22,\,24,\,26,\,28

PuzzleTypeAnirbidChandranathKoushikSuranjan
1V3423
2N7746
3V1010610
4N1313813
5N18161016
6N22191220
7V24221422
8V26241624
9V28261926
10V31282229

Suranjan's completion times are read from the left chart:

3, 6, 10, 13, 16, 20, 22, 24, 26, 293,\,6,\,10,\,13,\,16,\,20,\,22,\,24,\,26,\,29


The table is now complete. Every type and completion time is fixed by the two charts, with no ambiguity.

The puzzle sequence is V,N,V,N,N,N,V,V,V,VV,N,V,N,N,N,V,V,V,V (visual at 1,3,7,8,9,101,3,7,8,9,10; number-based at 2,4,5,62,4,5,6).

Total times are Koushik 2222, Chandranath 2828, Suranjan 2929, Anirbid 3131, so Koushik is the winner.


From the sequence, visual puzzles occupy positions 1,3,7,8,9,101,3,7,8,9,10. Hence the third visual puzzle is puzzle 77.

Suranjan finished puzzle 66 at minute 2020 and puzzle 77 at minute 2222.

Time on the third visual puzzle =22−20=2=22-20=2 minutes.

Answer: 2.

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