Comprehension
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 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: 1
Who had solved the largest number of puzzles by the 20th minute from the start of the competition?
Who had solved the largest number of puzzles by the 20th minute from the start of the competition?
Show Hint
When analyzing progress charts, focus on the values at specific time markers to answer questions about progress.
Updated On: Jul 2, 2026
- Suranjan
- Koushik
- Chandranath
- Anirbid
Show Solution
The Correct Option is B
Solution and Explanation
Approach: Rather than read all four heights, race only the front-runners. From the chart, Koushik and Suranjan are the two who get off to the fastest starts, so the winner at minute 20 is whichever of those two is ahead; the slower two cannot overtake.
Step 1: Eliminate the laggards. Anirbid and Chandranath are both still around the $5$-puzzle mark at $t=20$, so neither can be the leader.
Step 2: Compare the two fast starters at $t=20$. Suranjan stands at $6$ puzzles; Koushik stands at $7$. Koushik is the higher of the two.
Step 3: Conclude. The most puzzles solved by minute $20$ is $7$, by Koushik.
Final answer: Koushik.
Step 1: Eliminate the laggards. Anirbid and Chandranath are both still around the $5$-puzzle mark at $t=20$, so neither can be the leader.
Step 2: Compare the two fast starters at $t=20$. Suranjan stands at $6$ puzzles; Koushik stands at $7$. Koushik is the higher of the two.
Step 3: Conclude. The most puzzles solved by minute $20$ is $7$, by Koushik.
Final answer: Koushik.
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Question: 2
How many minutes did Suranjan take to solve the third visual puzzle in the competition?
How many minutes did Suranjan take to solve the third visual puzzle in the competition?
Show Hint
Carefully track the progress of each competitor on the chart to identify the exact time taken for solving each puzzle.
Updated On: Jul 4, 2026
Show Solution
Correct Answer: 2
Solution and Explanation
Step 1: On the "Visual puzzles" chart, trace Suranjan's (blue) line.
Step 2: It sits at level 2 from around \( t=18 \) minutes onward.
Step 3: It steps up to level 3 at approximately \( t=28 \) minutes — this is the third visual puzzle.
\[ \boxed{\approx 28 \text{ minutes}} \]
Step 2: It sits at level 2 from around \( t=18 \) minutes onward.
Step 3: It steps up to level 3 at approximately \( t=28 \) minutes — this is the third visual puzzle.
\[ \boxed{\approx 28 \text{ minutes}} \]
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Question: 3
At what number in the sequence was the fourth number-based puzzle?
At what number in the sequence was the fourth number-based puzzle?
Show Hint
Identifying the sequence of puzzle solving involves matching the puzzle number with the time it was solved in the chart.
Updated On: Jul 4, 2026
Show Solution
Correct Answer: 6
Solution and Explanation
Step 1: Match a competitor's visual-chart jumps to their all-puzzles chart jumps: visual puzzles occur at sequence positions 1, 4, 8, 9.
Step 2: The remaining positions — 2, 3, 5, 6, 7, 10 — are the six number-based puzzles, in that order.
Step 3: The fourth entry in this list is position 6.
\[ \boxed{6^{th} \text{ puzzle in the sequence}} \]
Step 2: The remaining positions — 2, 3, 5, 6, 7, 10 — are the six number-based puzzles, in that order.
Step 3: The fourth entry in this list is position 6.
\[ \boxed{6^{th} \text{ puzzle in the sequence}} \]
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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?
Which of the following is the closest to the average time taken by Anirbid to solve the number-based puzzles in the competition?
Show Hint
To calculate the average time, sum up the individual times and divide by the number of puzzles solved.
Updated On: Jul 2, 2026
- 2.5 minutes
- 3.8 minutes
- 3.3 minutes
- 4.0 minutes
Show Solution
The Correct Option is D
Solution and Explanation
Approach: Time Anirbid's number-based puzzles one by one from the left chart and average them \(-\) the brute-force read, useful as a cross-check on the subtraction method.
Step 1: Anirbid's finish times. His cumulative finishes land at about $4, 9, 11, 14, 19, 22, 27, 29, 33, 37$ minutes for puzzles $1$ to $10$.
Step 2: Pick out the number-based positions $2,3,5,6,7,10$ and take each puzzle's own duration (finish minus previous finish). 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: $37-33=4$.
Step 3: Average. $\dfrac{5+2+5+3+5+4}{6}=\dfrac{24}{6}=4.0$ minutes.
Final answer: 4.0 minutes.
Step 1: Anirbid's finish times. His cumulative finishes land at about $4, 9, 11, 14, 19, 22, 27, 29, 33, 37$ minutes for puzzles $1$ to $10$.
Step 2: Pick out the number-based positions $2,3,5,6,7,10$ and take each puzzle's own duration (finish minus previous finish). 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: $37-33=4$.
Step 3: Average. $\dfrac{5+2+5+3+5+4}{6}=\dfrac{24}{6}=4.0$ minutes.
Final answer: 4.0 minutes.
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