CAT — Line Graphs
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The air-conditioner (AC) in a large room can be operated either in REGULAR mode or in POWER mode to reduce the temperature.
If the AC operates in REGULAR mode, then it brings down the temperature inside the room (called inside temperature) at a constant rate to the set temperature in 1 hour. If it operates in POWER mode, then this is achieved in 30 minutes.
If the AC is switched off, then the inside temperature rises at a constant rate so as to reach the temperature outside at the time of switching off in 1 hour.
The temperature outside has been falling at a constant rate from 7 pm onward until 3 am on a particular night. The following graph shows the inside temperature between 11 pm (23:00) and 2 am (2:00) that night.
The following facts are known about the AC operation that night.
• The AC was turned on for the first time that night at 11 pm (23:00).
• The AC setting was changed (including turning it on/off, and/or setting different temperatures) only at the beginning of the hour or at 30 minutes after the hour.
• The AC was used in POWER mode for longer duration than in REGULAR mode during this 3-hour period.
How many times the AC must have been turned off between 11:01 pm and 1:59 am?
1
0
2
Cannot be determined
2
Step 1:
At 00:00 hours, the AC is switched off. In the next 30 minutes, the room temperature increases by 5°C. If the AC had remained off for one full hour, the temperature would have reached 36°C. Therefore, the outside temperature at 00:00 hours must have been 36°C.
At 01:00 hours, the AC is again switched off. During the next 30 minutes, the room temperature rises by 4°C. Had the AC remained off for the entire hour, the temperature would have become 34°C. Hence, the outside temperature at 01:00 hours was 34°C.
Thus, the outside temperature falls by 2°C between 00:00 and 01:00 (from 36°C to 34°C).
Since the outside temperature decreases at a constant rate between 7:00 PM and 3:00 AM, it drops by 1°C every 30 minutes. Using this, the outside temperatures at the remaining time points can be determined.
As the Power mode was active for a longer duration than the Regular mode, the only feasible distributions over the four half-hour intervals are (3, 1) or (4, 0).
From the line graph, we obtain the following values:
- 23:00 — Inside: 38°C, Outside: 38°C, AC Status: On
- 23:30 — Inside: 32°C, Outside: 37°C
- 00:00 — Inside: 26°C, Outside: 36°C, AC Status: Off
- 00:30 — Inside: 31°C, Outside: 35°C, AC Status: On
- 01:00 — Inside: 26°C, Outside: 34°C, AC Status: Off
- 01:30 — Inside: 30°C, Outside: 33°C, AC Status: On
- 02:00 — Inside: 28°C, Outside: 32°C
The AC was turned off twice between 11:00 and 1:59.
What was the temperature outside, in degree Celsius, at 1 am?
Step 1:
At 00:00 hours, the AC is switched off. In the next 30 minutes, the room temperature increases by 5°C. If the AC had remained off for one full hour, the temperature would have reached 36°C. Therefore, the outside temperature at 00:00 hours must have been 36°C.
At 01:00 hours, the AC is again switched off. During the next 30 minutes, the room temperature rises by 4°C. Had the AC remained off for the entire hour, the temperature would have become 34°C. Hence, the outside temperature at 01:00 hours was 34°C.
Thus, the outside temperature falls by 2°C between 00:00 and 01:00 (from 36°C to 34°C).
Since the outside temperature decreases at a constant rate between 7:00 PM and 3:00 AM, it drops by 1°C every 30 minutes. Using this, the outside temperatures at the remaining time points can be determined.
As the Power mode was active for a longer duration than the Regular mode, the only feasible distributions over the four half-hour intervals are (3, 1) or (4, 0).
From the line graph, we obtain the following values:
- 23:00 — Inside: 38°C, Outside: 38°C, AC Status: On
- 23:30 — Inside: 32°C, Outside: 37°C
- 00:00 — Inside: 26°C, Outside: 36°C, AC Status: Off
- 00:30 — Inside: 31°C, Outside: 35°C, AC Status: On
- 01:00 — Inside: 26°C, Outside: 34°C, AC Status: Off
- 01:30 — Inside: 30°C, Outside: 33°C, AC Status: On
- 02:00 — Inside: 28°C, Outside: 32°C
The temperature outside at 1 am was 34°C.
What was the temperature outside, in degree Celsius, at 9 pm?
Step 1:
At 00:00 hours, the AC is switched off. In the next 30 minutes, the room temperature increases by 5°C. If the AC had remained off for one full hour, the temperature would have reached 36°C. Therefore, the outside temperature at 00:00 hours must have been 36°C.
At 01:00 hours, the AC is again switched off. During the next 30 minutes, the room temperature rises by 4°C. Had the AC remained off for the entire hour, the temperature would have become 34°C. Hence, the outside temperature at 01:00 hours was 34°C.
Thus, the outside temperature falls by 2°C between 00:00 and 01:00 (from 36°C to 34°C).
Since the outside temperature decreases at a constant rate between 7:00 PM and 3:00 AM, it drops by 1°C every 30 minutes. Using this, the outside temperatures at the remaining time points can be determined.
As the Power mode was active for a longer duration than the Regular mode, the only feasible distributions over the four half-hour intervals are (3, 1) or (4, 0).
From the line graph, we obtain the following values:
- 23:00 — Inside: 38°C, Outside: 38°C, AC Status: On
- 23:30 — Inside: 32°C, Outside: 37°C
- 00:00 — Inside: 26°C, Outside: 36°C, AC Status: Off
- 00:30 — Inside: 31°C, Outside: 35°C, AC Status: On
- 01:00 — Inside: 26°C, Outside: 34°C, AC Status: Off
- 01:30 — Inside: 30°C, Outside: 33°C, AC Status: On
- 02:00 — Inside: 28°C, Outside: 32°C
The temperature outside at 9 pm was 38 + 2 + 2 = 42°C.
What best can be concluded about the number of times the AC must have either been turned on or the AC temperature setting been altered between 11:01 pm and 1:59 am?
Exactly 3
Either 2 or 3
Exactly 2
More than 3
Exactly 3
Step 1:
At 00:00 hours, the AC is switched off. In the next 30 minutes, the room temperature increases by 5°C. If the AC had remained off for one full hour, the temperature would have reached 36°C. Therefore, the outside temperature at 00:00 hours must have been 36°C.
At 01:00 hours, the AC is again switched off. During the next 30 minutes, the room temperature rises by 4°C. Had the AC remained off for the entire hour, the temperature would have become 34°C. Hence, the outside temperature at 01:00 hours was 34°C.
Thus, the outside temperature falls by 2°C between 00:00 and 01:00 (from 36°C to 34°C).
Since the outside temperature decreases at a constant rate between 7:00 PM and 3:00 AM, it drops by 1°C every 30 minutes. Using this, the outside temperatures at the remaining time points can be determined.
As the Power mode was active for a longer duration than the Regular mode, the only feasible distributions over the four half-hour intervals are (3, 1) or (4, 0).
From the line graph, we obtain the following values:
- 23:00 — Inside: 38°C, Outside: 38°C, AC Status: On
- 23:30 — Inside: 32°C, Outside: 37°C
- 00:00 — Inside: 26°C, Outside: 36°C, AC Status: Off
- 00:30 — Inside: 31°C, Outside: 35°C, AC Status: On
- 01:00 — Inside: 26°C, Outside: 34°C, AC Status: Off
- 01:30 — Inside: 30°C, Outside: 33°C, AC Status: On
- 02:00 — Inside: 28°C, Outside: 32°C
The AC settings could be changed only at the half-hour marks.
From the given information, we know that the AC was switched on at 00:30 hours and 01:30 hours, accounting for two setting changes.
It is also given that the Power mode was used for a longer duration than the Regular mode.
This leaves the following possible scenarios:
Case 1:
- At 23:00, the AC was set to Power mode with a target temperature of 32°C.
- At 23:30, the mode was changed from Power to Regular.
Case 2:
- At 23:00, the AC was set to Power mode with a target temperature of 32°C.
- At 23:30, the AC continued in Power mode, but the target temperature was changed to 26°C.
Case 3:
- At 23:00, the AC was set to Regular mode with a target temperature of 26°C.
- At 23:30, the mode was switched to Power, while the target temperature remained at 26°C.
In each of the above cases, the AC settings were changed exactly three times.
What was the maximum difference between temperature outside and inside temperature, in degree Celsius, between 11:01 pm and 1:59 am?
Step 1:
At 00:00 hours, the AC is switched off. In the next 30 minutes, the room temperature increases by 5°C. If the AC had remained off for one full hour, the temperature would have reached 36°C. Therefore, the outside temperature at 00:00 hours must have been 36°C.
At 01:00 hours, the AC is again switched off. During the next 30 minutes, the room temperature rises by 4°C. Had the AC remained off for the entire hour, the temperature would have become 34°C. Hence, the outside temperature at 01:00 hours was 34°C.
Thus, the outside temperature falls by 2°C between 00:00 and 01:00 (from 36°C to 34°C).
Since the outside temperature decreases at a constant rate between 7:00 PM and 3:00 AM, it drops by 1°C every 30 minutes. Using this, the outside temperatures at the remaining time points can be determined.
As the Power mode was active for a longer duration than the Regular mode, the only feasible distributions over the four half-hour intervals are (3, 1) or (4, 0).
From the line graph, we obtain the following values:
- 23:00 — Inside: 38°C, Outside: 38°C, AC Status: On
- 23:30 — Inside: 32°C, Outside: 37°C
- 00:00 — Inside: 26°C, Outside: 36°C, AC Status: Off
- 00:30 — Inside: 31°C, Outside: 35°C, AC Status: On
- 01:00 — Inside: 26°C, Outside: 34°C, AC Status: Off
- 01:30 — Inside: 30°C, Outside: 33°C, AC Status: On
- 02:00 — Inside: 28°C, Outside: 32°C
The maximum difference between temperature outside and inside between 11:01 pm and 1:59 am is 10°C at 00:00 hours.
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.
Who had solved the largest number of puzzles by the 20-th minute from the start of the competition?
Koushik
Anirbid
Chandranath
Suranjan
Koushik
How many minutes did Suranjan take to solve the third visual puzzle in the competition?
At what number in the sequence was the fourth number-based puzzle?
Which of the following is the closest to the average time taken by Anirbid to solve the number-based puzzles in the competition?
4.0 minutes
3.8 minutes
2.5 minutes
3.3 minutes
4.0 minutes
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