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.
Question: 1
How many times the AC must have been turned off between 11:01 pm and 1:59 am?
From the given facts and the temperature graph, the AC must have been turned off twice: once when the temperature rose after the first POWER mode session and once more before switching it back on to adjust the temperature. This can be deduced from the pattern of the temperature increase and decrease, consistent with the switching on and off of the AC.
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Question: 2
What was the temperature outside, in degree Celsius, at 1 am?
The temperature outside at 1 am can be determined from the graph provided. By checking the corresponding time on the graph, we find the temperature to be 34°C.
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Question: 3
What was the temperature outside, in degree Celsius, at 9 pm?
The temperature outside at 9 pm can be estimated by referring to the graph. At 9 pm, the outside temperature is shown to be 42°C.
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Question: 4
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?
The AC must have been turned on or its settings altered three times during the given period: once when it was first switched on, again when the mode was changed, and possibly again before switching it off. These adjustments are consistent with the temperature graph patterns.
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Question: 5
What was the maximum difference between temperature outside and inside temperature, in degree Celsius, between 11:01 pm and 1:59 am?
From the graph, the maximum difference between the outside and inside temperatures occurs when the inside temperature is highest while the outside temperature is lowest. The maximum difference is found to be 10°C.
