CAT 2024 Slot 3 · DILR · Question 20

CAT 2024 Slot 3 previous year question on Reasoning Based DI, with the answer and a step-by-step solution.

Reasoning Based DIDATA INTERPRETATION -High LevelType in the answer (TITA)Medium

Set 5: Air-Conditioner and Room Temperature — this question belongs to a set. Read the full set with all 5 questions →

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.

What was the temperature outside, in degree Celsius, at 9 pm?

Answer & solution

Answer: 42

Solving the set

Step 1 – Read the graph and decide when the AC was on or off. A fall in inside temperature means the AC is cooling; a rise means it is off.

Interval	Inside temperature	Change	AC status	What it tells us
23:00–23:30	38 → 32	−6	On	Cooling
23:30–0:00	32 → 26	−6	On	Cooling
0:00–0:30	26 → 31	+5	Off (at 0:00)	Rises 10 per hour ⇒ outside at 0:00 = 26 + 10 = 36
0:30–1:00	31 → 26	−5	On (at 0:30)	Cooling
1:00–1:30	26 → 30	+4	Off (at 1:00)	Rises 8 per hour ⇒ outside at 1:00 = 26 + 8 = 34
1:30–2:00	30 → 28	−2	On (at 1:30)	Cooling

Step 2 – Outside temperature. When the AC is switched off, the inside temperature rises to the outside temperature (at the moment of switching off) in exactly 1 hour. From 0:00: 26 → 31 in 30 minutes, so the full hour would give 26 + 10 = 36 = outside at 0:00. From 1:00: 26 → 30 in 30 minutes, so outside at 1:00 = 26 + 8 = 34. The outside temperature falls at a constant rate: 2° per hour (1° per 30 minutes).

Time	21:00	22:00	23:00	23:30	0:00	0:30	1:00	1:30	2:00
Outside	42	40	38	37	36	35	34	33	32
Inside	—	—	38	32	26	31	26	30	28
Outside − Inside	—	—	0	5	10	4	8	3	4

Step 3 – Modes. In REGULAR mode the drop in 30 minutes is half the gap to the set temperature; in POWER mode the set temperature is reached in 30 minutes. The AC runs for 2 hours in total (23:00–0:00, 0:30–1:00, 1:30–2:00), and POWER must be used for more than 1 hour.

• If 23:00–0:00 were one REGULAR setting (38 → 26 in 1 hour), POWER could be at most 1 hour (the other two half-hours). Not allowed.

• A single POWER setting cannot produce the straight 38 → 26 line over a whole hour, because POWER reaches its set temperature in 30 minutes and then holds it.

• So the setting must be changed at 23:30 (for example, POWER to 32 at 23:00, then POWER to 26 at 23:30).

Time	Event	Counts as 'turned on or setting altered'?
23:00	AC turned on (outside the 11:01–1:59 window)	Not counted
23:30	Setting changed (needed to get enough POWER time)	Yes
0:00	AC turned off	No (switch-off)
0:30	AC turned on	Yes
1:00	AC turned off	No (switch-off)
1:30	AC turned on	Yes

This question

From Step 2, the outside temperature falls 2° per hour and is 36 °C at midnight. At 9 pm (3 hours earlier): 36 + 6 = 42 °C.

Hence, the answer is 42.

CAT 2024 Slot 3 · DILR · Question 20

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