NinetynineCAT 2024 Slot 3 DILR Set 3 Q9–Q13
A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2024 Slot 3, with 5 questions (Charts & Tables). Answers are CAT's official key.
The set
This set relies on a figure in the original paper, which is not reproduced here. The questions and answers are below.
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.
[Figure in the original paper]
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.
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.
[Figure in the original paper]
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 9
How many times the AC must have been turned off between 11:01 pm and 1:59 am?
- A1
- B2
- Ccannot be determined
- D0
Answer: (B) 2 Charts & Tables MCQ
Solution
- Read the graph: 38 (23:00), 32, 26 (0:00), 31 (0:30), 26 (1:00), 30 (1:30), 28 (2:00). Rises happen only with the AC off.
- Off from 0:00: inside rises 10 per hour, so outside at 0:00 \(= 26 + 10 = 36\). Off from 1:00: rises 8 per hour, so outside at 1:00 \(= 26 + 8 = 34\). Outside falls 2 degrees per hour.
- The temperature rises only in 0:00-0:30 and 1:00-1:30, so the AC was switched off at 0:00 and at 1:00: 2 times.
Question 10
What was the temperature outside, in degree Celsius, at 1 am?
TITA: type in the answer. There are no options and no negative marking.
Answer: 34 Charts & Tables TITA
Solution
- Read the graph: 38 (23:00), 32, 26 (0:00), 31 (0:30), 26 (1:00), 30 (1:30), 28 (2:00). Rises happen only with the AC off.
- Off from 0:00: inside rises 10 per hour, so outside at 0:00 \(= 26 + 10 = 36\). Off from 1:00: rises 8 per hour, so outside at 1:00 \(= 26 + 8 = 34\). Outside falls 2 degrees per hour.
- Outside at 1 am \(= 34\).
Question 11
What was the temperature outside, in degree Celsius, at 9 pm?
TITA: type in the answer. There are no options and no negative marking.
Answer: 42 Charts & Tables TITA
Solution
- Read the graph: 38 (23:00), 32, 26 (0:00), 31 (0:30), 26 (1:00), 30 (1:30), 28 (2:00). Rises happen only with the AC off.
- Off from 0:00: inside rises 10 per hour, so outside at 0:00 \(= 26 + 10 = 36\). Off from 1:00: rises 8 per hour, so outside at 1:00 \(= 26 + 8 = 34\). Outside falls 2 degrees per hour.
- Outside at 9 pm \(= 36 + 3 \times 2 = 42\).
Question 12
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?
- AMore than 3
- BExactly 2
- CEither 2 or 3
- DExactly 3
Answer: (D) Exactly 3 Charts & Tables MCQ
Solution
- Read the graph: 38 (23:00), 32, 26 (0:00), 31 (0:30), 26 (1:00), 30 (1:30), 28 (2:00). Rises happen only with the AC off.
- Off from 0:00: inside rises 10 per hour, so outside at 0:00 \(= 26 + 10 = 36\). Off from 1:00: rises 8 per hour, so outside at 1:00 \(= 26 + 8 = 34\). Outside falls 2 degrees per hour.
- AC is on 23:00-0:00, 0:30-1:00, 1:30-2:00 (2 hours). POWER must exceed 1 hour. A single REGULAR hour from 23:00 (38 to 26) would leave only 1 hour of POWER, so 23:00-0:00 must include a POWER half-hour, which needs a setting or mode change at 23:30 (POWER cannot take 38 to 26 at slope 12 per hour in one go).
- So changes: setting/mode change at 23:30, AC turned on at 0:30 and at 1:30. No other change is needed. Exactly 3.
Question 13
What was the maximum difference between temperature outside and inside temperature, in degree Celsius, between 11:01 pm and 1:59 am?
TITA: type in the answer. There are no options and no negative marking.
Answer: 10 Charts & Tables TITA
Solution
- Read the graph: 38 (23:00), 32, 26 (0:00), 31 (0:30), 26 (1:00), 30 (1:30), 28 (2:00). Rises happen only with the AC off.
- Off from 0:00: inside rises 10 per hour, so outside at 0:00 \(= 26 + 10 = 36\). Off from 1:00: rises 8 per hour, so outside at 1:00 \(= 26 + 8 = 34\). Outside falls 2 degrees per hour.
- Outside: 38 at 23:00, falling 2 per hour. Differences: 23:00 0, 0:00 \(36 - 26 = 10\), 0:30 \(35 - 31 = 4\), 1:00 \(34 - 26 = 8\), 1:30 \(33 - 30 = 3\), near 2:00 \(32 - 28 = 4\).
- Differences change linearly in between, so the maximum is 10 (at midnight).