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CAT 2024 Slot 3 DILR · Set 4 of 5Data InterpretationModerate DifficultyQ14–Q18 · 2 MCQ + 3 TITA

CAT 2024 Slot 3 DILR Set 4: Bar Graphs (5 Questions) with Solutions

The Bar Graphs set from the official CAT 2024 Slot 3 DILR paper: the caselet, all 5 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2024 Slot 3 DILR · Questions 14–18
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 11pm(23:00)11 \mathrm{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 3030 minutes after the hour.
The AC was used in POWER mode for longer duration than in REGULAR mode during this3-hour period.
Official Reference Chart - CAT 2024 Slot 3 Official Reference Chart - CAT 2024 Slot 3

In the exam this set competed with 4 others for 40 minutes. Budget about 8 minutes if you attempt it.

Q14. Bar Graphs

MCQ · +3 / −1
How many times the AC must have been turned off between 11:01 pm and 1:59 am?
  1. A) 0
  2. B) 2
  3. C) 1
  4. D) cannot be determined
Correct Answer
B) 2
Step-by-step solution
📌 Core Concept
The inside temperature rises only when the AC is off, so each rising segment of the graph marks a switch-off.
🔢 Step-by-Step Solution
1
From 23:00 to 00:00 the line falls steadily from 38 to 26, so the AC is running and cooling.
2
From 00:00 to 00:30 the line rises from 26 to 31. The temperature can only rise if the AC is off, so it was switched off at 00:00 (it had just reached the set temperature of 26).
3
From 00:30 to 01:00 the line falls from 31 to 26, so the AC was turned on again at 00:30.
4
From 01:00 to 01:30 the line rises from 26 to 30, so the AC was switched off a second time at 01:00.
5
From 01:30 to 02:00 the line falls from 30 to 28, so the AC was on again from 01:30. No further switch-off is needed before 1:59.
6
Switch-offs: at 00:00 and at 01:00, which makes 2.
Why Not the Others
0 and 1: the graph has two separate rising segments, and each needs its own switch-off.
Cannot be determined: both rises are visible directly, so the count is fixed.
Correct Answer: B

Q15. Bar Graphs

TITA · +3 / 0
What was the temperature outside, in degree Celsius, at 1 am?
Correct Answer
34
Step-by-step solution
📌 Core Concept
When the AC is off, the inside temperature rises at a constant rate so as to reach the outside temperature in 1 hour. So the rise per hour equals the gap between outside and inside at the moment of switch-off.
🔢 Step-by-Step Solution
1
From 01:00 to 01:30 the AC is off and the inside temperature rises from 26 to 30, a rise of 4 in 30 minutes.
2
That is 8 per hour. The inside temperature would reach the outside temperature in 1 hour, so the outside temperature at 01:00 is 26+8=3426 + 8 = 34.
3
Check with the earlier off period: from 00:00 to 00:30 the inside temperature rises from 26 to 31, which is 10 per hour. So the outside temperature at 00:00 is 26+10=3626 + 10 = 36.
4
The outside temperature falls at a constant rate, and it fell from 36 at 00:00 to 34 at 01:00, which is 2 per hour. This agrees with both readings.
Quick Check
36−2=3436 - 2 = 34 at 1 am.
Correct Answer: 34

Q16. Bar Graphs

TITA · +3 / 0
What was the temperature outside, in degree Celsius, at 9 pm?
Correct Answer
42
Step-by-step solution
📌 Core Concept
When the AC is off, the inside temperature climbs toward the outside temperature and would reach it in 1 hour. This gives the outside temperature at each switch-off. The outside temperature falls at a constant rate, so it can be extended backwards to 9 pm.
🔢 Step-by-Step Solution
1
From 00:00 to 00:30 the AC is off and the inside temperature rises from 26 to 31, which is 10 per hour. The outside temperature at 00:00 is therefore 26+10=3626 + 10 = 36.
2
From 01:00 to 01:30 the AC is off and the inside temperature rises from 26 to 30, which is 8 per hour. The outside temperature at 01:00 is therefore 26+8=3426 + 8 = 34.
3
The outside temperature falls 36−34=236 - 34 = 2 per hour.
4
Going back from 00:00 to 21:00 is 3 hours, during which the outside temperature was higher by 3×2=63 \times 2 = 6.
5
Outside temperature at 9 pm: 36+6=4236 + 6 = 42.
Quick Check
42−2×3=3642 - 2 \times 3 = 36 at midnight, which matches step 1.
Correct Answer: 42

Q17. Bar Graphs

MCQ · +3 / −1
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?
  1. A) Exactly 2
  2. B) Either 2 or 3
  3. C) More than 3
  4. D) Exactly 3
Correct Answer
D) Exactly 3
Step-by-step solution
📌 Core Concept
Count the moments the AC must have been turned on or had its setting changed. The deciding fact is that POWER mode must have been used for longer than REGULAR mode.
🔢 Step-by-Step Solution
1
The AC is on for 23:00 to 00:00, 00:30 to 01:00 and 01:30 to 02:00, which is 2 hours in all. POWER being used for longer than REGULAR means POWER ran for more than 1 hour.
2
The first hour (38 to 26) shows a constant fall of 12 per hour. REGULAR for the whole hour with set temperature 26 would give exactly that slope, but then POWER could total at most 1 hour, which only ties REGULAR. So the first hour must include POWER.
3
POWER cannot run the whole hour at this slope, because it would reach a set temperature in 30 minutes. Instead, POWER with set temperature 32 gives (38−32)/0.5=12(38-32)/0.5 = 12 per hour. Then POWER with set temperature 26 from 23:30 gives (32−26)/0.5=12(32-26)/0.5 = 12 per hour.
4
So the setting was changed at 23:30. That is the first required alteration.
5
The AC was turned on again at 00:30, because the temperature falls after the rise at 00:00. That is the second.
6
The AC was turned on again at 01:30, because the temperature falls after the rise at 01:00. That is the third.
7
No other change is needed, so the count is exactly 3.
Why Not the Others
Exactly 2 and Either 2 or 3: the first hour needs POWER, and that forces the extra setting change at 23:30.
More than 3: nothing else in the graph requires a further change.
Correct Answer: D

Q18. Bar Graphs

TITA · +3 / 0
What was the maximum difference between temperature outside and inside temperature, in degree Celsius, between 11:01 pm and 1:59 am?
Correct Answer
10
Step-by-step solution
📌 Core Concept
The outside temperature is a straight line falling at 2 per hour. Compare it with the inside temperature at each turning point of the graph.
🔢 Step-by-Step Solution
1
Off-periods give the outside temperature: 36 at 00:00 (inside rises 26→3126 \to 31 in 30 minutes, which is 10 per hour) and 34 at 01:00 (inside rises 26→3026 \to 30, which is 8 per hour). So the outside temperature falls 2 per hour.
2
The outside temperature is therefore 38 at 23:00, 37 at 23:30, 36 at 00:00, 35 at 00:30, 34 at 01:00, 33 at 01:30 and 32 at 02:00.
3
Differences (outside minus inside) at those times:
23:30: 37−32=537 - 32 = 5
00:00: 36−26=1036 - 26 = 10
00:30: 35−31=435 - 31 = 4
01:00: 34−26=834 - 26 = 8
01:30: 33−30=333 - 30 = 3
02:00: 32−28=432 - 28 = 4
4
Between turning points both lines are straight, so the largest gap occurs at one of these points. The largest is 10, at 00:00.
Quick Check
At 00:00 the inside temperature is at its minimum of 26 while the outside temperature is still 36, so the gap is 36−26=1036 - 26 = 10.
Correct Answer: 10
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CAT 2024 Slot 3 DILR at a Glance

Sets in this section5
Questions in this section22
Section time40 minutes
Convenor IIMIIM Calcutta

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