Which of the following statements is correct?
Solution
(R-C, V2) holds 9 in both arrangements.
Answer: (B) The ATM placed at the (R-C, V2) intersection has a cash requirement of Rs. 9 Lakhs.
CAT 2024 · Slot 3 · DILR
CAT 2024 Slot 3 DILR paper with solutions
5 sets, 22 questions, in exam order.
5
sets
22
questions
Sets in this slot
ATMs on a 3×3 road grid
The figure below shows a network with three parallel roads represented by horizontal lines R-A, R-B, and R-C and another three parallel roads represented by vertical lines V1, V2, and V3. The figure also shows the distance (in km) between two adjacent intersections.Six ATMs are placed at six of the nine road intersections. Each ATM has a distinct integer cash requirement (in Rs. Lakhs), and the numbers at the end of each line in the figure indicate the total cash requirements of all ATMs placed on the corresponding road. For example, the total cash requirement of the ATM(s) placed on road R-A is Rs. 22 Lakhs.
The following additional information is known.
1. The ATMs with the minimum and maximum cash requirements of Rs. 7 Lakhs and Rs. 15 Lakhs are placed on the same road.
2. The road distance between the ATM with the second highest cash requirement and the ATM located at the intersection of R-C and V3 is 12 km.
Set solution: how to crack this set
Six distinct values between 7 and 15 add to 62 (row totals ).
A row can't hold three ATMs () or one (max 15), so every row has exactly two.
V1 totals 15: it holds either just 15, or 7 and 8.
Case V1 : 7 is on 15's road, so RA has 15 (V1) and 7; that forces 7 at (RA, V3). Then , and each row sums to 20. Two fillings exist, and the 12-km condition (second highest = 12) keeps: RB: 12 (V2), 8 (V3); RC: 9 (V2), 11 (V3).
Case V1 : RA has 7 (V1) and 15 (V3). The 12-km condition keeps: RB: 8 (V1), 12 (V2); RC: 9 (V2), 11 (V3).
| Road | Arrangement 1 | Arrangement 2 |
|---|---|---|
| R-A | V1 15, V3 7 | V1 7, V3 15 |
| R-B | V2 12, V3 8 | V1 8, V2 12 |
| R-C | V2 9, V3 11 | V2 9, V3 11 |
How many ATMs have cash requirements of Rs. 10 Lakhs or more?
Solution
15, 12 and 11 are at least 10: ATMs.
Answer: 3
Which of the following two statements is/are DEFINITELY true?
Statement A: Each of R-A, R-B, and R-C has two ATMs.
Statement B: Each of V1, V2, and V3 has two ATMs.
Solution
Every row always has two ATMs; in Arrangement 1, V1 has only one. Only Statement A.
Answer: (A) Only Statement A
What best can be said about the road distance (in km) between the ATMs having the second highest and the second lowest cash requirements?
Solution
Second highest 12 is at (R-B, V2); second lowest 8 is at (R-B, V3) or (R-B, V1): 7 km or 4 km.
Answer: (D) Either 4 km or 7 km
What is the number of ATMs whose locations and cash requirements can both be uniquely determined?
Solution
Same in both arrangements: 12 at (R-B, V2), 9 at (R-C, V2), 11 at (R-C, V3), i.e. ATMs.
Answer: 3
Nutrient composition of seven food grains
The table given below shows the amount, in grams, of carbohydrate, protein, fat and all other nutrients, per 100 grams of nutrients in seven food grains. The first column shows the food grain category and the second column its codename. The table has some missing values.
The following additional facts are known.
1. Both the pseudo-cereals had higher amounts of carbohydrate as well as higher amounts of protein than any millet.
2. Both the cereals had higher amounts of carbohydrate than any pseudo-cereal.
3. All the missing values of carbohydrate amounts (in grams) for all the food grains are non-zero multiples of 5.
4. All the missing values of protein, fat and other nutrients amounts (in grams) for all the food grains are non-zero multiples of 4.
5. P1 contained double the amount of protein that M3 contains.
Set solution: how to crack this set
Each row sums to 100. Missing carbohydrate values are multiples of 5; other missing values are multiples of 4.
C1: carb + protein , so carb is a multiple of 20 and above 66: 80, protein 8. C2: carb + protein : carb 75, protein 12.
P2: carb + fat , with carb between the millets and the cereals: 70, fat 8.
M3: protein + other . P1 protein M3 protein, above every millet's protein, with P1 fat protein non-zero: M3 protein 8 (other 24), P1 protein 16 (fat 8).
M2: carb + protein , carb below 66, protein below 14: carb 65, protein 12.
| Grain | Carb | Protein | Fat | Other |
|---|---|---|---|---|
| C1 | 80 | 8 | 0 | 12 |
| C2 | 75 | 12 | 3 | 10 |
| M1 | 62 | 10 | – | – |
| M2 | 65 | 12 | 7 | 16 |
| M3 | 56 | 8 | 12 | 24 |
| P1 | 66 | 16 | 8 | 10 |
| P2 | 70 | 14 | 8 | 8 |
How many foodgrains had a higher amount of carbohydrate per 100 grams ofnutrients than M1?
Solution
Above 62: C1, C2, M2, P1, P2, i.e. .
Answer: 5
How many grams of protein were there in 100 grams of nutrients in M2?
Solution
M2 protein .
Answer: 12
How many grams of other nutrients were there in 100 grams of nutrients in M3?
Solution
M3 other nutrients .
Answer: 24
What is the median of the number of grams of protein in 100 grams of nutrients among these food grains?
Solution
Proteins: 8, 8, 10, 12, 12, 14, 16. Median .
Answer: 12
OTT subscribers by category and apps used
Over the top (OTT) subscribers of a platform are segregated into three categories: i) Kid, ii)Elder, and iii) Others. Some of the subscribers used one app and the others used multiple apps to access the platform. The figure below shows the percentage of the total number of subscribers in 2023 and 2024 who belong to the ‘Kid’ and ‘Elder’ categories.
The following additional facts are known about the numbers of subscribers.
1. The total number of subscribers increased by 10% from 2023 to 2024.
2. In 2024, 1/2 of the subscribers from the ‘Kid’ category and 2/3 of the subscribers from the ‘Elder’ category subscribers use one app.
3. In 2023, the number of subscribers from the ‘Kid’ category who used multiple apps was the same as the number of subscribers from the ‘Elder’ category who used one app.
4. 10,000 subscribers from the ‘Kid’ category used one app and 15,000 subscribers from the ‘Elder’ category used multiple apps in 2023.
Set solution: how to crack this set
Let the 2023 total be (2024: ). Kid: 15% (2023), 20% (2024). Elder: 20%, 30%.
2023: Kid one-app and Elder multi-app . Kid multi-app Elder one-app .
and , .
2024 total : Kid 22000, Elder 33000, Others 55000.
How many subscribers belonged to the ‘Others’ category in 2024?
Solution
Others in 2024 of 110000 .
Answer: (C) 55000
What percentage of subscribers in the ‘Kid’ category used multiple apps in 2023?
Solution
Kid 2023 , of which 5000 used multiple apps: .
Answer: (A) 33.33%
What was the percentage increase in the number of subscribers in the ‘Elder’ categoryfrom 2023 to 2024?
Solution
Elder: 20000 → 33000, an increase of .
Answer: (C) 65%
What could be the minimum percentage of subscribers who used multiple apps in 2024?
Solution
2024 multi-app: Kid , Elder ; Others could all use one app.
Minimum .
Answer: (B) 20.0%
GDP, GDP per capita and growth of ten countries
Out of 10 countries -- Country 1 through Country 10 -- Country 9 has the highest gross domestic product (GDP), and Country 10 has the highest GDP per capita. GDP per capita is the GDP of a country divided by its population. The table below provides the following data about Country 1 through Country 8 for the year 2024.
• Column 1 gives the country's identity.
• Column 2 gives the country’s GDP as a fraction of the GDP of Country 9.
• Column 3 gives the country’s GDP per capita as a fraction of the GDP per capita of Country10.
• Column 4 gives the country’s annual GDP growth rate.
• Column 5 gives the country’s annual population growth rate.
Assume that the GDP growth rates and population growth rates of the countries will remain constant for the next three years.
Set solution: how to crack this set
Population (in the table's units):
Country 1: 0.366, 2: 0.56, 3: 6.5, 4: 0.316, 5: 0.278, 6: 1.0, 7: 0.267, 8: 0.171.
Future values: multiply by .
Which one among the countries 1 through 8, has the smallest population in 2024?
Solution
Smallest population ratio: Country 8 ().
Answer: (A) Country 8
The ratio of Country 4’s GDP to Country 5’s GDP in 2026 will be closest to
Solution
.
Answer: (A) 1.195
Which one among the countries 1, 4, 5, and 7 will have the largest population in 2027?
Solution
2027 populations: 1: ; 4: ; 5: ; 7: . Largest: Country 1.
Answer: (A) Country 1
For how many countries among Country 1 through Country 8 will the GDP per capita in 2027 be lower than that in 2024?
Solution
Per capita falls only if population grows faster than GDP. Every country's GDP growth beats its population growth (closest: Country 4, 0.5% vs 0.49%). Answer: .
Answer: 0
AC modes and inside temperature
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.
Set solution: how to crack this set
23:00–0:00: 38 → 26 at a steady /hour.
0:00–0:30: AC off, 26 → 31. When off, the room rises to the outside temperature in 1 hour, so outside at 0:00 .
0:30–1:00: AC on, 31 → 26.
1:00–1:30: AC off, 26 → 30, so outside at 1:00 . Outside falls /hour (42 at 21:00).
1:30–2:00: AC on, 30 → 28.
Power mode must be used for longer than regular mode. If 23:00–0:00 were regular (60 min), power could total at most 60 min. So 23:00–0:00 is power mode: set 32 (reached at 23:30), then reset to 26 at 23:30.
How many times the AC must have been turned off between 11:01 pm and 1:59 am?
Solution
The AC was switched off at 0:00 and at 1:00: times.
Answer: (B) 2
What was the temperature outside, in degree Celsius, at 1 am?
Solution
C at 1 am.
Answer: 34
What was the temperature outside, in degree Celsius, at 9 pm?
Solution
Outside falls per hour: 36 at midnight, so C at 9 pm.
Answer: 42
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?
Solution
Changes after 23:00: reset at 23:30, on at 0:30, on at 1:30. Exactly .
Answer: (D) Exactly 3
What was the maximum difference between temperature outside and inside temperature, in degree Celsius, between 11:01 pm and 1:59 am?
Solution
At 0:00 the inside is 26 and outside 36: difference C, the largest in the period.
Answer: 10
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