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CAT 2025 Lesson : DILR: Jul '25 to Aug '25 - Live Solving - 24 Jul 2025
Details for Questions 1 to 5 are provided below
An air conditioner (AC) company has four dealers – D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of ACs – Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant.
The following information is also known:
1. Every dealer sold at least two window ACs.
2. D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs.
3. A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.
4. The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.
5. D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.
6. D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.
7. D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.
1) How many Split Inverter ACs did D2 sell?
Answer:
2) What percentage of ACs sold were of Non-inverter type?
(1) 25.00%
(2) 75.00%
(3) 20.00%
(4) 33.33%
3) What was the total number of ACs sold by D2 and D4?
Answer:
4) Which of the following statements is necessarily false?
(1) D4 sold more Split ACs as compared to D3.
(2) D1 and D3 sold an equal number of Split ACs.
(3) D2 sold the highest number of ACs.
(4) D1 and D3 together sold more ACs as compared to D2 and D4 together.
5) If D3 and D4 sold an equal number of ACs, then what was the number of Non-inverter ACs sold by D2?
(1) 6
(2) 4
(3) 5
(4) 7
Details for Questions 6 to 10 are provided below
There are only three female students – Amala, Koli and Rini – and only three male students – Biman, Mathew and Shyamal – in a course. The course has two evaluation components, a project and a test. The aggregate score in the course is a weighted average of the two components, with the weights being positive and adding to 1.
The projects are done in groups of two, with each group consisting of a female and a male student. Both the group members obtain the same score in the project.
The following additional facts are known about the scores in the project and the test.
1. The minimum, maximum and the average of both project and test scores were identical – 40, 80 and 60, respectively.
2. The test scores of the students were all multiples of 10; four of them were distinct and the remaining two were equal to the average test scores.
3. Amala’s score in the project was double that of Koli in the same, but Koli scored 20 more than Amala in the test. Yet Amala had the highest aggregate score.
4. Shyamal scored the second highest in the test. He scored two more than Koli, but two less than Amala in the aggregate.
5. Biman scored the second lowest in the test and the lowest in the aggregate.
6. Mathew scored more than Rini in the project, but less than her in the test.
6) What was Rini’s score in the project?
Answer:
7) What was the weight of the test component?
(1) 0.60
(2) 0.50
(3) 0.40
(4) 0.75
8) What was the maximum aggregate score obtained by the students?
(1) 62
(2) 66
(3) 80
(4) 68
9) What was Mathew’s score in the test?
Answer:
10) Which of the following pairs of students were part of the same project team?
i) Amala and Biman
ii) Koli and Mathew
(1) Neither i) nor ii)
(2) Only ii)
(3) Only i)
(4) Both i) and ii)
An air conditioner (AC) company has four dealers – D1, D2, D3 and D4 in a city. It is evaluating sales performances of these dealers. The company sells two variants of ACs – Window and Split. Both these variants can be either Inverter type or Non-inverter type. It is known that of the total number of ACs sold in the city, 25% were of Window variant, while the rest were of Split variant. Among the Inverter ACs sold, 20% were of Window variant.
The following information is also known:
1. Every dealer sold at least two window ACs.
2. D1 sold 13 inverter ACs, while D3 sold 5 Non-inverter ACs.
3. A total of six Window Non-inverter ACs and 36 Split Inverter ACs were sold in the city.
4. The number of Split ACs sold by D1 was twice the number of Window ACs sold by it.
5. D3 and D4 sold an equal number of Window ACs and this number was one-third of the number of similar ACs sold by D2.
6. D2 and D3 were the only ones who sold Window Non-inverter ACs. The number of these ACs sold by D2 was twice the number of these ACs sold by D3.
7. D3 and D4 sold an equal number of Split Inverter ACs. This number was half the number of similar ACs sold by D2.
1) How many Split Inverter ACs did D2 sell?
Answer:
2) What percentage of ACs sold were of Non-inverter type?
(1) 25.00%
(2) 75.00%
(3) 20.00%
(4) 33.33%
3) What was the total number of ACs sold by D2 and D4?
Answer:
4) Which of the following statements is necessarily false?
(1) D4 sold more Split ACs as compared to D3.
(2) D1 and D3 sold an equal number of Split ACs.
(3) D2 sold the highest number of ACs.
(4) D1 and D3 together sold more ACs as compared to D2 and D4 together.
5) If D3 and D4 sold an equal number of ACs, then what was the number of Non-inverter ACs sold by D2?
(1) 6
(2) 4
(3) 5
(4) 7
Details for Questions 6 to 10 are provided below
There are only three female students – Amala, Koli and Rini – and only three male students – Biman, Mathew and Shyamal – in a course. The course has two evaluation components, a project and a test. The aggregate score in the course is a weighted average of the two components, with the weights being positive and adding to 1.
The projects are done in groups of two, with each group consisting of a female and a male student. Both the group members obtain the same score in the project.
The following additional facts are known about the scores in the project and the test.
1. The minimum, maximum and the average of both project and test scores were identical – 40, 80 and 60, respectively.
2. The test scores of the students were all multiples of 10; four of them were distinct and the remaining two were equal to the average test scores.
3. Amala’s score in the project was double that of Koli in the same, but Koli scored 20 more than Amala in the test. Yet Amala had the highest aggregate score.
4. Shyamal scored the second highest in the test. He scored two more than Koli, but two less than Amala in the aggregate.
5. Biman scored the second lowest in the test and the lowest in the aggregate.
6. Mathew scored more than Rini in the project, but less than her in the test.
6) What was Rini’s score in the project?
Answer:
7) What was the weight of the test component?
(1) 0.60
(2) 0.50
(3) 0.40
(4) 0.75
8) What was the maximum aggregate score obtained by the students?
(1) 62
(2) 66
(3) 80
(4) 68
9) What was Mathew’s score in the test?
Answer:
10) Which of the following pairs of students were part of the same project team?
i) Amala and Biman
ii) Koli and Mathew
(1) Neither i) nor ii)
(2) Only ii)
(3) Only i)
(4) Both i) and ii)
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