LR - Selection & Distribution - Previous Year CAT/MBA Questions

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Answer the following questions based on the information given 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. CAT 2023 LRDI Slot 3 | LR - Selection & Distribution CAT Question

How many Split Inverter ACs did D2 sell?

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2. CAT 2023 LRDI Slot 3 | LR - Selection & Distribution CAT Question

What percentage of ACs sold were of Non-inverter type?

(a)
33.33%
(b)
75.00%
(c)
20.00%
(d)
25.00%

3. CAT 2023 LRDI Slot 3 | LR - Selection & Distribution CAT Question

What was the total number of ACs sold by D2 and D4?

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4. CAT 2023 LRDI Slot 3 | LR - Selection & Distribution CAT Question

Which of the following statements is necessarily false?

(a)
D1 and D3 sold an equal number of Split ACs.
(b)
D1 and D3 together sold more ACs as compared to D2 and D4 together.
(c)
D2 sold the highest number of ACs.
(d)
D4 sold more Split ACs as compared to D3.

5. CAT 2023 LRDI Slot 3 | LR - Selection & Distribution CAT Question

If D3 and D4 sold an equal number of ACs, then what was the number of Non-inverter ACs sold by D2?

(a)
7
(b)
5
(c)
6
(d)
4

Answer the next 5 questions based on the information given below:

A few salesmen are employed to sell a product called TRICCEK among households in various housing complexes. On each day, a salesman is assigned to visit one housing complex. Once a salesman enters a housing complex, he can meet any number of households in the time available. However, if a household makes a complaint against the salesman, then he must leave the housing complex immediately and cannot meet any other household on that day. A household may buy any number of TRICCEK items or may not buy any item. The salesman needs to record the total number of TRICCEK items sold as well as the number of households met in each day. The success rate of a salesman for a day is defined as the ratio of the number of items sold to the number of households met on that day. Some details about the performances of three salesmen - Tohri, Hokli and Lahur, on two particular days are given below.

1. Over the two days, all three of them met the same total number of households, and each of them sold a total of 100 items.
2. On both days, Lahur met the same number of households and sold the same number of items.
3. Hokli could not sell any item on the second day because the first household he met on that day complained against him.
4. Tohri met 30 more households on the second day than on the first day.
5. Tohri’s success rate was twice that of Lahur’s on the first day, and it was 75% of Lahur’s on the second day.

6. CAT 2022 LRDI Slot 2 | LR - Selection & Distribution CAT Question

What was the total number of households met by Tohri, Hokli and Lahur on the first day?

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Answer: 84

Video Explanation

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Text Explanation :

From (4): Let Tohri visit x houses on day 1, hence he visits (x + 30) houses on day 2.
⇒ Total houses visited in 2 days = 2x + 30

Let Tohri visit n houses on day 2, hence he visits (100 – n) houses on day 1.

From (1) & (2): Lahur visited half the total houses on both days = x + 15
From (2): Lahur sold half the products on each day = 50

From (1) & (3): Hokli sold all 100 items on day 1, while he visited only 1 house on day 2.
Hence he visited (2x + 29) houses on day 1.

From (5): $\frac{100 - n}{x}$ = 2 $[\frac{50}{x + 15}]$

⇒ 100x + 1500 – nx – 15x = 100x
⇒ nx + 15x = 1500

⇒ n = $\frac{1500}{x + 15}$ ...(1)

From (5): $\frac{n}{x + 30}$ = $\frac{3}{4}$ $[\frac{50}{x + 15}]$

⇒ 4nx + 60n = 150x + 4500

⇒ 4x × $\frac{1500}{x + 15}$ + 60 × $\frac{1500}{x + 15}$ = 150x + 4500

⇒ 4x × $\frac{10}{x + 15}$ + 60 × $\frac{10}{x + 15}$ = x + 30

⇒ 40x + 600 = (x + 15)(x + 30)

⇒ 40x + 600 = x² + 45x + 450

⇒ x² + 5x - 150 = 0

⇒ (x + 15)(x - 10) = 0

⇒ x = 10 (-15 is rejected)

From (1)

⇒ n = $\frac{1500}{x + 15}$ = 60

∴ The table can be filled as follows:

∴ Total number of households met by Tohri, Hokli and Lahur on the first day = 10 + 49 + 25 = 84.

Hence, 84.

7. CAT 2022 LRDI Slot 2 | LR - Selection & Distribution CAT Question

How many TRICCEK items were sold by Tohri on the first day?

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8. CAT 2022 LRDI Slot 2 | LR - Selection & Distribution CAT Question

How many households did Lahur meet on the second day?

(a)
more than 35
(b)
between 21 and 29
(c)
between 30 and 35
(d)
20 or less

9. CAT 2022 LRDI Slot 2 | LR - Selection & Distribution CAT Question

How many households did Tohri meet on the first day?

(a)
between 11 and 20
(b)
10 or less
(c)
more than 40
(d)
between 21 and 40

10. CAT 2022 LRDI Slot 2 | LR - Selection & Distribution CAT Question

Which of the following statements is FALSE?

(a)
Tohri had a higher success rate on the first day compared to the second day.
(b)
Among the three, Tohri had the highest success rate on the first day.
(c)
Among the three, Lahur had the lowest success rate on the first day.
(d)
Among the three, Tohri had the highest success rate on the second day.

Answer the next 4 questions based on the information given

Ganga, Kaveri, and Narmada are three women who buy four raw materials (Mango, Apple, Banana and Milk) and sell five finished products (Mango smoothie, Apple smoothie, Banana smoothie, Mixed fruit smoothie and Fruit salad). Table-1 gives information about the raw materials required to produce the five finished products. One unit of a finished product requires one unit of each of the raw materials mentioned in the second column of the table.

Table - 1

One unit of milk, mango, apple, and banana cost ₹5, ₹3, ₹2, and ₹1 respectively. Each unit of a finished product is sold for a profit equal to two times the number of raw materials used to make that product. For example, apple smoothie is made with two raw materials (apple and milk) and will be sold for a profit of ₹4 per unit. Leftover raw materials are sold during the last business hour of the day for a loss of ₹1 per unit. The amount, in rupees, received from sales (revenue) for each woman in each of the four business hours of the day is given in Table-2.

Table - 2

The following additional facts are known.

No one except possibly Ganga sold any Mango smoothie.
Each woman sold either zero or one unit of any single finished product in any hour.
Each woman had exactly one unit each of two different raw materials as leftovers.
No one had any banana leftover.

11. CAT 2021 LRDI Slot 1 | LR - Selection & Distribution CAT Question

What BEST can be concluded about the number of units of fruit salad sold in the first hour?

(a)
Either 0 or 2
(b)
Exactly 2
(c)
Exactly 1
(d)
Either 1 or 2

Answer: Option D

Video Explanation

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Text Explanation :

One unit of milk, mango, apple, and banana cost ₹5, ₹3, ₹2, and ₹1 respectively

We can make the following table for Cost price, Profit and Selling price of each of the products.

Now, we can make the following table for types of products sold be each of the three based on selling price

Note: No one except Ganga sells Mango Smoothie.

After the last hour each woman had exactly one unit each of two different raw materials as leftovers but no one had any banana.

Also, leftover raw materials are sold during the last business hour of the day for a loss of ₹1 per unit

∴ Items left could be
(Milk + Mango) ⇒ CP = 8 ⇒ sold at Rs. 6
(Milk + Apple) ⇒ CP = 7 ⇒ sold at Rs. 5
(Apple + Mango) ⇒ CP = 5 ⇒ sold at Rs. 3

Ganga sells items worth Rs. 30 in last hour, out of these

Case 1: Rs. 6 could be earned from left-overs hence Rs. 24 would be earned from finished products. This is possible by selling Mango Smoothie and Fruit Salad.
Case 2: Rs. 5 could be earned from left-overs hence Rs. 25 would be earned from finished products. This is not possible.
Case 3: Rs. 3 could be earned from left-overs hence Rs. 27 would be earned from finished products. This is not possible.

Hence, Ganga sells Mango Smoothie and Fruit Salad in the last hour and the left-over items are one unit of Milk and Mango each .

Kaveri sells items worth Rs. 27 in last hour, out of these

Case 1: Rs. 6 could be earned from left-overs hence Rs. 21 would be earned from finished products. This is possible by selling Apple Smoothie and Banana Smoothie.
Case 2: Rs. 5 could be earned from left-overs hence Rs. 22 would be earned from finished products. This is possible by selling Banana Smoothie and Fruit Salad.
Case 3: Rs. 3 could be earned from left-overs hence Rs. 24 would be earned from finished products. This is not possible.

Hence, we have 2 cases for Kaveri.

Narmada sells items worth Rs. 22 in last hour, out of these

Case 1: Rs. 6 could be earned from left-overs hence Rs. 16 would be earned from finished products. This is not possible.
Case 2: Rs. 5 could be earned from left-overs hence Rs. 17 would be earned from finished products. This is not possible.
Case 3: Rs. 3 could be earned from left-overs hence Rs. 19 would be earned from finished products. This is possible by selling Mixed Fruit Smoothie.

Hence, Narmada sells Mixed Fruit Smoothie in the last hour and if left with one unit of Apple and Mango each.

Hence, we have the following final table

Narmada sells one unit of Fruit Salad while Ganga may or may not sell one unit of Fruit Salad.

∴ Number of Fruit Salads sold in first hour can be either 1 unit or 2 units.

Hence, option (d).

12. CAT 2021 LRDI Slot 1 | LR - Selection & Distribution CAT Question

Which of the following is NECESSARILY true?

(a)
Kaveri sold one unit of leftover mangoes.
(b)
Ganga did not sell any leftover apples.
(c)
Narmada sold one unit of leftover milk.
(d)
Ganga did not sell any leftover mangoes.

13. CAT 2021 LRDI Slot 1 | LR - Selection & Distribution CAT Question

What BEST can be concluded about the total number of units of milk the three women had in the beginning?

(a)
Either 18 or 19 or 20 units.
(b)
Either 19 or 20 units.
(c)
Either 17 or 18 or 19 units.
(d)
Either 18 or 19 units.

14. CAT 2021 LRDI Slot 1 | LR - Selection & Distribution CAT Question

If it is known that three leftover units of mangoes were sold during the last business hour of the day, how many apple smoothies were sold during the day?

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Answer the next 6 questions based on the information given

A journal plans to publish 18 research papers, written by eight authors (A, B, C, D, E, F, G, and H) in four issues of the journal scheduled in January, April, July and October. Each of the research papers was written by exactly one of the eight authors. Five papers were scheduled in each of the first two issues, while four were scheduled in each of the last two issues. Every author wrote at least one paper and at most three papers. The total number of papers written by A, D, G and H was double the total number of papers written by the other four authors. Four of the authors were from India and two each were from Japan and China. Each author belonged to exactly one of the three areas — Manufacturing, Automation and Logistics. Four of the authors were from the Logistics area and two were from the Automation area. As per the journal policy, none of the authors could have more than one paper in any issue of the journal.

The following facts are also known.

F, an Indian author from the Logistics area, wrote only one paper. It was scheduled in the October issue.
A was from the Automation area and did not have a paper scheduled in the October issue.
None of the Indian authors were from the Manufacturing area and none of the Japanese or Chinese authors were from the Automation area.
A and H were from different countries, but had their papers scheduled in exactly the same issues.
C and E, both Chinese authors from different areas, had the same number of papers scheduled. Further, E had papers scheduled in consecutive issues of the journal but C did not.
B, from the Logistics area, had a paper scheduled in the April issue of the journal.
B and G belonged to the same country. None of their papers were scheduled in the same issue of the journal.
D, a Japanese author from the Manufacturing area, did not have a paper scheduled in the July issue.
C and H belonged to different areas.

15. CAT 2021 LRDI Slot 1 | LR - Selection & Distribution CAT Question

What is the correct sequence of number of papers written by B, C, E and G, respectively?

(a)
1, 2, 2, 3
(b)
1, 3, 3, 1
(c)
3, 1, 1, 3
(d)
1, 2, 2, 1

Answer: Option A

Video Explanation

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Text Explanation :

The information given in the question can be written as follows

Point (2) & (3): A has to be from India

The total number of papers written by A, D, G and H was double the total number of papers written by the other four authors

⇒ A + D + G + H = 2(B + C + E + F)

Also, A + D + G + H + B + C + E + F = 18
⇒ 3(B + C + E + F) = 18
⇒ B + C + E + F = 6 …(1)
⇒ A + D + G + H = 12 …(2)

Point (5): C = E ≥ 2 (since E has papers scheduled in consecutive issues, E must have written more than 1 paper)

From (1) we can conclude that E must have written exactly 2 papers. C would also have written exactly 2 papers.
∴ B + 2 + 2 + 1 = 6
⇒ B = 1

Also, A + D + G + H = 12. Since each person can write a maximum of 3 papers, hence the only possible value of A, D, G and H will be 3 each.

Point (7): B and G both can only be from India. Hence, H has to be from Japan.

Point (5) & (3): C and E cannot be from Automation since they are Chinese. Hence, one of C or E is from Manufacturing and the other from Logistics.

Now, since H is from Japan he cannot be from Automation, hence H can only be from Logistics.
Since, C and H have to be from different areas (9), C has to be from Manufacturing and E from Logistics.

This leaves us with G who has to be from Automation.

A has to write 3 papers and an author can write only one paper in a single issue, hence A must have written one paper each in Jan, Apr and Jul issue.

A and H had papers scheduled in same issues (4). Hence, must have written one paper each in Jan, Apr and Jul issue.

Similarly, D must have written one paper each in Jan, Apr and Oct issue.

Point (7): None of B and G’s papers were scheduled in the same issue of the journal. Hence, G must have written papers in Jan, Jul and Oct.

Point (5): E wrote papers in successive issues while C did not write in successive issues. Only possible way this can happen is when E writes in Apr and Jul while C writes in Jan and Oct.

Number of papers written by B, C, E and G is 1, 2, 2 and 3 respectively.

Hence, option (a).

16. CAT 2021 LRDI Slot 1 | LR - Selection & Distribution CAT Question

How many papers were written by Indian authors?

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17. CAT 2021 LRDI Slot 1 | LR - Selection & Distribution CAT Question

Which of the following statement(s) MUST be true?

Statement A: Every issue had at least one paper by author(s) from each country.
Statement B: Every issue had at most two papers by author(s) from each area.

(a)
Neither of the statements
(b)
Both the statements
(c)
Only Statement A
(d)
Only Statement B

18. CAT 2021 LRDI Slot 1 | LR - Selection & Distribution CAT Question

Which of the following statements is FALSE?

(a)
Every issue had at least one paper by author(s) from Automation area.
(b)
Every issue had exactly two papers by Indian authors.
(c)
Every issue had exactly two papers by authors from Logistics area.
(d)
Every issue had exactly one paper by a Chinese author.

19. CAT 2021 LRDI Slot 1 | LR - Selection & Distribution CAT Question

Which of the following statements is FALSE?

(a)
There was exactly one paper by an author from Manufacturing area in the April issue.
(b)
There was exactly one paper by an author from Logistics area in the October issue.
(c)
There were exactly two papers by authors from Manufacturing area in the January issue.
(d)
There were exactly two papers by authors from Manufacturing area in the July issue.

20. CAT 2021 LRDI Slot 1 | LR - Selection & Distribution CAT Question

Which of the following is the correct sequence of number of papers by authors from Automation, Manufacturing and Logistics areas, respectively?

(a)
6, 6, 6
(b)
6, 5, 7
(c)
6, 7, 5
(d)
5, 6, 7

Answer the next 6 questions based on the information given

Ravi works in an online food-delivery company. After each delivery, customers rate Ravi on each of four parameters – Behaviour, Packaging, Hygiene, and Timeliness, on a scale from 1 to 9. If the total of the four rating points is 25 or more, then Ravi gets a bonus of ₹20 for that delivery. Additionally, a customer may or may not give Ravi a tip. If the customer gives a tip, it
is either ₹30 or ₹50.

One day, Ravi made four deliveries - one to each of Atal, Bihari, Chirag and Deepak, and received a total of ₹120 in bonus and tips. He did not get both a bonus and a tip from the same customer.

The following additional facts are also known.

In Timeliness, Ravi received a total of 21 points, and three of the customers gave him the same rating points in this parameter. Atal gave higher rating points than Bihari and Chirag in this parameter.
Ravi received distinct rating points in Packaging from the four customers adding up to 29 points. Similarly, Ravi received distinct rating points in Hygiene from the four customers adding up to 26 points.
Chirag gave the same rating points for Packaging and Hygiene.
Among the four customers, Bihari gave the highest rating points in Packaging, and Chirag gave the highest rating points in Hygiene.
Everyone rated Ravi between 5 and 7 in Behaviour. Unique maximum and minimum ratings in this parameter were given by Atal and Deepak respectively.
If the customers are ranked based on ratings given by them in individual parameters, then Atal’s rank based on Packaging is the same as that based on Hygiene. This is also true for Deepak.

21. CAT 2021 LRDI Slot 2 | LR - Selection & Distribution CAT Question

What was the minimum rating that Ravi received from any customer in any parameter?

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Answer: 5

Video Explanation

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Text Explanation :

Timeliness:
From (1): Ravi’s rating in Timeliness by 4 customers can be either (6, 5, 5, 5) or (9, 4, 4, 4) where Atal’s rating will be higher than the other 3 customers.

Packaging:
From (2): Ravi’s rating in Packaging by 4 customers will be (9, 8, 7, 5) in any order.
From (4): Bihari’s rating in Packaging will be 9.

Hygiene:
From (3 and 4): Chirag gave highest rating in hygiene which is same as his rating in packaging. Since Chirag can not give a rating of 9 in packaging (which is given by Bihari), highest rating Chirag can give in hygiene can be 8 or lower, which is same as the rating given by him in packaging.

From (2 and 3 and 4): Ravi’s rating in Hygiene by 4 customers is (8, 7, 6, 5).

∴ Ratings given by Chirag in packaging and hygiene is 8.

Behaviour:
From (5): Ravi’s rating in Behaviour given by Atal and Deepak is 7 and 5 respectively and rating given by Bihari and Chirag is 6.

We can make the following table from the information we have so far.

From (6): If Atal and Deepak will have the same ranking in packaging and hygiene.

Since Bihari and Chirag are given the two best rating in packaging, Atal and Deepak will give the two least ratings in packaging and hygiene.

∴ Rating given by Bihari in hygiene is 7.

Hence, we have two cases

Case 1:

Case 2:

[Note: Ravi gets a bonus of Rs. 20 from a customer if the total of four rating points by that customer is 25 or more. Else Ravi may or may not get a tip amount of Rs. 30 or Rs. 50.]

Consider Case 1: It is not possible for Ravi to earn a total amount of Rs. 120. Hence we can reject case 1.

Consider Case 2: For Ravi to earn a total amount of Rs. 120, he should not receive bonus from Atal.

∴ Ravi gets a total rating of < 25 from Atal. This is possible when Atal gives a rating of 6 for Timeliness.

Also, a total of Rs. 120 will be possible when Atal or Deepak give Ravi a tip amount of Rs. 30 or Rs. 50 in any order.

∴ We get the final table as below.

∴ Minimum rating received by Ravi in any parameter is 5.

i.e., by Deepak in Behaviour, by Atal in Packaging etc.

Hence, 5.

22. CAT 2021 LRDI Slot 2 | LR - Selection & Distribution CAT Question

The COMPLETE list of customers who gave the maximum total rating points to Ravi is

(a)
Atal
(b)
Bihari
(c)
Atal and Bihari
(d)
Bihari and Chirag

23. CAT 2021 LRDI Slot 2 | LR - Selection & Distribution CAT Question

What rating did Atal give on Timeliness?

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24. CAT 2021 LRDI Slot 2 | LR - Selection & Distribution CAT Question

What BEST can be concluded about the tip amount given by Deepak?

(a)
Either Rs. 0, or Rs. 30 or Rs. 50
(b)
Either Rs. 30 or Rs. 50
(c)
Rs. 50
(d)
Rs. 30

25. CAT 2021 LRDI Slot 2 | LR - Selection & Distribution CAT Question

In which parameter did Atal give the maximum rating points to Ravi?

(a)
Timeliness
(b)
Hygiene
(c)
Behaviour
(d)
Packaging

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LR - Selection & Distribution - Previous Year CAT/MBA Questions

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