# CAT 2022 LRDI Slot 2 | Previous Year CAT Paper

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

Every day a widget supplier supplies widgets from the warehouse (W) to four locations – Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis) are given against each location (A, B, C, and D) in the figure below. For example, there is a 40% chance that the demand in Ahmednagar will be 50 units and a 60% chance that the demand will be 70 units. The lines in the figure connecting the locations and warehouse represent two-way roads connecting those places with the distances (in km) shown beside the line. The distances in both the directions along a road are equal. For example, the road from Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km long.

Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.

**1. CAT 2022 LRDI Slot 2 | DI - Routes & Networks**

If the last location visited is Ahmednagar, then what is the total distance covered in the route (in km)?

[**Note**: There is an ambiguity in this question and hence was discarded by IIM Bangalore.]

Answer: 35

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**Explanation** :

This questions was discarded by IIM Bangalore.

A cannot be the last city to be visited while satisfying all the conditions given in the caselet.

**Explanation**:

Demand

A – 50 (40%); 70 (60%)

B – 40 (30%); 60 (70%)

C – 70 (30%); 100 (70%)

D – 30 (40%); 50 (60%)

For Ahmednagar to be last, it should have the least demand of the 4 cities.

⇒ The only way Ahmednagar’s demand can be the least of the 4 cities is when its demand is 50.

Now, demand of all other cities should be greater than or equal to 50.

⇒ Demand at

B = 60

C = 70 or 100

D = 50

∴ Sequence of cities according to demand will be C → B → D → A

Distance travelled from

Warehouse → C = 12

C → B = 4

B → W → D = 12

D → W → A = 7 [shortest route from D to A is through Warehouse and not the direct route]

∴ Total distance travelled = 12 + 4 + 12 + 7 = 35.

**Ambiguity**: There is some ambiguity in this question. Once you reach B, demand at both A and D is same (i.e., 50). You would go the nearest of A and D which is A and hence A cannot be the last city to be visited then.

Hence, this question was discarded.

**Note**: The answer given by IIM-B in the cadidate response sheet was 35.

Workspace:

**2. CAT 2022 LRDI Slot 2 | DI - Routes & Networks**

If the total number of widgets delivered in a day is 250 units, then what is the total distance covered in the route (in km)?

Answer: 38

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**Explanation** :

Demand

A – 50 (40%); 70 (60%)

B – 40 (30%); 60 (70%)

C – 70 (30%); 100 (70%)

D – 30 (40%); 50 (60%)

Maximum demand possible = 70 + 60 + 100 + 50 = 280

Actual demand is 250. This is possible only when demand at C is 70 instead of 100.

∴ Actual demands at various cities is:

A → 70

B → 60

C → 70

D → 50

Sequence of cities visited is: A → C → B → D

[A is closer to warehouse than C, hence first city to be visited will be A.]

∴ Total distance travelled = 5 + 17 + 4 + 12 = 38.

Hence, 38.

Workspace:

**3. CAT 2022 LRDI Slot 2 | DI - Routes & Networks**

What is the chance that the total number of widgets delivered in a day is 260 units and the route ends at Bikrampore?

- A.
7.56%

- B.
10.80%

- C.
17.64%

- D.
33.33%

Answer: Option A

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**Explanation** :

Demand

A – 50 (40%); 70 (60%)

B – 40 (30%); 60 (70%)

C – 70 (30%); 100 (70%)

D – 30 (40%); 50 (60%)

For route to end at B, B should have least demand i.e., 40.

Total demand is 260, hence demand at other cities should be higher of the two values.

∴ Demand at A = 70 (60%)

Demand at B = 40 (30%)

Demand at C = 100 (70%)

Demand at D = 50 (60%)

∴ Required possibility = 60% × 30% × 70% × 60%

= 0.6 × 0.3 × 0.7 × 0.6 = 0.0756 = 7.56%

Hence, option (a).

Workspace:

**4. CAT 2022 LRDI Slot 2 | DI - Routes & Networks**

If the first location visited from the warehouse is Ahmednagar, then what is the chance that the total distance covered in the route is 40 km?

- A.
3.24%

- B.
5.4%

- C.
18%

- D.
30%

Answer: Option C

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**Explanation** :

Demand

A – 50 (40%); 70 (60%)

B – 40 (30%); 60 (70%)

C – 70 (30%); 100 (70%)

D – 30 (40%); 50 (60%)

If first city visited is Ahmednagar, this is possible when A’s demand is highest. This is only possible when A’s demand is 70.

∴ Demand at C should be 70

Demand at B = 40 or 60

Demand at D = 30 or 50

∴ Sequence of cities can be

A → C → B → D: distance travelled = 38 kms

A → C → D → B: distance travelled = 40 kms

∴ Demand at D ≥ B

⇒ Demand at D = 50 (60%) and demand at B = 40 (30%)

⇒ Required possibility = 60% × 30% = 18%

Hence, option (c).

Workspace:

**5. CAT 2022 LRDI Slot 2 | DI - Routes & Networks**

If Ahmednagar is not the first location to be visited in a route and the total route distance is 29 km, then which of the following is a possible number of widgets delivered on that day?

- A.
210

- B.
250

- C.
200

- D.
220

Answer: Option A

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**Explanation** :

Demand

A – 50 (40%); 70 (60%)

B – 40 (30%); 60 (70%)

C – 70 (30%); 100 (70%)

D – 30 (40%); 50 (60%)

If A is not the first city to be visited, the first city will have to be C.

Distance travelled from Warehouse to C = 12 kms.

∴ To visit the remaining 3 cities, distance travelled should be (29 – 12 =) 17 kms.

There are two possibilities for this.

Case 1: W → C → B → A → D

Here,

highest demand is from C i.e., 70 or 100

2^{nd} highest demand is from B i.e., 60

3^{rd} highest demand is from A i.e., 50

4^{th} highest demand is from D i.e., 30

Total widgets delivered can be 210 or 240

Case 2: W → C → D → A → B

Here,

highest demand is from C i.e., 70 or 100

2^{nd} highest demand is from D i.e., 50

3^{rd} highest demand is from A i.e., 50

4^{th} highest demand is from B i.e., 40

Total widgets delivered can be 210 or 240.

[**Note**: shortest route from A to D or vice-versa is through the warehouse.]

Hence, option (a).

Workspace:

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

A speciality supermarket sells 320 products. Each of these products was either a cosmetic product or a nutrition product. Each of these products was also either a foreign product or a domestic product. Each of these products had at least one of the two approvals – FDA or EU.

The following facts are also known:

1. There were equal numbers of domestic and foreign products.

2. Half of the domestic products were FDA approved cosmetic products.

3. None of the foreign products had both the approvals, while 60 domestic products had both the approvals.

4. There were 140 nutrition products, half of them were foreign products.

5. There were 200 FDA approved products. 70 of them were foreign products and 120 of them were cosmetic products.

**6. CAT 2022 LRDI Slot 2 | LR - Venn Diagram**

How many foreign products were FDA approved cosmetic products?

Answer: 40

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**Explanation** :

There were equal numbers of domestic and foreign products.

∴ There will be 160 foreign as well as domestic products.

Half of the domestic products were FDA approved cosmetic products.

∴ 80 products are domestic, FDA approved and cosmetic products.

None of the foreign products had both the approvals while 60 domestic products had both the approvals.

There were 140 nutrition products, half of them were foreign products.

∴ Number of cosmetic products = 320 – 140 = 180

There were 200 FDA approved products, 70 of them were foreign products

FDA approved products = FDA foreign + FDA domestic

⇒ 200 = 70 + (60 + only FDA domestic products)

⇒ only FDA domestic products = 70

and 120 of them were cosmetic products.

FDA approved cometic products = FDA approved foreign cosmetic + FDA approved domestic cosmetic

⇒ 120 = (0 + only FDA approved cosmetic foreign products) + 80

⇒ only FDA approved cosmetic foreign products = 40

Since there are total 70 foreign FDA approved products out of which 40 are only FDA approved cosmetic foreign products, hence approved nutrition foreign products = 70 – 40 = 30.

⇒ only EU approved nutrition foreign products = 70 – 30 = 40

Total foreign products = 160

⇒ only EU approved cosmetic foreign products = 160 – 40 – 30 – 40 = 50

Total Cosmetic products is 180 = cosmetic foreign + cosmetic domestic

⇒ 180 = (50 + 0 + 40) + (only EU approved domestic cosmetic products + 80)

⇒ only EU approved domestic cosmetic products = 10

Total domestic products = 160 = (10 + only EU nutrition domestic products) + 60 + 70

⇒ only EU nutrition domestic products = 20

With the given information we can tabulate this much.

∴ Number of foreign FDA approved cosmetic products = 0 + 40 = 40

Hence, 40.

Workspace:

**7. CAT 2022 LRDI Slot 2 | LR - Venn Diagram**

How many cosmetic products did not have FDA approval?

- A.
60

- B.
10

- C.
50

- D.
Cannot be determined

Answer: Option A

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**Explanation** :

Consider the solution to first question of this set.

Number of cosmetic products that did not have FDA approval = 50 + 10 = 60

Hence, option (a).

Workspace:

**8. CAT 2022 LRDI Slot 2 | LR - Venn Diagram**

Which among the following options best represents the number of domestic cosmetic products that had both the approvals?

- A.
At least 20 and at most 70

- B.
At least 10 and at most 60

- C.
At least 20 and at most 50

- D.
At least 10 and at most 80

Answer: Option B

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**Explanation** :

Consider the solution to first question of this set.

Domestic products which have both approvals = 60.

∴ Domestic cosmetic products with both approvals cannot be more than 60.

Maximum only FDA approved cosmetic domestic products can be 70, hence minimum cosmetic domestic products with both approvals can be 10.

Hence, option (b).

Workspace:

**9. CAT 2022 LRDI Slot 2 | LR - Venn Diagram**

If 70 cosmetic products did not have EU approval, then how many nutrition products had both the approvals?

- A.
30

- B.
50

- C.
10

- D.
20

Answer: Option C

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**Explanation** :

Consider the solution to first question of this set.

We have:

If 70 cosmetic products did not have EU approval, then number of nutrition products with both approvals = only FDA approved cosmetic (foreign + domestic) products

⇒ 70 = 40 + only FDA approved cosmetic domestic products

⇒ only FDA approved cosmetic domestic products = 30

We can fill the remaining table as follows.

Number of nutrition products with both approvals = 0 + 10 = 10

Hence, option (c).

Workspace:

**10. CAT 2022 LRDI Slot 2 | LR - Venn Diagram**

If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval?

Answer: 50

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**Explanation** :

Consider the solution to first question of this set.

We have:

50 nutrition products did not have EU approval = 30 + only FDA domestic nutrition products

⇒ only FDA domestic nutrition products = 20

We can fill the table as follows:

We have:

∴ Number of domestic cosmetic products without EU approval = 50

Hence, 50.

Workspace:

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

The two plots below show data for four companies code-named A, B, C, and D over three years - 2019, 2020, and 2021.

The first plot shows the revenues and costs incurred by the companies during these years. For example, in 2021, company C earned Rs.100 crores in revenue and spent Rs.30 crores. The profit of a company is defined as its revenue minus its costs.

The second plot shows the number of employees employed by the company (employee strength) at the start of each of these three years, as well as the number of new employees hired each year (new hires). For example, Company B had 250 employees at the start of 2021, and 30 new employees joined the company during the year.

**11. CAT 2022 LRDI Slot 2 | DI - Tables & Graphs**

Considering all three years, which company had the highest annual profit?

- A.
Company D

- B.
Company C

- C.
Company B

- D.
Company A

Answer: Option B

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**Explanation** :

The given data can be tabulated as given below:

Income / Expense / Profit

Employees

Cumulative profit of 3 years for

A = 5 + 25 + 30 = Rs. 60 crores profit

B = 25 + 50 + 0 = Rs. 75 crores profit

C = 5 + 10 + 70 = Rs. 85 crores profit

D = 10 – 30 + 0 = Rs. 20 crores loss

Highest cumulative profit if for company C.

Hence, option (b).

Workspace:

**12. CAT 2022 LRDI Slot 2 | DI - Tables & Graphs**

Which of the four companies experienced the highest annual loss in any of the years?

- A.
Company C

- B.
Company A

- C.
Company D

- D.
Company B

Answer: Option C

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**Explanation** :

Consider the solution for first question of this set.

Company D suffered highest loss for any particular year in 2020.

Hence, option (c).

Workspace:

**13. CAT 2022 LRDI Slot 2 | DI - Tables & Graphs**

The ratio of a company's annual profit to its annual costs is a measure of its performance. Which of the four companies had the lowest value of this ratio in 2019?

- A.
Company C

- B.
Company B

- C.
Company D

- D.
Company A

Answer: Option D

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**Explanation** :

Consider the solution for first question of this set.

Ratio of (Annual profit) / (Annual Cost) in 2019 for

A = 5/85 = 1/17

B = 25/75 = 1/3

C = 5/20 = 1/4

D = 10/40 = ¼

This ratio is lowest for Company A.

Hence, option (a).

Workspace:

**14. CAT 2022 LRDI Slot 2 | DI - Tables & Graphs**

The total number of employees lost in 2019 and 2020 was the least for:

- A.
Company B

- B.
Company A

- C.
Company D

- D.
Company C

Answer: Option A

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**Explanation** :

Consider the solution for first question of this set.

Employees lost in 2019 and 200 for

A = (170 - 140) = 30

B = (245 - 240) = 5

C = (370 - 325) = 45

D = (430 - 410) = 20

Least number of employees left is least for B.

Hence, option (a).

Workspace:

**15. CAT 2022 LRDI Slot 2 | DI - Tables & Graphs**

Profit per employee is the ratio of a company's profit to its employee strength. For this purpose, the employee strength in a year is the average of the employee strength at the beginning of that year and the beginning of the next year. In 2020, which of the four companies had the highest profit per employee?

- A.
Company B

- B.
Company C

- C.
Company D

- D.
Company A

Answer: Option A

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**Explanation** :

Consider the solution for first question of this set.

Profit / (Average employee) ratio in 2020 for

Income / Expense / Profit

Employees

A = $\frac{{\displaystyle \frac{25}{140+150}}}{2}$ = $\frac{50}{290}$ = $\frac{5}{29}$

B = $\frac{{\displaystyle \frac{50}{240+210}}}{2}$ = $\frac{100}{450}$ = $\frac{2}{9}$

C = $\frac{{\displaystyle \frac{10}{325+325}}}{2}$ = $\frac{20}{650}$ = $\frac{2}{65}$

D = $\frac{{\displaystyle \frac{-30}{410+400}}}{2}$ = -$\frac{60}{810}$

This ratio is highest for Company B.

Hence, option (a).

Workspace:

**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.

**16. CAT 2022 LRDI Slot 2 | LR - Selection & Distribution**

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

Answer: 84

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**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$\left[\frac{50}{x+15}\right]$

⇒ 100x + 1500 – nx – 15x = 100x

⇒ nx + 15x = 1500

⇒ n = $\frac{1500}{x+15}$ ...(1)

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

⇒ 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 = x^{2} + 45x + 450

⇒ x^{2} + 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.

Workspace:

**17. CAT 2022 LRDI Slot 2 | LR - Selection & Distribution**

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

Answer: 40

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**Explanation** :

Consider the solution to first question of this set.

TRICCEK items were sold by Tohri on the first day = 40.

Hence, 40.

Workspace:

**18. CAT 2022 LRDI Slot 2 | LR - Selection & Distribution**

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

Answer: Option B

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**Explanation** :

Consider the solution to first question of this set.

Number of households met by Lahur on 2nd day = 25.

Hence, option (b).

Workspace:

**19. CAT 2022 LRDI Slot 2 | LR - Selection & Distribution**

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

Answer: Option B

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**Explanation** :

Consider the solution to first question of this set.

Number of households met by Tohri on 1st day = 10.

Hence, option (b).

Workspace:

**20. CAT 2022 LRDI Slot 2 | LR - Selection & Distribution**

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: Option D

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**Explanation** :

Consider the solution to first question of this set.

Option (d) is wrong.

Hence, option (d).

Workspace:

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