CAT 2021 Slot 1 · DILR · Set 2: Smoothies Sold by Three Women

The full set and all 4 questions (Q7–Q10) from CAT 2021 Slot 1, with answers and solutions.

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

Finished product

Raw materials required

Mango smoothie

Mango, Milk

Apple smoothie

Apple, Milk

Banana smoothie

Banana, Milk

Mixed fruit smoothie

Mango, Apple, Banana, Milk

Fruit salad

Mango, Apple, Banana

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

Business Hour

Ganga

Kaveri

Narmada

Hour 1

23

19

31

Hour 2

21

22

21

Hour 3

29

30

23

Hour 4 (last hour)

30

27

22

The following additional facts are known.

1. No one except possibly Ganga sold any Mango smoothie.

2. Each woman sold either zero or one unit of any single finished product in any hour.

3. Each woman had exactly one unit each of two different raw materials as leftovers.

4. No one had any banana leftover.

Question 7 · Caselet DI

What BEST can be concluded about the number of units of fruit salad sold in the first hour?
  1. A
    Either 1 or 2.
  2. B
    Either 0 or 1 or 2.
  3. C
    Exactly 2.
  4. D
    Exactly 1.
Pick an option, then check.
Answer & solution

Answer: Option A

Solving the set

Step 1 – Selling price of each product = cost + 2 × (number of raw materials).

Product

Raw materials

Cost (₹)

Profit (₹)

Price (₹)

Mango smoothie (MS)

Mango, Milk

3 + 5 = 8

2 × 2 = 4

12

Apple smoothie (AS)

Apple, Milk

2 + 5 = 7

4

11

Banana smoothie (BS)

Banana, Milk

1 + 5 = 6

4

10

Mixed fruit smoothie (MF)

Mango, Apple, Banana, Milk

11

2 × 4 = 8

19

Fruit salad (FS)

Mango, Apple, Banana

6

2 × 3 = 6

12

Step 2 – Leftovers. Each woman has exactly one unit each of two different raw materials, none of them banana; they are sold at ₹1 below cost.

Leftover pair

Sale value (cost − 1 each)

Total (₹)

Milk + Mango

4 + 2

6

Milk + Apple

4 + 1

5

Mango + Apple

2 + 1

3

Step 3 – Match each hour's revenue. A woman sells at most one unit of each product per hour, and only Ganga may sell Mango smoothies. In Hour 4 the revenue also includes the leftovers.

Hour

Ganga

Kaveri

Narmada

1

23 = MS + AS or AS + FS

19 = MF

31 = MF + FS

2

21 = AS + BS

22 = BS + FS

21 = AS + BS

3

29 = BS + MF

30 = AS + MF

23 = AS + FS

4

30 = MS + FS (24) + Milk & Mango (6)

27 = AS + BS (21) + Milk & Mango (6), or BS + FS (22) + Milk & Apple (5)

22 = MF (19) + Mango & Apple (3)

For example, Narmada's Hour 1 revenue of 31 can only be 19 + 12 (MF + FS), and Kaveri's Hour 1 revenue of 19 can only be MF. Ganga's Hour 1 revenue of 23 can be 12 + 11 (MS + AS) or 11 + 12 (AS + FS).

This question

From the hour-by-hour table, Hour 1 fruit salads: Ganga 0 (MS + AS) or 1 (AS + FS), Kaveri 0, Narmada 1. Total = 1 or 2.

Hence, the answer is option 1.

Question 8 · Caselet DI

Which of the following is NECESSARILY true?
  1. A
    Ganga did not sell any leftover mangoes.
  2. B
    Ganga did not sell any leftover apples.
  3. C
    Narmada sold one unit of leftover milk.
  4. D
    Kaveri sold one unit of leftover mangoes.
Pick an option, then check.
Answer & solution

Answer: Option B

Solving the set

Step 1 – Selling price of each product = cost + 2 × (number of raw materials).

Product

Raw materials

Cost (₹)

Profit (₹)

Price (₹)

Mango smoothie (MS)

Mango, Milk

3 + 5 = 8

2 × 2 = 4

12

Apple smoothie (AS)

Apple, Milk

2 + 5 = 7

4

11

Banana smoothie (BS)

Banana, Milk

1 + 5 = 6

4

10

Mixed fruit smoothie (MF)

Mango, Apple, Banana, Milk

11

2 × 4 = 8

19

Fruit salad (FS)

Mango, Apple, Banana

6

2 × 3 = 6

12

Step 2 – Leftovers. Each woman has exactly one unit each of two different raw materials, none of them banana; they are sold at ₹1 below cost.

Leftover pair

Sale value (cost − 1 each)

Total (₹)

Milk + Mango

4 + 2

6

Milk + Apple

4 + 1

5

Mango + Apple

2 + 1

3

Step 3 – Match each hour's revenue. A woman sells at most one unit of each product per hour, and only Ganga may sell Mango smoothies. In Hour 4 the revenue also includes the leftovers.

Hour

Ganga

Kaveri

Narmada

1

23 = MS + AS or AS + FS

19 = MF

31 = MF + FS

2

21 = AS + BS

22 = BS + FS

21 = AS + BS

3

29 = BS + MF

30 = AS + MF

23 = AS + FS

4

30 = MS + FS (24) + Milk & Mango (6)

27 = AS + BS (21) + Milk & Mango (6), or BS + FS (22) + Milk & Apple (5)

22 = MF (19) + Mango & Apple (3)

For example, Narmada's Hour 1 revenue of 31 can only be 19 + 12 (MF + FS), and Kaveri's Hour 1 revenue of 19 can only be MF. Ganga's Hour 1 revenue of 23 can be 12 + 11 (MS + AS) or 11 + 12 (AS + FS).

This question

Ganga's Hour 4 (₹30) works only as MS + FS + (milk + mango): with milk + apple (5) she would need 25 from products, and with mango + apple (3) she would need 27 – neither can be formed. So her leftovers are milk and mango, and she sold no leftover apples. Narmada's leftovers are mango and apple (no milk), and Kaveri's may be milk + mango or milk + apple.

Hence, the answer is option 2.

Question 9 · Caselet DI

What BEST can be concluded about the total number of units of milk the three women had in the beginning?
  1. A
    Either 19 or 20 units.
  2. B
    Either 18 or 19 or 20 units.
  3. C
    Either 18 or 19 units.
  4. D
    Either 17 or 18 or 19 units.
Pick an option, then check.
Answer & solution

Answer: Option B

Solving the set

Step 1 – Selling price of each product = cost + 2 × (number of raw materials).

Product

Raw materials

Cost (₹)

Profit (₹)

Price (₹)

Mango smoothie (MS)

Mango, Milk

3 + 5 = 8

2 × 2 = 4

12

Apple smoothie (AS)

Apple, Milk

2 + 5 = 7

4

11

Banana smoothie (BS)

Banana, Milk

1 + 5 = 6

4

10

Mixed fruit smoothie (MF)

Mango, Apple, Banana, Milk

11

2 × 4 = 8

19

Fruit salad (FS)

Mango, Apple, Banana

6

2 × 3 = 6

12

Step 2 – Leftovers. Each woman has exactly one unit each of two different raw materials, none of them banana; they are sold at ₹1 below cost.

Leftover pair

Sale value (cost − 1 each)

Total (₹)

Milk + Mango

4 + 2

6

Milk + Apple

4 + 1

5

Mango + Apple

2 + 1

3

Step 3 – Match each hour's revenue. A woman sells at most one unit of each product per hour, and only Ganga may sell Mango smoothies. In Hour 4 the revenue also includes the leftovers.

Hour

Ganga

Kaveri

Narmada

1

23 = MS + AS or AS + FS

19 = MF

31 = MF + FS

2

21 = AS + BS

22 = BS + FS

21 = AS + BS

3

29 = BS + MF

30 = AS + MF

23 = AS + FS

4

30 = MS + FS (24) + Milk & Mango (6)

27 = AS + BS (21) + Milk & Mango (6), or BS + FS (22) + Milk & Apple (5)

22 = MF (19) + Mango & Apple (3)

For example, Narmada's Hour 1 revenue of 31 can only be 19 + 12 (MF + FS), and Kaveri's Hour 1 revenue of 19 can only be MF. Ganga's Hour 1 revenue of 23 can be 12 + 11 (MS + AS) or 11 + 12 (AS + FS).

This question

Woman

Milk used in products

Leftover milk

Total milk

Ganga

Hour 1: 2 or 1; Hour 2: 2; Hour 3: 2; Hour 4: 1 (MS)

1

8 or 7

Kaveri

Hour 1: 1; Hour 2: 1; Hour 3: 2; Hour 4: 2 or 1

1

7 or 6

Narmada

Hour 1: 1; Hour 2: 2; Hour 3: 1; Hour 4: 1

0

5

Total

18, 19 or 20

So the total milk at the start was 18, 19 or 20 units.

Hence, the answer is option 2.

Question 10 · Caselet DI

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?
Answer & solution

Answer: 6

Solving the set

Step 1 – Selling price of each product = cost + 2 × (number of raw materials).

Product

Raw materials

Cost (₹)

Profit (₹)

Price (₹)

Mango smoothie (MS)

Mango, Milk

3 + 5 = 8

2 × 2 = 4

12

Apple smoothie (AS)

Apple, Milk

2 + 5 = 7

4

11

Banana smoothie (BS)

Banana, Milk

1 + 5 = 6

4

10

Mixed fruit smoothie (MF)

Mango, Apple, Banana, Milk

11

2 × 4 = 8

19

Fruit salad (FS)

Mango, Apple, Banana

6

2 × 3 = 6

12

Step 2 – Leftovers. Each woman has exactly one unit each of two different raw materials, none of them banana; they are sold at ₹1 below cost.

Leftover pair

Sale value (cost − 1 each)

Total (₹)

Milk + Mango

4 + 2

6

Milk + Apple

4 + 1

5

Mango + Apple

2 + 1

3

Step 3 – Match each hour's revenue. A woman sells at most one unit of each product per hour, and only Ganga may sell Mango smoothies. In Hour 4 the revenue also includes the leftovers.

Hour

Ganga

Kaveri

Narmada

1

23 = MS + AS or AS + FS

19 = MF

31 = MF + FS

2

21 = AS + BS

22 = BS + FS

21 = AS + BS

3

29 = BS + MF

30 = AS + MF

23 = AS + FS

4

30 = MS + FS (24) + Milk & Mango (6)

27 = AS + BS (21) + Milk & Mango (6), or BS + FS (22) + Milk & Apple (5)

22 = MF (19) + Mango & Apple (3)

For example, Narmada's Hour 1 revenue of 31 can only be 19 + 12 (MF + FS), and Kaveri's Hour 1 revenue of 19 can only be MF. Ganga's Hour 1 revenue of 23 can be 12 + 11 (MS + AS) or 11 + 12 (AS + FS).

This question

Three leftover mangoes: Ganga (milk + mango) and Narmada (mango + apple) have one each, so Kaveri's leftover is milk + mango and her Hour 4 sales are AS + BS.

Apple smoothies: Ganga – Hours 1 and 2 (2); Kaveri – Hours 3 and 4 (2); Narmada – Hours 2 and 3 (2). Total 6.

Hence, the answer is 6.

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