ThinkCAT Logo
ThinkCAT
Sign up
QuestionsMocksResourcesAnalytics
CAT 2021 Slot 1 DILR · Set 2 of 4Logical ReasoningHard DifficultyQ5–Q8 · 3 MCQ + 1 TITA

CAT 2021 Slot 1 DILR Set 2: Arrangements (4 Questions) with Solutions

The Arrangements set from the official CAT 2021 Slot 1 DILR paper: the caselet, all 4 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2021 Slot 1 DILR · Questions 5–8
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.
Finished productRaw materials required
Mango smoothieMango, Milk
Apple smoothieApple, Milk
Banana smoothieBanana, Milk
Mixed fruit smoothieMango, Apple, Banana, Milk
Fruit saladMango, 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.
Business HourGangaKaveriNarmada
Hour 1231931
Hour 2212221
Hour 3293023
Hour 4 (last hour)302722
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.

In the exam this set competed with 3 others for 40 minutes. Budget about 10 minutes if you attempt it.

Q5. Arrangements

MCQ · +3 / −1
What BEST can be concluded about the number of units of fruit salad sold in the first hour?
  1. A) Exactly 2
  2. B) Either 0 or 1 or 2
  3. C) Either 1 or 2
  4. D) Exactly 1
Correct Answer
C) Either 1 or 2
Step-by-step solution
📌 Core Concept
Work out each product's selling price and each woman's leftover value. Then match every hourly revenue to the only product combination that gives that sum.
🔢 Step-by-Step Solution
1
Selling price = cost + profit. Mango smoothie: 8 + 4 = 12. Apple smoothie: 7 + 4 = 11. Banana smoothie: 6 + 4 = 10. Mixed fruit smoothie: 11 + 8 = 19. Fruit salad: 6 + 6 = 12.
2
Leftovers sell at cost − 1: milk 4, mango 2, apple 1, banana 0. No banana is left over, so each woman's two different leftovers are milk+mango (6), milk+apple (5) or mango+apple (3).
3
Kaveri and Narmada cannot sell mango smoothie. Their possible sums are: 19 = mixed fruit smoothie alone, 22 = banana smoothie + fruit salad, 30 = apple smoothie + mixed fruit smoothie, 21 = apple smoothie + banana smoothie, 23 = apple smoothie + fruit salad, 31 = mixed fruit smoothie + fruit salad.
4
Hour 1 for Narmada is 31, which only works as mixed fruit smoothie + fruit salad. That is 1 fruit salad.
5
Hour 1 for Kaveri is 19, which is mixed fruit smoothie alone. That is 0 fruit salad.
6
Hour 1 for Ganga is 23. Only 11 + 12 gives 23, so she sold an apple smoothie plus either a mango smoothie or a fruit salad, both priced 12. She sold 0 or 1 fruit salad, and the data do not decide which.
7
Total fruit salads in hour 1 = 1 (Narmada) + 0 (Kaveri) + 0 or 1 (Ganga) = 1 or 2.
Why Not the Others
A: Ganga could have sold a mango smoothie instead, giving only 1.
B: Narmada's fruit salad is certain, so 0 is impossible.
D: Ganga's choice could add a second unit, so exactly 1 is not guaranteed.
Correct Answer: C

Q6. Arrangements

MCQ · +3 / −1
Which of the following is NECESSARILY true?
  1. A) Narmada sold one unit of leftover milk.
  2. B) Ganga did not sell any leftover mangoes.
  3. C) Ganga did not sell any leftover apples.
  4. D) Kaveri sold one unit of leftover mangoes
Correct Answer
C) Ganga did not sell any leftover apples.
Step-by-step solution
📌 Core Concept
Find each woman's leftover pair from her last-hour revenue. Then test each option against those pairs.
🔢 Step-by-Step Solution
1
Selling prices are: mango smoothie 12, apple smoothie 11, banana smoothie 10, mixed fruit smoothie 19, fruit salad 12. Leftovers sell at milk 4, mango 2, apple 1. The possible leftover pairs are milk+mango (6), milk+apple (5) and mango+apple (3).
2
Ganga's hour-4 revenue is 30. Her product sales must be 30 − 6, 30 − 5 or 30 − 3, which is 24, 25 or 27. Only 24 can be made (mango smoothie 12 + fruit salad 12). So her leftovers are milk and mango.
3
Narmada's hour-4 revenue is 22, so her product sales are 16, 17 or 19. Only 19 can be made (mixed fruit smoothie alone). So her leftovers are mango and apple, with no milk.
4
Kaveri's hour-4 revenue is 27, so her product sales are 21 or 22. 21 is apple smoothie + banana smoothie, which means milk+mango left over. 22 is banana smoothie + fruit salad, which means milk+apple left over. Both are possible.
5
Check the options:
A is false, because Narmada has no leftover milk.
B is false, because Ganga's leftovers are milk and mango, so she sold a leftover mango.
C is true, because apple is not in Ganga's pair.
D is not forced, because Kaveri may have apple left over instead of mango.
Correct Answer: C

Q7. Tables

MCQ · +3 / −1
What BEST can be concluded about the total number of units of milk the three women had in the beginning?
  1. A) Either 17 or 18 or 19 units.
  2. B) Either 19 or 20 units.
  3. C) Either 18 or 19 units.
  4. D) Either 18 or 19 or 20 units.
Correct Answer
D) Either 18 or 19 or 20 units.
Step-by-step solution
📌 Core Concept
Fix each woman's hourly sales from the revenue figures. Then count the milk used in products plus the leftover milk, and note which cases remain open.
🔢 Step-by-Step Solution
1
Selling prices are: mango smoothie 12, apple smoothie 11, banana smoothie 10, mixed fruit smoothie 19, fruit salad 12. Every product uses milk except fruit salad.
2
Ganga: hour 1 is 23 = apple smoothie + (mango smoothie or fruit salad). Hour 2 is 21 = apple + banana smoothie. Hour 3 is 29 = banana smoothie + mixed fruit smoothie. Hour 4 is 24 + leftovers 6 = mango smoothie + fruit salad, with milk+mango left over. Her milk is (2 or 1) + 2 + 2 + 1 + 1 leftover = 8 or 7.
3
Narmada: hour 1 is 31 = mixed fruit smoothie + fruit salad. Hour 2 is 21 = apple + banana smoothie. Hour 3 is 23 = apple smoothie + fruit salad. Hour 4 is 19 = mixed fruit smoothie, with mango+apple left over. Her milk is 1 + 2 + 1 + 1 = 5.
4
Kaveri: hour 1 is 19 = mixed fruit smoothie. Hour 2 is 22 = banana smoothie + fruit salad. Hour 3 is 30 = apple smoothie + mixed fruit smoothie. Hour 4 is 27 and has two cases. Case (i) is apple + banana smoothie plus milk+mango left over, giving milk 1 + 1 + 2 + 2 + 1 = 7. Case (ii) is banana smoothie + fruit salad plus milk+apple left over, giving milk 1 + 1 + 2 + 1 + 1 = 6.
5
Total milk = (7 or 8) + (6 or 7) + 5. The possible totals are 18, 19 and 20, and all three can occur.
Correct Answer: D

Q8. Arrangements

TITA · +3 / 0
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?
Correct Answer
6
Step-by-step solution
📌 Core Concept
Deduce each woman's sales and leftovers from the revenues. The extra fact about mango leftovers then settles Kaveri's ambiguous last hour.
🔢 Step-by-Step Solution
1
Selling prices are: mango smoothie 12, apple smoothie 11, banana smoothie 10, mixed fruit smoothie 19, fruit salad 12. Leftovers sell at milk 4, mango 2, apple 1. So the possible leftover pairs are milk+mango (6), milk+apple (5) and mango+apple (3).
2
Ganga's hour 4 is 30. The only match is mango smoothie + fruit salad (24) with milk+mango left over. Her hour 2 is 21 = apple + banana smoothie, and her hour 1 is 23 = apple smoothie + one 12-priced item. Her hour 3 is 29 = banana smoothie + mixed fruit smoothie. That gives her 2 apple smoothies.
3
Narmada's hour 4 is 22, so her product sales must be 19 = mixed fruit smoothie, with mango+apple left over. Her hour 2 is 21 = apple + banana smoothie, and her hour 3 is 23 = apple smoothie + fruit salad. That gives her 2 apple smoothies.
4
Kaveri's hour 3 is 30 = apple smoothie + mixed fruit smoothie, which is 1 apple smoothie. Her hour 4 is 27, which is either apple + banana smoothie with milk+mango left over, or banana smoothie + fruit salad with milk+apple left over.
5
Ganga and Narmada together sold 2 leftover mangoes. Three leftover mangoes in total means Kaveri also had mango left over. That is the first case, so Kaveri sold an apple smoothie in hour 4 as well. That gives her 2 apple smoothies.
6
Apple smoothies sold = 2 + 2 + 2 = 6.
Correct Answer: 6
Timed Practice

Attempt the full CAT 2021 Slot 1 paper as a free mock

All three sections, 120 minutes, in the TCS iON-style simulator. Free, no sign-up.

Start Free Mock

CAT 2021 Slot 1 DILR at a Glance

Sets in this section4
Questions in this section20
Section time40 minutes
Convenor IIMIIM Ahmedabad

More CAT DILR Sets with Solutions