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CAT 2018 Slot 2 DILR · Set 6 of 8Logical ReasoningHard DifficultyQ21–Q24 · 4 MCQ

CAT 2018 Slot 2 DILR Set 6: Grids (4 Questions) with Solutions

The Grids set from the official CAT 2018 Slot 2 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 2018 Slot 2 DILR · Questions 21–24
Each of the 23 boxes in the picture below represents a product manufactured by one of the following three companies: Alfa, Bravo and Charlie. The area of a box is proportional to the revenue from the corresponding product, while its centre represents the Product popularity and Market potential scores of the product (out of 20). The shadings of some of the boxes have got erased.
The companies classified their products into four categories based on a combination of scores (out of 20) on the two parameters - Product popularity and Market potential as given below:
PromisingBlockbusterDoubtfulNo-hope
Product popularity score> 10> 10≤ 10≤ 10
Market potential score> 10≤ 10> 10≤ 10
The following facts are known:
1
Alfa and Bravo had the same number of products in the Blockbuster category.
2
Charlie had more products than Bravo but fewer products than Alfa in the No-hope category.
3
Each company had an equal number of products in the Promising category.
4
Charlie did not have any product in the Doubtful category, while Alfa had one product more than Bravo in this category.
5
Bravo had a higher revenue than Alfa from products in the Doubtful category.
6
Charlie had a higher revenue than Bravo from products in the Blockbuster category.
7
Bravo and Charlie had the same revenue from products in the No-hope category.
8
Alfa and Charlie had the same total revenue considering all products.
Official Reference Chart - CAT 2018 Slot 2 Official Reference Chart - CAT 2018 Slot 2

In the exam this set competed with 7 others for 60 minutes. Budget about 8 minutes if you attempt it.

Q21. Grids

MCQ · +3 / −1
Considering all companies' products, which product category had the highest revenue?
  1. A) Blockbuster
  2. B) Doubtful
  3. C) No-hope
  4. D) Promising
Correct Answer
A) Blockbuster
Step-by-step solution
📌 Core Concept
Place each box in a category using its centre (popularity, potential) against the cut-off of 10. Treat area as revenue, with the smallest box (1×1) as 1 unit. Use facts 1 to 8 to assign the unshaded boxes to companies.
🔢 Step-by-Step Solution
1
Promising (both scores > 10) has 3 boxes, of areas 2, 9 and 3. Fact 3 gives one box to each company.
2
Doubtful (popularity ≤ 10, potential > 10) has 7 boxes. The shaded ones are Alfa 4 and 1, and Bravo 6 and 2. The unshaded ones have areas 9, 6 and 1. Fact 4 gives Charlie none and Alfa one more than Bravo, so Alfa has 4 boxes and Bravo 3. Bravo therefore takes one unshaded box and Alfa takes two. Fact 5 (Bravo's revenue is higher) holds only if Bravo takes the 9: Bravo = 17 against Alfa = 5 + 6 + 1 = 12. Doubtful total = 29.
3
Blockbuster (popularity > 10, potential ≤ 10) has 7 boxes. Alfa has 3 and 6, Bravo has 6, and Charlie has 6 and 2. The unshaded boxes are 4 and 9. Fact 1 (Alfa and Bravo have equal counts) gives one unshaded box to Bravo and one to Charlie. Fact 6 (Charlie's revenue is higher) holds only if Charlie takes the 9: Charlie = 17 against Bravo = 10. Alfa = 9. Blockbuster total = 9 + 10 + 17 = 36.
4
No-hope (both scores ≤ 10) has 6 boxes. Alfa has 2, 1 and 4, and Bravo has 4. The unshaded boxes are 1 and 3. Fact 2 (Bravo < Charlie < Alfa) forces both unshaded boxes to Charlie. Both Bravo and Charlie then have revenue 4, which matches fact 7. No-hope total = 7 + 4 + 4 = 15.
5
Promising total = 2 + 9 + 3 = 14.
6
Revenues are Blockbuster 36, Doubtful 29, No-hope 15 and Promising 14. Blockbuster is the highest.
Quick Check
Charlie's total is 17 + 4 + 9 = 30, and Alfa's is 12 + 9 + 7 + 2 = 30. This matches fact 8.
Correct Answer: A

Q22. Grids

MCQ · +3 / −1
Which of the following statements is NOT correct?
  1. A) Alfa's revenue from Blockbuster products was the same as Charlie's revenue from Promising products.
  2. B) The total revenue from No-hope products was less than the total revenue from Doubtful products.
  3. C) Bravo's revenue from Blockbuster products was greater than Alfa's revenue from Doubtful products.
  4. D) Bravo and Charlie had the same revenues from No-hope products.
Correct Answer
C) Bravo's revenue from Blockbuster products was greater than Alfa's revenue from Doubtful products.
Step-by-step solution
📌 Core Concept
Work out each company's revenue in every category, taking the smallest box as 1 unit. Then test each statement against those figures.
🔢 Step-by-Step Solution
1
Doubtful (7 boxes): Alfa has 4 + 1 + 6 + 1 = 12 and Bravo has 6 + 2 + 9 = 17. Fact 4 (Alfa has one more box than Bravo) and fact 5 (Bravo earns more) force Bravo to take the unshaded 9-box. The other two unshaded boxes (6 and 1) go to Alfa. Charlie has none.
2
Blockbuster (7 boxes): Alfa has 3 + 6 = 9. Bravo has 6 plus one unshaded box. Charlie has 6 + 2 plus the other unshaded box. The unshaded boxes are 4 and 9. Fact 1 gives Bravo one of them, and fact 6 requires Charlie to take the 9. So Bravo = 6 + 4 = 10 and Charlie = 8 + 9 = 17.
3
No-hope (6 boxes): Alfa has 2 + 1 + 4 = 7 and Bravo has 4. Fact 2 (Bravo < Charlie < Alfa) puts both unshaded boxes (1 and 3) with Charlie, so Charlie = 4. This matches fact 7.
4
Promising (3 boxes, areas 2, 9 and 3): fact 8 requires Alfa's total to equal Charlie's. Alfa has 12 + 9 + 7 = 28 plus a Promising box. Charlie has 17 + 4 = 21 plus a Promising box. The gap of 7 is met by Alfa taking the 2 and Charlie taking the 9. Both totals are then 30. Bravo takes the 3.
5
Test each statement:
A: Alfa's Blockbuster revenue is 9 and Charlie's Promising revenue is 9. This is correct.
B: No-hope total is 15 and Doubtful total is 29. This is correct.
C: Bravo's Blockbuster revenue is 10 and Alfa's Doubtful revenue is 12. 10 is not greater than 12, so the statement is wrong.
D: Bravo and Charlie each have 4 from No-hope. This is correct.
Why Not the Others
A, B and D match the computed revenues, so they are correct statements and cannot be the answer.
Correct Answer: C

Q23. Grids

MCQ · +3 / −1
Which of the following is the correct sequence of numbers of products Bravo had in No-hope, Doubtful, Promising and Blockbuster categories respectively?
  1. A) 2 , 3 , 1 , 2
  2. B) 1 , 3 , 1 , 2
  3. C) 3 , 3 , 1 , 2
  4. D) 1 , 3 , 1 , 3
Correct Answer
B) 1 , 3 , 1 , 2
Step-by-step solution
📌 Core Concept
Count Bravo's boxes in each category. The red boxes fix part of the count, and the facts assign the unshaded boxes.
🔢 Step-by-Step Solution
1
Promising (both scores > 10): the chart has 3 such boxes. Fact 3 gives each company an equal number, so Bravo has 1.
2
Doubtful (popularity ≤ 10, potential > 10): Bravo has two red boxes, with areas 6 and 2. There are 7 boxes in all, and three of them are unshaded, with areas 9, 6 and 1. Fact 4 gives Charlie none and Alfa one more than Bravo, so Alfa has 4 and Bravo has 3. Bravo therefore needs one unshaded box. Fact 5 (Bravo earns more than Alfa) holds only if Bravo takes the 9: Bravo = 17 against Alfa = 5 + 6 + 1 = 12. Bravo has 3.
3
Blockbuster (popularity > 10, potential ≤ 10): there are 7 boxes. Alfa has 2 shaded, Bravo has 1 red and Charlie has 2. Two boxes are unshaded. Fact 1 (Alfa and Bravo equal) makes Alfa 2 and Bravo 2, so Bravo takes one unshaded box and Charlie takes the other. Bravo has 2. Fact 6 then puts the 9-box with Charlie and the 4-box with Bravo.
4
No-hope (both scores ≤ 10): there are 6 boxes. Alfa has 3 shaded and Bravo has 1 red. Two boxes are unshaded. Fact 2 (Bravo < Charlie < Alfa) needs Bravo = 1, Charlie = 2 and Alfa = 3. This gives Bravo 1.
5
In the order No-hope, Doubtful, Promising, Blockbuster, Bravo has 1, 3, 1, 2.
Why Not the Others
A and C give Bravo 2 or 3 No-hope boxes. Charlie could then not sit strictly between Bravo and Alfa, which breaks fact 2.
D gives 3 Blockbuster boxes, which breaks fact 1 given Alfa's 2.
Correct Answer: B

Q24. Grids

MCQ · +3 / −1
If the smallest box on the grid is equivalent to revenue of Rs.1 crore, then what approximately was the total revenue of Bravo in Rs. crore?
  1. A) 30
  2. B) 24
  3. C) 40
  4. D) 34
Correct Answer
D) 34
Step-by-step solution
📌 Core Concept
Bravo's revenue is the total area of its boxes, with the smallest box (1×1) taken as 1 crore. Bravo's red boxes are known from the chart. Its unshaded boxes must be found from the facts.
🔢 Step-by-Step Solution
1
Bravo's red boxes are:
Doubtful: areas 6 and 2.
Blockbuster: the 2×3 box, area 6.
No-hope: the 2×2 box, area 4.
2
Doubtful (7 boxes): the unshaded boxes have areas 9, 6 and 1. Fact 4 gives Charlie none and Alfa one more box than Bravo, so Alfa has 4 and Bravo has 3. Bravo therefore needs exactly one unshaded box. Fact 5 (Bravo earns more than Alfa) works only with the 9: Bravo = 6 + 2 + 9 = 17 against Alfa = 4 + 1 + 6 + 1 = 12. Taking the 6 or the 1 would leave Bravo behind.
3
Blockbuster: Alfa has 3 + 6 = 9 and Charlie has 6 + 2 = 8. Fact 1 (Alfa and Bravo equal in count) lets Bravo take one of the unshaded boxes, 4 or 9. Charlie takes the other. Fact 6 (Charlie earns more than Bravo) requires Charlie to take the 9. Bravo takes the 4, so Bravo's Blockbuster revenue is 6 + 4 = 10.
4
No-hope: fact 2 (Bravo < Charlie < Alfa) puts the unshaded boxes (1 and 3) with Charlie. Bravo has only its 4. Fact 7 is satisfied, since Charlie also has 4.
5
Promising: Alfa's total equals Charlie's (fact 8). That needs Alfa to take the 2 and Charlie the 9, which leaves Bravo with the 3.
6
Bravo's total = 17 + 10 + 4 + 3 = 34 crore.
Quick Check
Alfa's total is 12 + 9 + 7 + 2 = 30 and Charlie's is 17 + 4 + 9 = 30. This matches fact 8.
Correct Answer: D
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CAT 2018 Slot 2 DILR at a Glance

Sets in this section8
Questions in this section32
Section time60 minutes
Convenor IIMIIM Calcutta

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