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CAT 2023 Slot 1 DILR · Set 4 of 4Logical ReasoningHard DifficultyQ16–Q20 · 3 MCQ + 2 TITA

CAT 2023 Slot 1 DILR Set 4: Grids (5 Questions) with Solutions

The Grids set from the official CAT 2023 Slot 1 DILR paper: the caselet, all 5 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 2023 Slot 1 DILR · Questions 16–20
The schematic diagram below shows 12 rectangular houses in a housing complex. House numbers are mentioned in the rectangles representing the houses. The houses are located in six columns – Column-A through Column-F, and two rows – Row-1 and Row-2. The houses are divided into two blocks - Block XX and Block YY. The diagram also shows two roads, one passing in front of the houses in Row-2 and another between the two blocks.
Some of the houses are occupied. The remaining ones are vacant and are the only ones available for sale.
The road adjacency value of a house is the number of its sides adjacent to a road. For example, the road adjacency values of C2, F2, and B1 are 2, 1, and 0, respectively. The neighbour count of a house is the number of sides of that house adjacent to occupied houses in the same block. For example, E1 and C1 can have the maximum possible neighbour counts of 3 and 2, respectively.
The base price of a vacant house is Rs. 10 lakhs if the house does not have a parking space, and Rs. 12 lakhs if it does. The quoted price (in lakhs of Rs.) of a vacant house is calculated as (base price) + 5 ×\times (road adjacency value) + 3 ×\times (neighbour count).
The following information is also known.
1
The maximum quoted price of a house in Block XX is Rs. 24 lakhs. The minimum quoted price of a house in block YY is Rs. 15 lakhs, and one such house is in Column-E.
2
Row-1 has two occupied houses, one in each block.
3
Both houses in Column-E are vacant. Each of Column-D and Column-F has at least one occupied house.
4
There is only one house with parking space in Block YY.
Official Reference Chart - CAT 2023 Slot 1 Official Reference Chart - CAT 2023 Slot 1

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

Q16. Grids

TITA · +3 / 0
How many houses are vacant in Block XX? (in numerial value)
Correct Answer
3
Step-by-step solution
📌 Core Concept
Work out the road adjacency of each house, then use the price clues to fix which houses are occupied. The maximum price of 24 in Block XX is the key.
🔢 Step-by-Step Solution
1
Road adjacency values: A1, B1 and E1 are 0. C1, D1 and every house in Row-2 are 1, except C2 and D2, which touch both roads and have 2. F1 is 0 and F2 is 1.
2
A quoted price is base+5r+3n\text{base} + 5r + 3n. In Block XX, a price of 24 needs base 10 with 5r+3n=145r + 3n = 14. The only solution is r=1r = 1, n=3n = 3. A base of 12 would need 5r+3n=125r + 3n = 12, which has no valid solution.
3
A house with r=1r = 1 and three occupied neighbours must be in Row-2 with neighbours on both sides and above. That house is B2, with A2, C2 and B1 all occupied and B2 itself vacant.
4
Clue 2 says Row-1 has only one occupied house in each block. B1 is that house, so A1 and C1 are vacant.
5
Vacant houses in Block XX: A1, C1 and B2.
Quick Check
C1 costs 10+5+3×2=2110 + 5 + 3\times 2 = 21, or 23 with parking. A1 costs at most 18. Both are below 24, so the maximum of 24 comes only from B2.
Correct Answer: 3

Q17. Grids

MCQ · +3 / −1
Which of the following houses is definitely occupied?
  1. A) B1
  2. B) D1
  3. C) F2
  4. D) A1
Correct Answer
A) B1
Step-by-step solution
📌 Core Concept
Fix the occupied houses in Block XX from the maximum-price clue. Then check each option against what is forced.
🔢 Step-by-Step Solution
1
In Block XX a quoted price of 24 is only possible as 10+5×1+3×310 + 5\times 1 + 3\times 3. That is a no-parking house with r=1r = 1 and three occupied neighbours.
2
Only B2 has road adjacency 1 and three neighbours (A2, C2, B1). So B2 is vacant, and A2, C2 and B1 are occupied.
3
B1 is therefore occupied in every valid arrangement.
4
Clue 2 allows only one occupied house in Row-1 of Block XX. With B1 occupied, A1 is vacant.
5
In Block YY, clue 3 (Column-E vacant, Columns D and F each with an occupied house) and the minimum of 15 give D1 vacant, with F1 and D2 occupied. F2 can be either.
Why Not the Others
D1: vacant. If D1 were occupied, F1 and E1 would be vacant with prices of at most 15 each, and the minimum of 15 would need two parking houses. Clue 4 allows only one.
F2: not forced. It can be occupied or vacant.
A1: vacant, because B1 is the only occupied house in Row-1 of Block XX.
Correct Answer: A

Q18. Grids

MCQ · +3 / −1
Which of the following options best describes the number of vacant houses in Row-2?
  1. A) Either 3 or 4
  2. B) Either 2 or 3
  3. C) Exactly 3
  4. D) Exactly 2
Correct Answer
B) Either 2 or 3
Step-by-step solution
📌 Core Concept
Find which Row-2 houses are forced vacant in each block. Then see which house is left undetermined.
🔢 Step-by-Step Solution
1
Block XX: the maximum price of 24 forces B2 vacant, with A2, C2 and B1 occupied. So Row-2 has exactly one vacant house in Block XX, B2.
2
Block YY: Column-E is vacant (clue 3), so E2 is vacant.
3
If D1 were occupied, F1 and E1 would be vacant. F1 would cost at most 10+3=1310 + 3 = 13 or 12+3=1512 + 3 = 15, and E1 would cost similarly. The minimum of 15 would then need both to have parking, but clue 4 allows only one parking house. So F1 is occupied (the Row-1 house in Block YY), D1 is vacant, and Column-D needs D2 occupied.
4
F2 is not fixed. Column-F already has F1 occupied. If F2 is occupied, E2 costs 10+5+6=2110 + 5 + 6 = 21. If F2 is vacant, E2 costs 18, F2 costs 18 or 20, and the minimum of 15 still comes from E1. Both cases fit every clue.
5
Vacant houses in Row-2: B2 and E2, plus F2 if it is vacant. That makes 2 or 3.
Why Not the Others
Option A (3 or 4) and C (exactly 3): the count can be 2.
Option D (exactly 2): the count can be 3.
Correct Answer: B

Q19. Grids

TITA · +3 / 0
What is the maximum possible quoted price (in lakhs of Rs.) for a vacant house in Column-E? (in numerial value)
Correct Answer
21
Step-by-step solution
📌 Core Concept
For each vacant Column-E house, price it with the occupied neighbours that the clues allow. Take the largest.
🔢 Step-by-Step Solution
1
Block YY: Row-1 has one occupied house, and E1 is vacant, so it is D1 or F1. If D1 is occupied, then F1 and E1 are vacant, and each costs at most 15. The minimum of 15 would then need both to have parking, but clue 4 allows only one parking house. So F1 is occupied and D2 is occupied (Column-D needs an occupied house). D1 is vacant.
2
E1: road adjacency 0, and its only occupied neighbour is F1. Its price is 10+0+3=1310 + 0 + 3 = 13 without parking, or 12+3=1512 + 3 = 15 with parking. The minimum of 15 sits in Column-E, so E1 has parking and costs 15.
3
E2: road adjacency 1 gives 5. D2 is occupied. F2 may also be occupied.
4
With F2 vacant, E2 costs 10+5+3=1810 + 5 + 3 = 18. With F2 occupied, E2 costs 10+5+3×2=2110 + 5 + 3\times 2 = 21. E2 has no parking, because E1 has the only parking space in Block YY.
5
The maximum possible price in Column-E is 21.
Correct Answer: 21

Q20. Grids

MCQ · +3 / −1
Which house in Block YY has parking space?
  1. A) F1
  2. B) E2
  3. C) E1
  4. D) F2
Correct Answer
C) E1
Step-by-step solution
📌 Core Concept
The minimum quoted price of 15 in Block YY sits in Column-E. That price can only be reached with parking, and only one house in the block has parking.
🔢 Step-by-Step Solution
1
Row-1 has one occupied house in Block YY. E1 is vacant (clue 3), so it is D1 or F1.
2
Suppose D1 is occupied. Then E1 and F1 are vacant, and F2 must be occupied for Column-F. E1 has 0 road sides and costs 10+3×1=1310 + 3\times 1 = 13 or 15. F1 has 0 road sides and one occupied neighbour (F2), so it also costs 13 or 15. A minimum of exactly 15 would need both to have parking, which clue 4 forbids.
3
So F1 is occupied and D2 is occupied (Column-D needs an occupied house). D1 is vacant and costs at least 18.
4
E1 has road adjacency 0 and one occupied neighbour (F1). Without parking it costs 10+3=1310 + 3 = 13, which is below 15. With parking it costs 12+3=1512 + 3 = 15.
5
E2 costs at least 10+5+3=1810 + 5 + 3 = 18, and D1 costs at least 18. Neither can be the minimum of 15 in Column-E, so E1 must be the minimum house and must have the parking space.
Why Not the Others
F1 is occupied.
E2 and F2 cost at least 18 without parking, so parking there cannot produce the minimum of 15 in Column-E.
Correct Answer: C
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CAT 2023 Slot 1 DILR at a Glance

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

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