CAT 2023 Slot 1 DILR Set 4 Q16–Q20

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2023 Slot 1, with 5 questions (Grids & Matrices). Answers are CAT's official key.

The set

This set relies on a figure in the original paper, which is not reproduced here. The questions and answers are below.

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.
[Figure in the original paper]

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 × (road adjacency value) + 3 × (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.

Question 16

How many houses are vacant in Block XX?

TITA: type in the answer. There are no options and no negative marking.

Answer: 3 Grids & Matrices TITA

Solution

  1. Road adjacency: Row-2 houses 1 (C2, D2: 2), C1 and D1: 1, other Row-1 houses 0. The YY minimum of 15 in column E: E2 would need neighbour count 0, forcing both D1 and F1 occupied (two in Row-1 of YY), impossible. So E1 has the parking, base 12, neighbour count 1.
  2. If D1 were the occupied Row-1 house of YY, F2 would be occupied and vacant F1 would quote \(10+3 = 13 < 15\). So F1 and D2 are occupied, D1 vacant. In XX a quote of 24 needs base 10, road 1, neighbours 3: only B2 vacant with A2, C2, B1 occupied; then A1, C1 are vacant.
  3. Block XX: A2, B1, C2 occupied; A1, B2, C1 vacant, i.e. 3 vacant houses.

Question 17

Which of the following houses are definitely occupied?**
  1. A
    F2 and A2
  2. B
    D2 and B2
  3. C
    D2 and B1
  4. D
    A1 and D2

Answer: (C) D2 and B1 Grids & Matrices MCQ

Solution

  1. Road adjacency: Row-2 houses 1 (C2, D2: 2), C1 and D1: 1, other Row-1 houses 0. The YY minimum of 15 in column E: E2 would need neighbour count 0, forcing both D1 and F1 occupied (two in Row-1 of YY), impossible. So E1 has the parking, base 12, neighbour count 1.
  2. If D1 were the occupied Row-1 house of YY, F2 would be occupied and vacant F1 would quote \(10+3 = 13 < 15\). So F1 and D2 are occupied, D1 vacant. In XX a quote of 24 needs base 10, road 1, neighbours 3: only B2 vacant with A2, C2, B1 occupied; then A1, C1 are vacant.
  3. Definitely occupied: A2, B1, C2, D2, F1. F2 may or may not be occupied.
  4. Of the options, only D2 and B1 are both certain.

Question 18

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

Answer: (B) Either 2 or 3 Grids & Matrices MCQ

Solution

  1. Road adjacency: Row-2 houses 1 (C2, D2: 2), C1 and D1: 1, other Row-1 houses 0. The YY minimum of 15 in column E: E2 would need neighbour count 0, forcing both D1 and F1 occupied (two in Row-1 of YY), impossible. So E1 has the parking, base 12, neighbour count 1.
  2. If D1 were the occupied Row-1 house of YY, F2 would be occupied and vacant F1 would quote \(10+3 = 13 < 15\). So F1 and D2 are occupied, D1 vacant. In XX a quote of 24 needs base 10, road 1, neighbours 3: only B2 vacant with A2, C2, B1 occupied; then A1, C1 are vacant.
  3. Row-2: A2, C2, D2 occupied; B2, E2 vacant; F2 undetermined.
  4. So Row-2 has 2 or 3 vacant houses.

Question 19

What is the maximum possible quoted price (in lakhs of Rs.) for a vacant house in Column-E?

TITA: type in the answer. There are no options and no negative marking.

Answer: 21 Grids & Matrices TITA

Solution

  1. Road adjacency: Row-2 houses 1 (C2, D2: 2), C1 and D1: 1, other Row-1 houses 0. The YY minimum of 15 in column E: E2 would need neighbour count 0, forcing both D1 and F1 occupied (two in Row-1 of YY), impossible. So E1 has the parking, base 12, neighbour count 1.
  2. If D1 were the occupied Row-1 house of YY, F2 would be occupied and vacant F1 would quote \(10+3 = 13 < 15\). So F1 and D2 are occupied, D1 vacant. In XX a quote of 24 needs base 10, road 1, neighbours 3: only B2 vacant with A2, C2, B1 occupied; then A1, C1 are vacant.
  3. E1's quote is fixed at 15. E2 has no parking (YY's only one is E1): \(10 + 5\times1 + 3\times n\).
  4. Its neighbours D2 (occupied) and F2 (occupied in the best case) give \(n = 2\): \(10 + 5 + 6 = 21\).

Question 20

Which house in Block YY has parking space?
  1. A
    F2
  2. B
    F1
  3. C
    E2
  4. D
    E1

Answer: (D) E1 Grids & Matrices MCQ

Solution

  1. Road adjacency: Row-2 houses 1 (C2, D2: 2), C1 and D1: 1, other Row-1 houses 0. The YY minimum of 15 in column E: E2 would need neighbour count 0, forcing both D1 and F1 occupied (two in Row-1 of YY), impossible. So E1 has the parking, base 12, neighbour count 1.
  2. E1 with base 12 and one occupied neighbour is the only way to quote 15 in column E, so E1 has YY's only parking space.

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