Housing Complex Pricing and Vacancy

CAT 2023 Slot 1 · DILR · Hard · Logical Reasoning

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Passage / data set

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 (Columns A, B, C) and Block YY (Columns D, E, F). The diagram also shows two roads, one passing in front of the houses in Row-2 and another between the two blocks (between Column-C and Column-D).

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: Quoted Price=Base Price+5×(Road Adjacency Value)+3×(Neighbour Count)\text{Quoted Price} = \text{Base Price} + 5 \times (\text{Road Adjacency Value}) + 3 \times (\text{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 1 of 5

How many houses are vacant in Block XX?

Answer

5

Explanation

Block XX has 6 houses total. Row-1 has 1 occupied house in Block XX (specifically B1). The remaining 5 houses in Block XX are vacant.

Question 2 of 5

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

Explanation

From constraint analysis: Row-1 has 1 occupied house in Block XX (B1) and 1 in Block YY (F1). In Row-2, D2 must be occupied to satisfy the neighbor counts and price constraints in Block YY. Thus, D2 and B1 are definitely occupied.

Question 3 of 5

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

Explanation

Row-2 has 6 houses. D2 is occupied. F2 may or may not be occupied depending on the case. Thus, Row-2 has either 2 or 3 vacant houses.

Question 4 of 5

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

Answer

23

Explanation

For house E2: Road Adjacency = 1 (bottom road). Maximum Neighbour Count = 2 (if both D2 and F2 are occupied). Base price with parking = 12 lakhs. Max price = 12+5(1)+3(2)=2312 + 5(1) + 3(2) = 23 lakhs.

Question 5 of 5

Which house in Block YY has parking space?

  1. A.

    F2

  2. B.

    F1

  3. C.

    E2

  4. D.

    E1

Answer

A

Explanation

To satisfy the minimum price constraint of 15 lakhs for a house in Column-E (E1) without parking, and accounting for the single parking space in Block YY, the parking space must belong to F2.

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