CAT 2023 Slot 1 — DILR Question 12

Linear ArrangementEasy

Passage / Data

Answer the following questions based on the information given 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.

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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.

Which of the following houses is definitely occupied?

[Two options are correct in this question and both were accepted as correct answer by IIM Lucknow]

Answer & solution

A
D2
B
F2
B1
D
A1

Solution

Easy

Use the shared set-up and read off which houses are forced to be occupied (not "maybe").

From the master solve: occupied for certain $= A2,\ B1,\ C2$ (Block XX) and $D2,\ F1$ (Block YY). The only uncertain house is $F2$ .

Test each option against the certainties.

\begin{aligned} &D2:\ \text{occupied (column D needs an occupant, } D1 \text{ vacant)} \;\checkmark\\ &F2:\ \text{undetermined — could be vacant} \;\times\\ &B1:\ \text{occupied (neighbour of } B2, \text{ and the XX Row-1 occupant)} \;\checkmark\\ &A1:\ \text{vacant} \;\times \end{aligned}

Both $D2$ and $B1$ are definitely occupied. IIM Lucknow accepted two correct options for this question; our stored key marks $B1$ .

$B1$ (and $D2$ ) — definitely occupied.