CAT 2023 Set-1 | Data Interpretation and Logical Reasoning | Question: 6

Question

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-$\text{A}$ through Column-$\text{F}$, and two rows - Row-$1$ and Row- $2$. The houses are divided into two blocks - Block $\text{XX}$ and Block $\text{YY}$. 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 $\text{C}2$, $\text{F}2$, and $\text{B}1$ 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, $\mathrm{E} 1$ and $\mathrm{C} 1$ 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 $\text{XX}$ is Rs. $24$ lakhs. The minimum quoted price of a house in block $\text{YY}$ is Rs. $15$ lakhs, and one such house is in Column$\text{E}$.
2. Row-$1$ has two occupied houses, one in each block.
3. Both houses in Column-$\text{E}$ are vacant. Each of Column-$\text{D}$ and Column-$\text{F}$ has at least one occupied house.
4. There is only one house with parking space in Block $\text{YY}$.

How many houses are vacant in Block XX?