Question:medium
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.
![12 rectangular houses in a housing complex. House numbers are mentioned in the rectangles representing the houses]()
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.
How many houses are vacant in Block XX? [This question was asked as TITA]
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.
![12 rectangular houses in a housing complex. House numbers are mentioned in the rectangles representing the houses]()
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.
How many houses are vacant in Block XX? [This question was asked as TITA]
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.
How many houses are vacant in Block XX? [This question was asked as TITA]
Updated On: Nov 25, 2025
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The Correct Option is C
Solution and Explanation
The process to identify vacant houses in Block XX is as follows.
1. The houses are segregated into two blocks: Block XX (Columns A, B, C) and Block YY (Columns D, E, F).
2. For Block XX, the maximum quoted price is ₹24 lakhs.
3. For Block YY, the minimum quoted price is ₹15 lakhs, and only houses in Column E are vacant.
4. Row-1 contains two occupied houses, one in each block.
5. Columns D and F each have at least one occupied house, confirming at least one occupied house in Block YY.
6. Vacant houses will be marked based on their base price (₹10 lakhs without parking, ₹12 lakhs with parking if specified).
7. Evaluate potential vacant houses in Block XX that meet the price criteria. Assume maximum road adjacency and neighbor counts to determine the highest possible quotes in Block XX.
8. If Block XX houses exhibit maximum occupancy and matching prices, deduce the occupancy of others based on vacancy indicators: C1 or C2 might have maximized adjacency, leading to their vacancy.
9. Consequently, the vacant houses in Block XX are: A1, B1, C1.
Therefore, Block XX has 3 vacant houses.
1. The houses are segregated into two blocks: Block XX (Columns A, B, C) and Block YY (Columns D, E, F).
2. For Block XX, the maximum quoted price is ₹24 lakhs.
3. For Block YY, the minimum quoted price is ₹15 lakhs, and only houses in Column E are vacant.
4. Row-1 contains two occupied houses, one in each block.
5. Columns D and F each have at least one occupied house, confirming at least one occupied house in Block YY.
6. Vacant houses will be marked based on their base price (₹10 lakhs without parking, ₹12 lakhs with parking if specified).
| Column | House | Occupied |
|---|---|---|
| A | A1, A2 | No occupancy info |
| B | B1, B2 | No occupancy info |
| C | C1, C2 | No occupancy info |
| D | D1, D2 | At least one |
| E | E1, E2 | Both vacant |
| F | F1, F2 | At least one |
7. Evaluate potential vacant houses in Block XX that meet the price criteria. Assume maximum road adjacency and neighbor counts to determine the highest possible quotes in Block XX.
8. If Block XX houses exhibit maximum occupancy and matching prices, deduce the occupancy of others based on vacancy indicators: C1 or C2 might have maximized adjacency, leading to their vacancy.
9. Consequently, the vacant houses in Block XX are: A1, B1, C1.
Therefore, Block XX has 3 vacant houses.
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