Question

How many houses are vacant in Block XX?

• A. D2
• B. A1
• C. B1
• D. F2
• A. Either 2 or 3
• B. Exactly 3
• C. Exactly 2
• D. Either 3 or 4
• A. E2
• B. F2
• C. E1
• D. F1

Answer 1

The Correct Option is C

The correct answer is 3.

Answer 2

Given:
Some houses are already taken, but others are empty and available for sale. The base price for an empty house is either Rs. 10 lakhs if it doesn't have a parking spot and Rs. 12 lakhs if it does have a parking lot. 
So the price of a vacant house is calculated as = Base price+5(road adjacency value)+3(neighbor count). We know the most expensive house in Block XX costs Rs. 24 lakhs.

Now calculate for the maximum price of a house in block XX.
1. House with parking lot;
road adjacency value = a, neighbor count = b
12+5a+3b=24
5a+3b=12
The equation only works if a equals 0 and b equals 4. However, b can't be 4 because the most neighbors a house can have is 3.
So, it is invalid.

2. House without parking lot:
10+5a+3b=24
5a+3b=14 , (a,b)=(1,3)
So, the house must have 3 neighbors and 1 road connected to it. Therefore, the only possible case is B2. Thus, the neighboring houses of B2, which are B1, A2, and C2, are also occupied. Since we know that Row 1 has two occupied houses, with one in each block, and B1 is already occupied, it implies that A1 and C1 are vacant.
That means 3 houses are occupied in Block XX.

In Block YY, both E1 and E2 are vacant, and one of them costs 15 lakhs. Let's focus on E1. For E1:
Neighbor count = 1 (exactly one of D1 or F1 is occupied)
Road adjacency = 0
So, the cost of E1 would be: \((10 \text{ or } 12) + 5 \times 0 + 3 \times 1 = 13 \text{ or } 15\) lakhs.
Since 15 lakhs is the minimum cost of a house in block YY, E1 must cost 15 lakhs. Therefore, E1 is the only house in YY that has a parking space.
Given that Row-1 has two occupied houses, one in each block, and exactly one of D1 or F1 is occupied, it further confirms that E1 is occupied, leaving either D1 or F1 to be occupied.

If F1 is vacant, let's calculate its price. Since only one house has a parking space in block YY, F1 should not have a parking space, making its base price 10 lakhs. Now, even if F2 is occupied, F1's price would be \(10+0+3 = 13\) lakhs.
However, this is not possible as the lowest price for a house in YY is 15 lakhs. Therefore, F1 should be occupied.
As a consequence, D1 is vacant.

Since at least one house in column D is occupied, D2 must be occupied.
For F2, both possibilities are valid:
F2 may be vacant or occupied.

Block XX has 3 vacant houses.

So, the answer is 3.

Answer 3

To determine which house is definitely occupied, let’s examine the conditions provided in the comprehension:

1. Row-1 and Row-2 each have two occupied houses, one in each block**. This implies that in both Block XX and Block YY, there is at least one occupied house in each row.

2. Both houses in Column-E are vacant**. Since Column-E in Block YY has both houses vacant, none of the houses labeled "E1" and "E2" are occupied.

3. Each of Columns D and F has at least one occupied house**. This tells us that in Block YY, at least one of the houses in Column-D and one in Column-F are occupied.

4. Given this information, we analyze each option:

  - Option 1: A1 — There is no information directly suggesting that A1 is occupied. Thus, this option is **incorrect**.
  
  - Option 2: B1 — This house is in Column-B of Block XX. The conditions indicate that Row-1 has one occupied house in Block XX. Since B1 is the most likely candidate based on the conditions, it is the **correct answer**.
  
  - Option 3: D2 — This house is in Column-D of Block YY. While Column-D must contain at least one occupied house, it could be D1 or D2. Hence, we cannot be certain that D2 is occupied. This option is **incorrect**.
  
  - Option 4: F2 — Similarly, F2 is in Column-F of Block YY, where at least one house must be occupied. However, this could be F1 or F2, making F2 uncertain. This option is incorrect.

Therefore, the only house that we can definitively conclude is occupied based on the conditions given is B1.

Answer 4

The correct option is (A): Either 2 or 3

Answer 5

In the solution to the first question of this set:

In row 2, B2 and E2 are definitely vacant.
Out of D2 and F2, at least one is occupied, which means either one is vacant or none are vacant.

1. One of D2 or F2 is vacant.
In this case, we have B2, F2, and either D2 or F2 vacant, totaling 3 vacant houses in row 2.

2. None of D2 or F2 is vacant.
Here, we have B2 and F2 vacant, totaling 2 vacant houses in row 2.

Therefore, in row 2, either only 2 houses are vacant or 3 houses are vacant.

So, the correct option is (A): Either 2 or 3

Answer 6

The correct answer is 21.

Answer 7

Given: The price for an empty house is either Rs. 10 lakhs if it doesn't have a parking spot or Rs. 12 lakhs if it does.
In Block YY, both E1 and E2 are vacant, and one of them costs 15 lakhs. Let's focus on E1.

For E1:
Neighbor count = 1 (exactly one of D1 or F1 is occupied)
Road adjacency = 0
So, the cost of E1 would be: \((10 \text{ or } 12) + 5 \times 0 + 3 \times 1 = 13 \text{ or } 15\) lakhs.
Since 15 lakhs is the lowest cost for a house in Block YY, E1 must cost 15 lakhs. This implies E1 is the only house in YY with a parking space.

let's calculate the maximum possible price of E2.
E2's base price is 10 lakhs since it cannot have a parking space (only one house in YY, E1, has a parking space). The road adjacency for E2 is 1, and the maximum neighbor count of E2 will be 2 (both D2 and F2 are occupied, and E1 is vacant).
So, E2's price would be: \(10 + 5 \times 1 + 3 \times 2 = 21\) lakhs.
Hence, the maximum possible price for E2 is 21 lakhs.

So, the answer is 21 lakhs.

Answer 8

To determine which house in Block YY has parking space, let’s review the information provided in the comprehension:

1. According to the given information, only one house in Block YY has parking space. This implies that among all houses in Block YY, only a single house is equipped with parking.

2. The problem specifies that Column-E contains both vacant houses in Block YY. This suggests that among E1 and E2, one of these vacant houses may be the one with parking space.

3. Since there is no additional indication about F1 or F2 having parking, and we know only one house in Block YY is designated with parking, **E1 is identified as the most likely candidate based on the provided options and the conditions.
Therefore, the house with parking space in Block YY is E1.