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Question:

How many houses are vacant in Block XX?

Explanation:

[Note: There might be discrepancy in one of the questions of this set. We will update the solution once the objections window closes and answers are updated by IIM Lucknow.]

Price of a house = (base price)  + 5 × (road adjacency value) + 3 × (neighbor count)

Block XX:
Maximum price of a house in XX is 24
∴ 24 = (10 or 12)  + 5 × (0 or 1 or 2) + 3 × (0 or 1 or 2 or 3)
This is only possible when: 
base price = 10 lakhs, road adjacency = 1 and neighbor count = 3.
⇒ Only house B2 satisfies the given criteria i.e., road adjacency = 1 and neighbor count = 3.
∴ B2 is vacant and its price is 24 lakhs.

⇒ A2, B1 and C2 are occupied houses.

There is only one occupied house in Row 1 and block XX.
Since B1 is occupied, ⇒ A1 and C1 are vacant.

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Block YY:
Both E1 and E2 are vacant and one of them costs 15 lakhs.

Let us focus on E1
For E1 neighbor count = 1 (exactly one of D1 or F1 is occupied)
For E1 road adjacency = 0
∴ Cost of E1 = (10 or 12) + 5 × 0 + 3 × 1 = 13 or 15 lakhs

Since 15 lakhs is the least cost of a house in block YY, E1 must cost 15 lakhs.
⇒ E1 is the only house in YY which has a parking space.

Given, Row-1 has two occupied houses, one in each block.
∴ Exactly one of D1 or F1 is occupied.

If F1 is vacant, let’s calculate its price.
It should not have parking space as only 1 house has parking space in block YY. Hence, it’s base price is 10 lakhs. Now even if F2 is occupied, F1’s price will be 10 + 0 + 3 = 13 lakhs.
This is not possible as least price for a house in YY is 15 lakhs.
∴ F1 should be occupied.
⇒ D1 is vacant.

Also, at least one house in column D is occupied, hence D2 must be occupied.

Now, F2 may be vacant or occupied, both cases are possible.

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∴ 3 houses are vacant in block XX.

Hence, 3.