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CAT 2025 Lesson : DILR: Sep '25 to Oct '25 - Tough Cases - 11 Sep 2025
Read the following and answer the Questions that follow
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.
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.
1) How many houses are vacant in Block XX?
Answer:
2) Which of the following houses is definitely occupied?
(1) B1
(2) F2
(3) D2
(4) A1
3) Which of the following options best describes the number of vacant houses in Row-2?
(1) Exactly 2
(2) Exactly 3
(3) Either 3 or 4
(4) Either 2 or 3
4) What is the maximum possible quoted price (in lakhs of Rs.) for a vacant house in Column-E?
Answer:
5) Which house in Block YY has parking space?
(1) F2
(2) E1
(3) E2
(4) F1
Read the following and answer the Questions that follow
Ten players, as listed in the table below, participated in a rifle shooting competition comprising of 10 rounds. Each round had 6 participants. Players numbered 1 through 6 participated in Round 1, players 2 through 7 in Round 2,..., players 5 through 10 in Round 5, players 6 through 10 and 1 in Round 6, players 7 through 10, 1 and 2 in Round 7 and so on.
The top three performances in each round were awarded 7, 3 and 1 points respectively. There were no ties in any of the 10 rounds. The table below gives the total number of points obtained by the 10 players after Round 6 and Round 10.
The following information is known about Rounds 1 through 6:
1. Gordon did not score consecutively in any two rounds.
2. Eric and Fatima both scored in a round.
The following information is known about Rounds 7 through 10:
1. Only two players scored in three consecutive rounds. One of them was Chen. No other player scored in any two consecutive rounds.
2. Joshin scored in Round 7, while Amita scored in Round 10.
3. No player scored in all the four rounds.
6) What were the scores of Chen, David, and Eric respectively after Round 3?
(1) 3, 0, 3
(2) 3, 3, 3
(3) 3, 3, 0
(4) 3, 6, 3
7) Which three players were in the last three positions after Round 4?
(1) Hansa, Ikea, Joshin
(2) Bala, Hansa, Ikea
(3) Bala, Ikea, Joshin
(4) Bala, Chen, Gordon
8) Which player scored points in maximum number of rounds?
(1) Amita
(2) Chen
(3) Joshin
(4) Ikea
9) Which players scored points in the last round?
(1) Amita, Eric, Joshin
(2) Amita, Bala, Chen
(3) Amita, Chen, Eric
(4) Amita, Chen, David
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.
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.
1) How many houses are vacant in Block XX?
Answer:
2) Which of the following houses is definitely occupied?
(1) B1
(2) F2
(3) D2
(4) A1
3) Which of the following options best describes the number of vacant houses in Row-2?
(1) Exactly 2
(2) Exactly 3
(3) Either 3 or 4
(4) Either 2 or 3
4) What is the maximum possible quoted price (in lakhs of Rs.) for a vacant house in Column-E?
Answer:
5) Which house in Block YY has parking space?
(1) F2
(2) E1
(3) E2
(4) F1
Read the following and answer the Questions that follow
Ten players, as listed in the table below, participated in a rifle shooting competition comprising of 10 rounds. Each round had 6 participants. Players numbered 1 through 6 participated in Round 1, players 2 through 7 in Round 2,..., players 5 through 10 in Round 5, players 6 through 10 and 1 in Round 6, players 7 through 10, 1 and 2 in Round 7 and so on.
The top three performances in each round were awarded 7, 3 and 1 points respectively. There were no ties in any of the 10 rounds. The table below gives the total number of points obtained by the 10 players after Round 6 and Round 10.
The following information is known about Rounds 1 through 6:
1. Gordon did not score consecutively in any two rounds.
2. Eric and Fatima both scored in a round.
The following information is known about Rounds 7 through 10:
1. Only two players scored in three consecutive rounds. One of them was Chen. No other player scored in any two consecutive rounds.
2. Joshin scored in Round 7, while Amita scored in Round 10.
3. No player scored in all the four rounds.
6) What were the scores of Chen, David, and Eric respectively after Round 3?
(1) 3, 0, 3
(2) 3, 3, 3
(3) 3, 3, 0
(4) 3, 6, 3
7) Which three players were in the last three positions after Round 4?
(1) Hansa, Ikea, Joshin
(2) Bala, Hansa, Ikea
(3) Bala, Ikea, Joshin
(4) Bala, Chen, Gordon
8) Which player scored points in maximum number of rounds?
(1) Amita
(2) Chen
(3) Joshin
(4) Ikea
9) Which players scored points in the last round?
(1) Amita, Eric, Joshin
(2) Amita, Bala, Chen
(3) Amita, Chen, Eric
(4) Amita, Chen, David
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