LR - Arrangements - Previous Year CAT/MBA Questions
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Answer the following questions based on the information given below:
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.
How many houses are vacant in Block XX?
Solution
Discuss
ReportWhich of the following houses is definitely occupied?
[Two options are correct in this question and both were accepted as correct answer by IIM Lucknow]
- (a)
D2
- (b)
F2
- (c)
B1
- (d)
A1
Which of the following options best describes the number of vacant houses in Row-2?
- (a)
Exactly 3
- (b)
Exactly 2
- (c)
Either 3 or 4
- (d)
Either 2 or 3
What is the maximum possible quoted price (in lakhs of Rs.) for a vacant house in Column-E?
Which house in Block YY has parking space?
- (a)
F2
- (b)
E2
- (c)
E1
- (d)
F1
Answer the following questions based on the information given below:
There are nine boxes arranged in a 3×3 array as shown in Tables 1 and 2. Each box contains three sacks. Each sack has a certain number of coins, between 1 and 9, both inclusive.
The average number of coins per sack in the boxes are all distinct integers. The total number of coins in each row is the same. The total number of coins in each column is also the same.
Table 1 gives information regarding the median of the numbers of coins in the three sacks in a box for some of the boxes. In Table 2 each box has a number which represents the number of sacks in that box having more than 5 coins. That number is followed by a * if the sacks in that box satisfy exactly one among the following three conditions, and it is followed by ** if two or more of these conditions are satisfied.
- The minimum among the numbers of coins in the three sacks in the box is 1.
- The median of the numbers of coins in the three sacks is 1.
- The maximum among the numbers of coins in the three sacks in the box is 9.
What is the total number of coins in all the boxes in the 3rd row?
- (a)
36
- (b)
30
- (c)
15
- (d)
45
How many boxes have at least one sack containing 9 coins?
- (a)
3
- (b)
8
- (c)
5
- (d)
4
For how many boxes are the average and median of the numbers of coins contained in the three sacks in that box the same?
How many sacks have exactly one coin?
In how many boxes do all three sacks contain different numbers of coins?
Answer the next 5 questions based on the information given below:
There are only four neighbourhoods in a city - Levmisto, Tyhrmisto, Pesmisto and Kitmisto. During the onset of a pandemic, the number of new cases of a disease in each of these neighbourhoods was recorded over a period of five days. On each day, the number of new cases recorded in any of the neighbourhoods was either 0, 1, 2 or 3.
The following facts are also known:
1. There was at least one new case in every neighbourhood on Day 1.
2. On each of the five days, there were more new cases in Kitmisto than in Pesmisto.
3. The number of new cases in the city in a day kept increasing during the five-day period. The number of new cases on Day 3 was exactly one more than that on Day 2.
4. The maximum number of new cases in a day in Pesmisto was 2, and this happened only once during the five-day period.
5. Kitmisto is the only place to have 3 new cases on Day 2.
6. The total numbers of new cases in Levmisto, Tyhrmisto, Pesmisto and Kitmisto over the five-day period were 12, 12, 5 and 14 respectively.
What BEST can be concluded about the total number of new cases in the city on Day 2?
- (a)
Exactly 7
- (b)
Either 7 or 8
- (c)
Either 6 or 7
- (d)
Exactly 8
What BEST can be concluded about the number of new cases in Levmisto on Day 3?
- (a)
Either 2 or 3
- (b)
Exactly 3
- (c)
Either 0 or 1
- (d)
Exactly 2
On which day(s) did Pesmisto not have any new case?
- (a)
Both Day 2 and Day 3
- (b)
Only Day 2
- (c)
Only Day 3
- (d)
Both Day 2 and Day 4
Which of the two statements below is/are necessarily false?
Statement A: There were 2 new cases in Tyhrmisto on Day 3.
Statement B: There were no new cases in Pesmisto on Day 2.
- (a)
Statement B only
- (b)
Statement A only
- (c)
Both Statement A and Statement B
- (d)
Neither Statement A nor Statement B
On how many days did Levmisto and Tyhrmisto have the same number of new cases?
- (a)
5
- (b)
4
- (c)
3
- (d)
2
Answer the following question based on the information given below.
A supermarket has to place 12 items (coded A to L) in shelves numbered 1 to 16. Five of these items are types of biscuits, three are types of candies and the rest are types of savouries. Only one item can be kept in a shelf. Items are to be placed such that all items of same type are clustered together with no empty shelf between items of the same type and at least one empty shelf between two different types of items. At most two empty shelves can have consecutive numbers.
The following additional facts are known.
- A and B are to be placed in consecutively numbered shelves in increasing order.
- I and J are to be placed in consecutively numbered shelves both higher numbered than the shelves in which A and B are kept.
- D, E and F are savouries and are to be placed in consecutively numbered shelves in increasing order after all the biscuits and candies.
- K is to be placed in shelf number 16.
- L and J are items of the same type, while H is an item of a different type.
- C is a candy and is to be placed in a shelf preceded by two empty shelves.
- L is to be placed in a shelf preceded by exactly one empty shelf.
In how many different ways can the items be arranged on the shelves?
- (a)
1
- (b)
8
- (c)
2
- (d)
4
Which of the following items is not a type of biscuit?
- (a)
A
- (b)
B
- (c)
L
- (d)
G
Which of the following can represent the numbers of the empty shelves in a possible arrangement?
- (a)
1,2,8,12
- (b)
1,7,11,12
- (c)
1,5,6,12
- (d)
1,2,6,12
Which of the following statements is necessarily true?
- (a)
There are at least four shelves between items B and C.
- (b)
There are two empty shelves between the biscuits and the candies.
- (c)
All biscuits are kept before candies.
- (d)
All candies are kept before biscuits.
Answer the following question based on the information given below.
In a square layout of size 5m × 5m, 25 equal-sized square platforms of different heights are built.
The heights (in metres) of individual platforms are as shown below:
6 1 2 4 3
9 5 3 2 8
7 8 4 6 5
3 9 5 1 2
1 7 6 3 9
Individuals (all of same height) are seated on these platforms. We say an individual A can reach an individual B if all the three following conditions are met:
(i) A and B are in the same row or column
(ii) A is at a lower height than B
(iii) If there is / are any individual(s) between A and B, such individual(s) must be at a height lower than that of A.
Thus in the table given above, consider the individual seated at height 8 on 3rd row and 2nd column. He can be reached by four individuals. He can be reached by the individual on his left at height 7, by the two individuals on his right at heights of 4 and 6 and by the individual above at height 5.
Rows in the layout are numbered from top to bottom and columns are numbered from left to right.
How many individuals in this layout can be reached by just one individual?
- (a)
3
- (b)
5
- (c)
7
- (d)
8
Which of the following is true for any individual at a platform of height 1 m in this layout?
- (a)
They can be reached by all the individuals in their own row and column.
- (b)
They can be reached by at least 4 individuals.
- (c)
They can be reached by at least one individual.
- (d)
They cannot be reached by anyone.
We can find two individuals who cannot be reached anyone in
- (a)
the last row.
- (b)
the fourth row.
- (c)
the fourth column.
- (d)
the middle column.
Which of the following statements is true about this layout?
- (a)
Each row has an individual who can be reached by 5 or more individuals.
- (b)
Each row has an individual who cannot be reached by anyone.
- (c)
Each row has at least two individuals who can be reached by an equal number of individuals.
- (d)
All individuals at the height of 9 m can be reached by at least 5 individuals.
Answer the following question based on the information given below.
A tea taster was assigned to rate teas from six different locations – Munnar, Wayanand, Ooty, Darjeeling, Assam and Himachal. These teas were placed in six cups, numbered 1 to 6, not necessarily in the same order. The tea taster was asked to rate these teas on the strength of their flavour on a scale of 1 to 10. He gave a unique integer rating to each tea. Some other information is given below:
- Cup 6 contained tea from Himachal.
- Tea from Ooty got the highest rating, but it was not in Cup 3.
- The rating of tea in Cup 3 was double the rating of the tea in Cup 5.
- Only two cups got ratings in even numbers.
- Cup 2 got the minimum rating and this rating was an even number.
- Tea in Cup 3 got a higher rating than that in Cup 1.
- The rating of tea from Wayanad was more than the rating of tea from Munnar, but less than that from Assam.
What was the second highest rating given?
What was the number of the cup that contained tea from Ooty?