CAT Seating Arrangement Questions [Download PDF]
Arrangement is one of the most important topics in the CAT Quant Section. You can check out these Arrangement questions in the CAT Previous year’s papers. If you want to learn the basics, you can watch these videos on Arrangement. This article will look into some important Arrangement Questions for CAT. These are good sources for practice; If you want to practice these questions, you can download this CAT Arrangement Most Important Questions PDF below, which is completely Free.
Download Arrangement Questions for CAT
Instructions
A shopping mall has a large basement parking lot with parking slots painted in it along a single row. These slots are quite narrow; a compact car can fit in a single slot but an SUV requires two slots. When a car arrives, the parking attendant guides the car to the first available slot from the beginning of the row into which the car can fit.
For our purpose, cars are numbered according to the order in which they arrive at the lot. For example, the first car to arrive is given a number 1, the second a number 2, and so on. This numbering does not indicate whether a car is a compact or an SUV. The configuration of a parking lot is a sequence of the car numbers in each slot. Each single vacant slot is represented by letter V.
For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 are compact cars and 2 and 4 are SUVs. At this point, the parking lot would be described by the sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parking lot would now be described as 1, V, V, 3, 4. If a compact car (numbered 6) arrives subsequently followed by an SUV (numbered 7), the parking lot would be described by the sequence 1, 6, V, 3, 4, 7.
Answer the following questions INDEPENDENTLY of each other.
Question 1: Initially cars numbered 1, 2, 3, and 4 arrive among which 1 and 4 are SUVs while 2 and 3 are compact cars. Car 1 then leaves, followed by the arrivals of car 5 (a compact car) and car 6 (an SUV). Car 4 then leaves. Then car 7 (an SUV) and car 8 (a compact car) arrive. At this moment, which among the following numbered car is parked next to car 3?
a)Â 8
b)Â 5
c)Â 6
d)Â 7
1) Answer (D)
Solution:
following is the order of arrival and departure of cars
As we can see that car 2 and car 7 are parked next to car 3
Question 2: Suppose eight cars have arrived, of which two have left. Also suppose that car 4 is a compact and car 7 is an SUV. Which of the following is a POSSIBLE current configuration of the parking lot?
a)Â 8, 2, 3, V, 6, 5, 7
b)Â V, 2, 3, 7, 5, 6, 8
c)Â 8, 2, 3, V, 5, 7, 6
d)Â 8, 2, 3, V, 5, 6, 7
2) Answer (D)
Solution:
Let’s look at option 4.
Order of cars is 8,2,3,V,5,6,7. This sequence is easily possible.
Let’s say cars 1,2,3,4,5,6,7 arrive one after the another.
Now Car 1 leaves and Car 8 takes that place.
Finally Car 4 leaves. Hence we can see that this combination of cars is possible
Question 3: Suppose the sequence at some point of time is 4, 5, 6, V, 3. Which of the following is NOT necessarily true?
a)Â Car 4 is a compact.
b)Â Car 1 is an SUV.
c)Â Car 3 is an SUV
d)Â Car 5 is a compact.
3) Answer (C)
Solution:
The original sequence as given in the question is 4,5,6,V,3
This is possible when cars 1,2,3 arrived and then cars 1 and 2 leave. After that cars 4,5 and 6 arrive.
Now there are 4 slots to the left of car 3. This is only possible when cars 1 and 2 were SUVs. Now out of these 4 slots,
3 slots are occupied by cars 4,5 and 6. As a result these are compact cars . Car 3 can be a SUV or a Compact car and it won’t impact the final solution.
Question 4: Suppose that car 4 is not the first car to leave and that the sequence at a time between the arrival of the car 7 and car 8 is V, 7, 3, 6, 5. Then which of the following statements MUST be false?
a)Â Car 2 is a compact.
b)Â Car 7 is a compact.
c)Â Car 4 is an SUV.
d)Â Car 6 is a compact.
4) Answer (D)
Solution:
Here we can see that cars 3 and 5 are still in their position. Thus car 4 was not the first car to leave, either 1 or 2 left before 4. Let’s say only car 2 left before car 4. Now supposingly if car 2 is an SUV, car 6 was parked in that lot. Thus car 2 and car 7 are compact cars. Option 4 is correct.
Instructions
Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either Red, Blue or Green. While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:
1. Two adjacent beads along the same row or column are always of different colours.
2. There is at least one Green bead between any two Blue beads along the same row or column.
3. There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.
Every unique, complete arrangement of twenty five beads is called a configuration.
Question 5:Â The total number of possible configurations using beads of only two colours is:
5)Â Answer:Â 2
Solution:
There are only 2 configurations possible
Question 6: What is the maximum possible number of Red beads that can appear in any configuration?
6)Â Answer:Â 9
Solution:
Maximum 9 red beads are possible as shown here
Question 7: What is the minimum number of Blue beads in any configuration?
7)Â Answer:Â 6
Solution:
To solve this question we can use the answer of the previous question, since maximum 9 red beads are possible, filling the remaining space with green and blue beads, in such a way that number of blue beads is minimised
Hence number of blue beads is 6
Question 8: Two Red beads have been placed in ‘second row, third column’ and ‘third row, second column’. How many more Red beads can be placed so as to maximise the number of Red beads used in the configuration?
8)Â Answer:Â 6
Solution:
6 more beads can be placed as shown
Instructions
Princess, Queen, Rani and Samragni were the four finalists in a dance competition. Ashman, Badal, Gagan and Dyu were the four music composers who individually assigned items to the dancers. Each dancer had to individually perform in two dance items assigned by the different composers. The first items performed by the four dancers were all assigned by different music composers. No dancer performed her second item before the performance of the first item by any other dancers. The dancers performed their second items in the same sequence of their performance of their first items.
The following additional facts are known.
i) No composer who assigned item to Princess, assigned any item to Queen.
ii) No composer who assigned item to Rani, assigned any item to Samragni.
iii) The first performance was by Princess; this item was assigned by Badal.
iv) The last performance was by Rani; this item was assigned by Gagan.
v) The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.
Question 9:Â Which of the following is true?
a)Â The second performance was composed by Dyu.
b)Â The third performance was composed by Dyu.
c)Â The third performance was composed by Ashman.
d)Â The second performance was composed by Gagan.
9) Answer (A)
Solution:
Since the dancers performed their second items in the same sequence of their performance of their first items. The table will be as follows:
The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.
Also, the first items performed by the four dancers were all assigned by different music composers. Badal can come only at the place as shown in the table.
Then Ashman can only compose for the following performances.
Hence Dyu will compose for the following performances:
From (i) No composer who assigned item to Princess, assigned any item to Queen.
From (ii)Â No composer who assigned item to Rani, assigned any item to Samragni.
Hence Dyu will compose for Samragni 1st Performance and Gagan will compose for Queen 1st Performance. Also, Badal will compose for Samragni 2nd Performance and Dyu will compose for Queens 2nd Performance.
Hence, the complete table is as follows:
The second performance was composed by Dyu. Hence A is the answer.
Question 10:Â Which of the following is FALSE?
a)Â Samragni did not perform in any item composed by Ashman.
b)Â Princess did not perform in any item composed by Dyu.
c)Â Rani did not perform in any item composed by Badal.
d)Â Queen did not perform in any item composed by Gagan.
10) Answer (D)
Solution:
Since the dancers performed their second items in the same sequence of their performance of their first items. The table will be as follows:
The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.
Also, the first items performed by the four dancers were all assigned by different music composers. Badal can come only at the place as shown in the table.
Then Ashman can only compose for the following performances.
Hence Dyu will compose for the following performances:
From (i) No composer who assigned item to Princess, assigned any item to Queen.
From (ii)Â No composer who assigned item to Rani, assigned any item to Samragni.
Hence Dyu will compose for Samragni 1st Performance and Gagan will compose for Queen 1st Performance. Also, Badal will compose for Samragni 2nd Performance and Dyu will compose for Queens 2nd Performance.
Hence, the complete table is as follows:
Option A:Â Samragni did not perform in any item composed by Ashman. This statement is true.
Option B:Â Princess did not perform in any item composed by Dyu. This is also true.
Option C:Â Rani did not perform in any item composed by Badal. This statement is true.
Option D:Â Queen did not perform in any item composed by Gagan. This statement is false.
Hence D is the answer.
Question 11:Â The sixth performance was composed by:
a)Â Badal
b)Â Dyu
c)Â Ashman
d)Â Gagan
11) Answer (A)
Solution:
Since the dancers performed their second items in the same sequence of their performance of their first items. The table will be as follows:
The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.
Also, the first items performed by the four dancers were all assigned by different music composers. Badal can come only at the place as shown in the table.
Then Ashman can only compose for the following performances.
Hence Dyu will compose for the following performances:
From (i) No composer who assigned item to Princess, assigned any item to Queen.
From (ii)Â No composer who assigned item to Rani, assigned any item to Samragni.
Hence Dyu will compose for Samragni 1st Performance and Gagan will compose for Queen 1st Performance. Also, Badal will compose for Samragni 2nd Performance and Dyu will compose for Queens 2nd Performance.
Hence, the complete table is as follows:
The sixth performance was composed by Badal. Hence C is the answer.
Question 12:Â Which pair of performances were composed by the same composer?
a)Â The first and the seventh
b)Â The third and the seventh
c)Â The second and the sixth
d)Â The first and the sixth
12) Answer (D)
Solution:
Since the dancers performed their second items in the same sequence of their performance of their first items. The table will be as follows:
The items assigned by Ashman were performed consecutively. The number of performances between items assigned by each of the remaining composers was the same.
Also, the first items performed by the four dancers were all assigned by different music composers. Badal can come only at the place as shown in the table.
Then Ashman can only compose for the following performances.
Hence Dyu will compose for the following performances:
From (i) No composer who assigned item to Princess, assigned any item to Queen.
From (ii)Â No composer who assigned item to Rani, assigned any item to Samragni.
Hence Dyu will compose for Samragni 1st Performance and Gagan will compose for Queen 1st Performance. Also, Badal will compose for Samragni 2nd Performance and Dyu will compose for Queens 2nd Performance.
Hence, the complete table is as follows:
The first and the sixth items were composed by Badal. Hence D is the answer.
