DILR Arrangement

One of the old-school topics CAT has to offer is probably the only topic we all have practised at some stage of our lives. Through this article, we’ll try to understand what Arrangement sets ask for, and what skill set you need to have to crack these sets.

Understanding DILR Arrangement​

Arrangement sets in the DILR section often involve arranging given data or elements in a specific order based on certain criteria or conditions. These sets can include:

  1. Seating Arrangement: Questions where individuals or objects are arranged in a specific order around a table or in a row based on given conditions or relationships.

  2. Sorting/Ordering Problems: Problems where items need to be arranged in a particular sequence based on certain parameters or rules.

  3. Puzzle-based Arrangements: Logical puzzles where different variables, elements, or entities need to be arranged following specific rules or conditions.

  4. Grouping and Distribution Problems: Tasks that involve allocating items or individuals into different groups or categories according to given constraints.

Arrangements can also be further divided into two categories, circular and linear based, both having their complexities, the trickiest sets include people sitting in no particular directions, some people sitting outside, and some inside, through the example sets taken, we’ll try to cover all the categories.

In Quantifiers, we cover around 700 sets in order to prepare you for what can come in the actual CAT examination, Quantifiers DILR sets are often positioned as closest to what comes in the actual CAT exam.

Practice Questions for CAT with Solutions

1. CAT - Arrangement

There are 12 volumes (books) of an Encyclopedia i.e. A to L. These are kept on a shelf in two rows – row 1 and row 2 such that row 1 is directly above row 2. All the books have identical dimensions and are at equal distances from their neighbours. There are six books in each row, and each book in row 2 has one book directly above it in row 1. There are no other books on this shelf. Further:

The distance between books F and L is the same as the distance between books G and D. This distance is more than the distance between any two books on the shelf.

Books A, D and E are in row 1. Books H, I and J are in row 2.

There is exactly one book to the left of book B.

Book A is equidistant from books J and H. Book E is equidistant from books I and L.

Book K is directly above book J.

The number of books between K and D is same as the number of books between J and L. 

There is no book below book G.

Q1. How many different arrangements of books are possible?

Q2. Which book can be directly above book C?

Q3. How many books are there between books D and F in the same row?

Q4. Ravi takes out book A from the shelf and pushes the rest of the books to the left. After finishing book A, he puts it back on the shelf in the empty slot. Now, how many books are there between F and E?

Correct Answer 1

2

Correct Answer 2

B

Correct Answer 3

4

Correct Answer 4

2

2. CAT - Arrangement

The table below shows the time table of Agra-Kolkata Express that leaves Agra at 5 pm and reaches Kolkata the next day at 5:20 pm. Distance at stations X and Y is distance from X upto Y.

Q1. What is the difference in the speed of the train excluding and including stoppages?

Q2. Between which two consecutive stations does the train run the slowest?
  1. Farrukhabad – Kanpur
  2. Kasganj – Farrukhabad
  3. Kanpur – Mughal Sara
  4. None of these
Q3. If the train runs the entire distance at the maximum speed with which it runs between any two stations, approximately how much time will it save? Assume that the stoppage time remain the same
  1. 205 minutes
  2. 245 minutes
  3. 330 minutes
  4. 370 minutes
Q4. On a certain day, the train is delayed due to fog. It leaves Kanpur 2 hours late than the usual time. What should be its average running speed (in km/min) for the remaining distance so that it arrives at Kolkata at the scheduled time? 

The stoppage time at the stations remain the same.

  1. 1.11
  2. 1.26
  3. 1.33
  4. 3.70

Correct Answer 1

3.7

Correct Answer 2

a. Farrukhabad – Kanpur

Correct Answer 3

d. 370 minutes

Correct Answer 4

b. 1.26

3. CAT - Arrangement

Goldcard, a credit card company, offers various cards. Goldcard Platina, a special kind of card, is given to elite customers. Some of the properties of the card are as follows :

  1. The credit card number is made of 16 digits (digits range from 0 to 9) and it cannot consist of all 0s.
  2. The sum of any three consecutive digits of the credit card number is N.

Every customer is given two other numbers (along with N), and y, which are the 3rd digit and the 14th digit of the number respectively, to help him remember his card number. 

Q1. Ravi bought a Goldcard Platina which had = 17. How many distinct digits can his card have?
  1. 2
  2. 3
  3. 2 or 3
  4. 3 or 4
Q2. If Shyam bought a card with N = 18 and = 7, then what is the maximum sum of any five consecutive digits?
  1. 27
  2. 29
  3. 33
  4. 34

Q3. For N = 26, what is the largest possible value of x + y?

Q4. Pradeep’s card has three unique digits and his lucky number is 20. How many different cards can he get to have his lucky number as N?

Correct Answer 1

c. 2 or 3

Correct Answer 2

d. 34

Correct Answer 3

18

Correct Answer 4

24

4. CAT - Arrangement

A group of five friends recently met in an alumni meet in their college. When asked about their whereabouts, likes and dislikes by their ex-professors, these friends tried to puzzle their professors by giving them certain clues.These friends, who lived in Kolkata, Chennai, Mumbai, Delhi and Hyderabad, labeled their cities as 1, 2, 3, 4 and 5 (not necessarily in that order) and arranged these labels on a piece of paper in ascending order of labels (from left to right). 

Their professions and habits (in any order) were:

Professions: Architect, Lawyer, Pilot, Scientist and Doctor.

Reading Habits: Fiction, Science, Business, Motivation and Literature

TV Viewing Habits: News, Sports, Business, Entertainment and Geography

Playing Habits: Football, Cricket, Tennis, Badminton and Chess

No two people shared a city or profession or habit. It was also known that:

  1. The Architect lives in Kolkata.
  2. The Lawyer watches Business channels.
  3. The Pilot reads books on Fiction.
  4. Chennai is placed to the immediate left of Mumbai.
  5. The person from Chennai likes books on Science.
  6. The person who plays Cricket prefers Sports channels.
  7. The person from Delhi plays Football.
  8. The person living in the city placed at the center prefers to read books on Motivation.
  9. The Scientist lives in the city labelled as 1.
  10. The person who plays Tennis is from the city adjacent to the person who likes watching the Geography channel.
  11. The person who watches the News channel lives in the city placed next to the city of the person who plays Football.
  12. The person who plays Badminton reads books on Business.
  13. The Doctor plays Chess.
  14. The Scientist lives in the city placed next to Hyderabad.
  15. The city of the person who plays Tennis is next to the person who likes reading Literature.
Q1. What is the profession of the person who lives in Hyderabad?
  1. Pilot
  2. Architect
  3. Doctor
  4. Indeterminate
Q2. Which TV channel does the person from Mumbai prefer to watch?
  1. Entertainment
  2. Sports
  3. Geography
  4. Indeterminate
Q3. Which game does the person, who prefers reading books on Motivation, play?
  1. Football
  2. Cricket
  3. Tennis
  4. Chess

Q4. Which book does the Doctor prefer to read?

  1. Literature
  2. Business
  3. Motivation
  4. Science

Correct Answer 1

a. Pilot

Correct Answer 2

b. Sports

Correct Answer 3

b. Cricket

Correct Answer 4

d. Science

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