Final Revision: Logical Reasoning & Data Interpretation For CAT | Logical Reasoning (LR) and Data Interpretation (DI) PDF Download

This document is like a guidebook to help you review all the important stuff about DILR topics. It's packed with simple explanations and examples to make it easy for you to understand and improve your skills. Whether you need a quick refresher or want to learn more, this document has got you covered!

Seating Arrangement

There is no set formula for solving the seating arrangement questions but there is a sort of set systematic logical approach for solving these. To exemplify this approach consider the following question:

Q: Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata by a flight operated by Cheap Air. In the flight, sitting is arranged in 30 rows, numbered 1 to 30, each consisting of 6 seats, marked by letters A to F from left to right, respectively. Seats A to C are to the left of the aisle (the passage running from the front of the aircraft to the back), and seats D to F are to the right of the aisle. Seats A and F are by the windows and referred to as Window seats, C and D are by the aisle and are referred to as Aisle seats while B and E are referred to as Middle seats. Seats marked by consecutive letters are called consecutive seats (or seats next to each other). A seat number is a combination of the row number, followed by the letter indicating the position in the row; e.g., 1A is the left window seat in the first row, while 12E is the right middle seat in the 12th row.
Cheap Air charges Rs. 1000 extra for any seats in Rows 1, 12 and 13 as those have extra legroom. For Rows 2-10, it charges Rs. 300 extra for Window seats and Rs. 500 extra for Aisle seats. For Rows 11 and 14 to 20, it charges Rs. 200 extra for Window seats and Rs. 400 extra for Aisle seats. All other seats are available at no extra charge.
The following are known:
1. The eight friends were seated in six different rows.
2. They occupied 3 Window seats, 4 Aisle seats and 1 Middle seat.
3. Seven of them had to pay extra amounts, totalling to Rs. 4600, for their choices of seats. One of them did not pay any additional amount for his/her choice of seat.
4. Jayanta, Ajit and Byomkesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but all of them paid different amounts for their choices of seat. One of these amounts may be zero.
5. Gargi was sitting next to Kikira, and Manik was sitting next to Jayanta.
6. Prodosh and Tapesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but they paid different amounts for their choices of seat. One of these amounts may be zero.

How much extra did Gargi pay for her choice of seat?
Option A: Rs.0
Option B: Rs.300
Option C: Rs.500
Option D: Rs.1000

Sol: Let us draw a simple diagram and visualize this.

4. Jayanta, Ajit and Byomkesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but all of them paid different amounts for their choices of seat. One of these amounts may be zero.
Where should these three be? J, A and B should be in rows 10, 11 and 12 and should be window or aisle seats.
J = Row 10, A = Row 11, B = Row 12. All three aisle or all three window.

6. Prodosh and Tapesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but they paid different amounts for their choices of seat. One of these amounts may be zero.
Where should these two be? They could be in rows 1 and 2, 13 & 14, or 20 & 21. They should be aisle seats if JAB take window . Window seats in JAB take aisle seats.

5. Gargi was sitting next to Kikira, and Manik was sitting next to Jayanta.
If seats are adjacent to each other, either they should both be aisle seats or we should have a middle seat involved.
So, JAB were aisle seats, then Manik also had to be an aisle seat, and GK had to be a window and middle seat. In which case P&T would have window seats
If JAB have window seats, M would have to have a middle seat. GK would have to be two aisle seats and PT would have to take two aisle seats.

Possibility 1 = JABM Aisle in row number 10, 11, 12 and 10
GK = window and middle seats, PT = two window seats.
Possibility 2 = JABM seated in 3 window seats and a middle seat row number 10, 11, 12 and 10
GK = aisle seats, PT = two aisle seats.

3. Seven of them had to pay extra amounts, totalling to Rs. 4600, for their choices of seat. One of them did not pay any additional amount for his/her choice of seat.

4600 across 7 members. This is a lot of extra money. There has to be at least one Rs. 1000 extra. This leaves 3600 across 6 members. An average of Rs. 600 extra per person. This is also high. This tells us that there should have been two folks paying Rs. 1000 extra. So, we have Rs. 1000, Rs. 1000 and Rs. 2600 distributed across 5 people. This also averages out to more than Rs. 500. This tells us that we should have had 3 people paying Rs. 1000 extra. So, we have Rs. 1000, Rs. 1000, Rs, 1000 and Rs. 1600 across 4 people. So, we could have someone sitting in rows 1, 12 and 13. We also have folks in 10 and 11.
5. Gargi was sitting next to Kikira, and Manik was sitting next to Jayanta.
Possibility 1 = JABM Aisle in row number 10, 11, 12 and 10
GK = window and middle seats, PT = two window seats.
Extra charge for JABM = 500+400+1000+500 = 2400
3 out of the other 4 should give 2200 – this should be 1000 + 1000 + 200. Or, GK could be Rs. 1000 seats in, row 13 or row 1. and PT could have window seats in rows 20 and 21.
Possibility 2 = JABM seated in 3 window seats and a middle seat row number 10, 11, 12 and 10
GK = aisle seats, PT = two aisle seats.
Extra charge for JABM = 300+200+1000+0 = 1500
The other 4 should add up to 3100. This should be as 1000 + 1000 + remaining. The remaining two cannot add up to 1100. So, this possibility can be eliminated.
Final State

JABM Aisle in row number 10, 11, 12 and 10

GK = window and middle seats in row 1 or row 13

PT = two window seats in rows 20 and 21.
Extra charge for JABM = 500+400+1000+500 = 2400
Extra charge for G and K = 1000 + 1000 = 2000
Extra charge for P and T = Rs. 200 + 0.
G and K sat in window and aisle seats of row 1 or 13. So, an additional amount of Rs. 1000 was paid.

The question is "How much extra did Gargi pay for her choice of seat?"
Hence, the answer is "Rs.1000".
Ans: Choice D is the correct answer.

Syllogism

CAT syllogism questions involve reading a bunch of sentences and then figuring out a conclusion based on them. It's like solving a puzzle where you use logical thinking to reach an answer. So, basically, syllogism is about finding a conclusion by carefully thinking through the information given.

• Some + All= Some
• Some + Some= No Conclusion
• Some + No= Some Not
• No + No= No Conclusion
• No +All = Some Not Reversed
• No + Some = Some Not ( Reversed )
• Some Not/ Some Not Reversed + Anything= No Conclusion
• No + All = Some not Reversed
• All + Some = No Conclusion
• All + All= All
• All + No= No

Formulas for Syllogism and Concept

To understand the syllogism formulas it is important to understand the below 4 points. Before stating further.

Universal Positive Statement:

Universal positive statement indicates something positive applicable to all the items in that category. This is represented by the letter ‘A’. These statement begin with All, Every and Even.

Universal Negative Statement:

It implies that it refers to that kind of statements, which are universal and giving a negative impression. These types of statements begin with No, None of the, Not a single etc. and are represented by the letter ‘E’

Particular Positive Statement:

These type of statements begins with some, any, a few and are represented by the letter ‘I’.

Particular Negative Statement:

These kinds of statements are represented by the letter ‘O’. Some examples of this are:

• Some girls are not crazy
• Some files are not pencils
• Some M is not N
• Some Rohits are not Dhawans.
• Few vegetables are not green.

Q: Which of the two conclusions can be concluded on the basis of given statements?
Statements:
All flowers are candles.
All lanterns are candles.
Conclusions:
Some flowers are lanterns.
Some candles are lanterns.
Solution: Three possible diagrams is show in the above for the given statements.
Conclusion I follows from last two possible solutions, but does not follow from the first possible solution. Therefore, this conclusion is false.
Conclusion II follows from all the three possible solutions.

Ans: Therefore, conclusion II is true.

Venn Diagrams & Set Theory

• Its one of the easiest topics of CAT.
• Most of the formulae in this section can be deduced logically with little effort.
• The difficult part of the problem is translating the sentences into areas of the Venn diagram.
• While solving, pay careful attention to phrases like and, or, not, only, in as these generally signify the relationship.
• Set is defined as a collection of well defined objects. Ex. Set of whole numbers
• Every object is called Element of the set.
• The number of elements in the set is called cardinal number

Types of Sets

1. Null set: A set with zero or no elements is called Null set. It is denoted by or Ø. Null set cardinal number is 0

2. Singleton set: Sets with only one element in them are called singleton sets. Ex. { 2},{ a},{0}

3. Finite and Infinite set: A set having finite number of elements is called finite set. A set having infinite or uncountable elements in it is called infinite set.

4. Universal set: A set which contains all the elements of all the sets and all the other sets in it, is called universal set.

5. Subset: A set is said to be subset of another set i f all the elements contained in it are also part of another set. Ex. If A = {1,2}, B = {1,2,3,4} then, Set “A” is said t o be subset of set B.

6. Equal sets: Two sets are said to be equal sets when they contain same elements
Ex. A = {a, b, c } and B = {a, b, c } then A and B are called equal

7. Disjoint sets: When two sets have no elements in common then the two sets are called disjoint sets
Ex. A = {1,2,3} and B = {6,8,9} then A and B are disjoint sets.

8. Power set: 

• A power set is defined as the collection of all the subsets of a set and is denoted by P(A)
• If A = { a, b } then P(A) = { { }, {a}, {b}, {a, b}}
• For a set having n elements, the number of subsets are 2ⁿ

Properties of Sets:

• The null set is a subset of all sets
• Every set is subset of itself
• A U (BUC) = (AUB) U C
• A ∩ (B C ) = A B ) C
• A U B C ) ==(AUB) ∩ AUC)
• A BUC ) = A B ) U (A C)
• A U Ø = A

Venn diagrams: 

A Venn diagram is a figure to represent various sets and their relationship.

I,II,III are the elements in only A, only B and only C respectively
IV- Elements which are in all of A, B and C.
V- Elements which are in A and B but not in C.
VI - Elements which are in A and C but not in B.
VII - Elements which are in B and C but not in A.
VIII- Elements which are not in either A or B or C.

Union of sets is defined as the collection of elements either in A or B or both. It is represented by symbol “U”. Intersection of set is the collection of elements which are in both A and B.

• Let there are two sets A and B then,
  n(AUB) = n(A) + n(B) n(A ∩
• If there are 3 sets A, B and C then
  n(AUBUC) = n(A) + n(B) + n(C) n(A ∩ n(B ∩ n(C ∩A) + n(A ∩B∩

To maximize overlap,

• Union should be as small as possible
• Calculate the surplus = n (A ) + n (B) + n (C ) n AUBUC)
• This can be attributed to n (A∩B∩C ′), n (A∩B′∩C n (A′∩B∩C ), n (A∩B∩C).
• To maximize the overlap, set the other three terms to zero.

To minimize overlap

• Union should be as large as possible
• Calculate the surplus = n (A ) +n(B) +n(C ) n (
• This can be attributed to n(A∩B∩C ′), n (A∩B′∩ n (A′∩B∩ n (A∩B∩C).
• To minimize the overlap, set the other three terms to maximum possible.

Some other important properties

• A’ is called complement of set A, or A’ = U A
• n( A B) = n( A) n( A∩B)
• A B A∩B’
• B A = A’∩B
• (A B) U B = A U B

Q: A club has 256 members of whom 144 can play football, 123 can play tennis, and 132 can play cricket. Moreover, 58 members can play both football and tennis, 25 can play both cricket and tennis, and 63 can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is
Option A: 32
Option B: 43
Option C: 38
Option D: 45
Answer: Option B

n(FUTUC) = 256; n(F) = 144; n(T) = 123; n(C) = 132; n(F∩T) = 58; n(C∩T) = 25; n(F∩C) = 63
Also, we know that
We know that (AUBUC) = n(A) + n(B) +n(C) - n(A∩B) - n(B ∩C) - n(C∩A) + n(A ∩B∩C)1695626457618
So, 256 = 144 + 123 + 132 - 58 - 25 - 63 + n (F T ∩C)n (F∩T∩C) = 256 - 253 = 3
So, number of students who play Table Tennis only = n(T) – n(F∩T) – n(T∩C) + n(F∩T∩C)
Number of students who play Table Tennis only = 123 – 58 – 25 + 3 = 43

Pie Chart

• Focus on practicing as much as you can: The questions in DILR are based on data in tables, charts, graphs, diagrams, case studies, logical games, calendars, clocks, cubes, seating arrangements, blood relations, etc. Hence to be able to solve these questions on time and accurately, candidates have to practice as many questions as possible in the last few days. Mock test and previous year paper are the best resource to do so.
• Practice time management: This year the candidates shall get 40 mins per section. Hence the candidates have to ensure that they are not spending a lot of time in one particular questions, but their time is equally divided among all the 3 sections. The best is to practice the DILR questions in a manner that all the questions are completed within 40 mins and with 100% accuracy.
• Do not start any new topic in DILR now: Suppose a candidate has not yet practice the pie chart type question, then it is advised to just have a look at those type of questions. Do not start the topic from the scratch as this will only lead to confusion in concepts. Since CAT has negative marking, it is always better to focus on the strengths and get as many correct answers as possible.
• Question selection: In the last week is for strategising, the candidates must figure out what type of questions they are most comfortable to solve. These questions must be solved first on the exam day. This will enable the candidates to stay high on confidence while solving the problems and will save time as well.
• Accuracy is important: The candidates have to focus on getting a question accurate in one go. The level of practice must be such that the candidates can solve the question and get the correct answer in one go.
• Practice to scan the questions: Most of the answers in the DILR section is hidden in the question itself. Hence, candidates need a sharp eye, out of box thinking, and ability to read between the lines. This can come from regular practice, try to understand the questions and read it more than once.