CAT Prodigy: Nailing Set Theory, Mathematical Grids, and Depth understanding of Idioms & Phrases- Day 50

Part-1: Quantitative Aptitude for CAT exam

Quantitative Aptitude is a crucial section in the CAT exam, testing your numerical ability and problem-solving skills. It includes topics like arithmetic, algebra, geometry, and number systems. Strong basics, regular practice, and smart shortcuts are key to scoring well. Mastering this section boosts your overall CAT percentile significantly.

• Set Notation

Ex: Set of Even numbers between 1 to 10

S = {2, 4, 6, 8, 10}

• Cardinality of a Set: The number of elements in a set

In the above example, it is 5.

• Types of Sets:

Null/Empty Set: does not contain any element, i.e. { }

Singleton Set: contains one element only.

Finite Set: elements in that set are finite.

Ex: S = {2, 4, 6, 8, 10}

Infinite Set: elements are not finite, whether countable or Uncountable.

ex, A = {x: x Є N}

Subset of A Set: B = {1,2} and S = {1, 2, 3, 4, 5}; B is a subset of S.

Equal Sets: Contain the same number of elements.

Universal Set: Contains all the objects.

CAT Set theory questions, Union and Intersection

• Union of Sets: A = {1, 2} and B = {2, 3, 4}, then

AᴜB = {1, 2, 3, 4}

• Intersection of Sets: A = {1, 2} and B = {2, 3, 4}, then A∩B = {2}

Complement of a set: If U = {1, 2, 3, 4, 5} and A = {1, 2}, then A’ = {3, 4, 5}

CAT Previous Year Questions on Set Theory

CAT Previous Year Questions on Set Theory, especially Venn diagram-based questions, are essential for understanding the types and difficulty levels of actual exam problems. They help students master logical grouping, intersection, and union concepts through real CAT exam patterns. Practising these CAT Set Theory PYQs builds accuracy, speed, and confidence for the Quant and DILR sections.

Q1. For two sets A and B, let AΔB denote the set of elements that belong to A or B but not both. If P = {1,2,3,4}, Q = {2,3,5,6,}, R = {1,3,7,8,9}, S = {2,4,9,10}, then the number of elements in (PΔQ)Δ(RΔS) is [CAT 2018, slot 2]

1. 7

2. 8

3. 9

4. 6

Set theory questions CAT with solutions are given below:

Solution: [1]

The following Venn diagram best represents AΔB

Therefore, AΔB = AUB - A∩B

So, PΔQ = PUQ - P∩Q = {1, 4, 5, 6}

And RΔS = RUS - R∩S = {1, 2, 3, 4, 7, 8, 10}

Then, (PΔQ)Δ(RΔS) = (PΔQ)U(RΔS) - (PΔQ) ∩ (RΔS) = {2, 3, 5, 6, 7, 8, 10}

So, the number of elements in (PΔQ)Δ(RΔS) = 7.

Q2. Set theory MCQ is given below:

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 [CAT 2019, Slot 1]

1. 32

2. 43

3. 38

4. 45

Set theory questions CAT with solutions are given below:

Answer: [2]

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)

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

CAT Exam Important Topic: Strategy to Prepare CAT: Set Theory and Set Theory Questions for CAT.

Find the tips and tricks of set theory for the CAT exam below:

1. Learn the laws of Algebra (for SET)

• AUB = BUA

• A∩B = B∩A

• (AUB)UC = AU(BUC)

• (A∩B)∩C = A∩(B∩C)

• AU(B∩C) = (AUB)∩(AUC)

• A∩(BUC) = (A∩B)U(A∩C)

• AᴜU = A

• A∩U = A

• AUA’ = U

• A∩A’ = { }

2. Use a Venn diagram while solving the questions.

3. Learn the concept of Boolean Algebra.

4. Practice Previous Years Set Theory CAT Questions to get an idea of the questions.

CAT entrance exam: Prerequisite to CAT Set Theory

You must be well aware of the following before solving set theory questions for a competitive exam:

1. Venn Diagram

2. Boolean Algebra

References to Study (Theory) CAT Set Theory

Study below given resources for set theory questions for competitive exams:

1. NCERT Mathematics Class 11 and 12

2. How to Prepare Quantitative Aptitude by Arun Sharma (7th Edition)

CAT study material: References to Practice CAT Questions on Set Theory

CAT Exam 2025: Set Theory

1. Quantitative Aptitude by R.S. Agrawal.

2. Easy Ganit: YouTube (https://www.youtube.com/watch?v=fi8YO7k1trY)

3. https://www.youtube.com/watch?v=iul2Y3bvsXM

4. Practice Sample Papers on Solved Set Theory Questions

Part 2: CAT 2025 Preparation Tips for Logical Reasoning and Data Interpretation

DILR tests your ability to think logically and interpret data quickly. Regular practice, clear thinking, and a calm approach help improve performance. Focus on understanding question patterns, choosing the right sets, and managing time wisely during the exam.

These questions are basically the application of topics such as Arrangement, Permutation and Combination, and Average. So, students must have a higher degree of understanding of these.

Grid-ins Sample Question Based on CAT Previous Years' Questions:

In an 8 X 8 chessboard, a queen placed anywhere can attack another piece if the piece is present in the same row, or in the same column or in any diagonal position in any possible 4 directions, provided there is no other piece in between in the path from the queen to that piece. The columns are labelled a to h (left to right), and the rows are numbered 1 to 8 (bottom to top). The position of a piece is given by the combination of column and row labels. For example, position c5 means that the piece is in the cth column and 5th row.

Q1) Grid-ins Sample Question is given below:

If the queen is at c5, and the other pieces are at positions c2, g1, g3, g5 and a3, how many are under attack by the queen? There are no other pieces on the board.

1. 2

2. 3

3. 4

4. 5

Ans: [C]

According to the given question Queen can move UP, DOWN, LEFT, RIGHT and DIAGONALLY, so the Queen positioned in the above matrix can attack L1, L4, L2 and L5 as well, so only 4 positions are under attack.

Q2) CAT questions on grid puzzles are given below:

If the other pieces are only at positions al, a3, b4, d7, h7 and h8, then which of the following positions of the queen results in the maximum number of pieces being under attack?

1. f8

2. a7

3. c1

4. d3

Ans: [D]

According to the given question, we need to position the Queen such that she can attack the maximum number of fighters. So, the trick is to use each option one by one, and you will find that D3 is the only option in which we attack 3 fighters and on the rest options, Queen can attack at max 2 fighters. So, the answer must be D3.

Tips/Tricks for CAT math grid quadrants

1. Solve as many Sudokus as possible

2. Solve puzzles books like Shakuntla Devi, George Summer’s

3. Solve Arrangement Reasoning Puzzles

4. Formulae related to Permutation &Combination and Averages must be thoroughly covered before attending these types of questions

CAT entrance exam: Pre-requisite

1. Puzzle

2. Sudoku

References to the CAT Study (Theory)math grid quadrants

1. LRDI by Nishit K. Sinha

2. CAT Funda (YouTube link: https://www.youtube.com/watch?v=z69ElNGKPFs)

3. Quantifiers cat Academy https://www.youtube.com/watch?v=DARbWHBZiv4

References to Study (Practice) Problems on Grids

1. Cat Wordpandit Website

2. MBA Entrance: Previous Years Papers and Sample Papers.

3. Cat Pepration-iquanta https://www.youtube.com/watch?v=aizuiNK9BW4

Part-3: CAT Exam Preparation 2025 for Verbal Ability & Reading Comprehension

To master idioms and phrases for CAT 2025, build a habit of reading newspapers, editorials, and quality fiction daily. Note down unfamiliar phrases, understand their usage in context, and revise regularly. Practice through topic-wise exercises and mock tests to improve recall and accuracy. A strong grasp of idiomatic language boosts both comprehension and verbal ability.

Previous Years' Questions on Idioms and Phrases for MBA exams

Tips and tricks for idioms and phrases using CAT's previous years' questions are given below:

Q1. Idioms for the MBA exam are given below:

She took one of the cookies, but I turned a blind eye.

1. To condemn someone

2. To overlook

3. To ignore something wrong

4. To protest against something right

5. To become blind after an accident

Ans. Option C

Explanation: To “turn a blind eye” to something means to pretend not to have noticed it.

Idioms Trick: Eliminate wrong options

Option D and E are wrong according to the context of the sentence.

A can be eliminated as condemning has nothing to do with the meaning.

Option B and option C are close, but if you closely look at option B, the word overlook means to fail something, and blind eye means to ignore; hence, option C is correct.

Q2. Idioms for the MBA exam are given below:

Yesterday’s test was a piece of cake:

1. Very Sweet

2. Very Tough

3. Contains many questions

4. Very Easy

Ans: D

Explanation:

Idioms Trick: See the context of the Idiom

As a piece of cake is very easy to cut and eat, in the same context, this idiom signifies something that is very easy for you.

Q3. Phrases for MBA Exam are given below:

In the sentence below, replace the phrase underlined to make the sentence grammatically correct. If the sentence is correct, mark (d), i.e. “No correction required” is the answer.

Whether I stay in Delhi or Gurugram, it is all and one to me.

1. all but one

2. all one

3. one and all

4. No correction required

Ans: [b]

CAT Trick on Phrases: See the context of the Phrase

Here, Delhi or Gurugram makes no difference to me. Therefore, ‘all one’ will be the right choice.

Q4. In the following question, an idiom or proverb has been highlighted. Choose its correct meaning in the given context from the alternatives given below.

Rani played a cat-and-mouse game with all her friends.

1. Rani played a game

2. Rani had a cat

3. Her friends gave her cats and mice

4. She played like a cat with her friends, who were all mice

Ans: [a]

CAT Trick: See the meaning of the Idiom and the context in which it is used

‘Cat and Mouse’ game means ‘to play a trick’. Option ‘a seems to be the best choice.

CAT 2025: Pre-requisite to Idioms and Phrases

1. The basic idea of sentence structure.

2. Good Vocabulary.

References to Study (Theory) idioms for the CAT 2025 exam

1. 200 Practical English Idioms by Alex Makar

2. Knowation (YouTube: https://www.youtube.com/watch?v=trft83xQqyM)

References to Practice idioms and phrases questions for the CAT exam

1. 200 Practical English Idioms by Alex Makar

2. engvid.com (Web)

3. Ck cetking (YouTube: https://www.youtube.com/watch?v=XOJo60Jteb8)

Practice and remain focused; Day 51 will be posted tomorrow.

Thank you!

All the Best!