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

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

Edited By Irshad Anwar | Updated on Sep 25, 2023 01:11 PM IST | #CAT

Hello, aspiring CAT 2023 candidates, The CAT exam 2023, scheduled for November 26 in preparation for MBA admissions from 2024 - 2026, has released its admit cards. In the continuation of the CAT 2023 60 days preparation guide series of Careers360, on day 50 we will discuss the strategies for Set Theory questions for the CAT exam, problems on grids and idioms and phrases for CAT 2023 that can help you prepare well and crack the CAT entrance test 2023. Students can download the Set Theory CAT Questions pdf.

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

This article mainly includes Set theory for CAT exam,Solved set theory questions,Venn diagram CAT questions, Maths Grid Quadrants and Idioms for MBA exam.

CAT Preparation 2023 in 60 days

Part-1: Quantitative Aptitude for CAT exam

Important Concepts/Formula Used in Set Theory Questions for CAT. CAT questions on grid puzzles with solutions are given below:

Concepts are Formulas Used in set theory for CAT exam are given below:

  • Set Notation

Ex: Set of Even numbers between 1 to 10

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

  • Cardinality of Set: number of elements in a set

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In the above example it is 5.

  • Types of Sets:

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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: Contain 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 past year venn diagram questions):

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

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Set theory questions CAT with solutions are given below:

Solution: [1]

The following Venn diagram best represents AΔB

1695626457020

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]

1695626458096

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

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

Find the tips and trick of set theory for 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’ = { }

  1. Use a Venn diagram while solving the questions.

  1. Learn the concept of Boolean Algebra.

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

CAT entrance exam: Prerequisite to CAT Set Theory

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

  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 2023: 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 2023 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)

CAT 2023 Syllabus Topic: Strategy to prepare “Mathematical Grid” for CAT

Important Concept/Formula Used in Problems on Grids

These questions are basically the application of topics such as Arrangement, Permutation and Combination, 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]

1695626458155

According to given question Queen can move UP, DOWN, LEFT, RIGHT and DIAGONALLY so Queen positioned in the above matrix it 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]

1695626458293


According to the given question, we need to position 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 much Sudoku 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. Puzzles

  2. Sudoku

References to 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 2023: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)

CAT Exam Important Topic: Strategy to Prepare “Idioms and Phrases” (Part-2) for CAT 2023 exam

Students can download the following for more practice tests idioms and phrases for CAT exam pdf

Previous Years Questions on Idioms and Phrases for MBA exams

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

Q1. Idioms for 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 meeting 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 is wrong according to the context of the sentence.

A can be eliminated as condemning has to do nothing 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 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 Idiom

As a piece of cake is very easy to cut and eat, in the same context this idiom signifies that 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 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 2023: Pre-requisite to Idioms and Phrases

  1. The basic idea of sentence structure.

  2. Good Vocabulary.

References to Study (Theory) idioms for CAT 2023 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 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!

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Questions related to CAT

Have a question related to CAT ?

It seems unlikely that you would be able to get admission in the BTech CS branch at BIT Sindri or Mesra with a CML rank of 2058 and category rank of 433.

Key points:

1. The search results indicate that a CML (Common Merit List) rank of 2058 is quite low for admission to premier engineering colleges like BIT Sindri or NIT Mesra.

2. The cutoff ranks for BTech CS branch at these institutes are usually much higher, often in the range of 1000-2000 for the general category.

3. With a category rank of 433, you may have a better chance of getting admission in the reserved category quota, but the competition is still quite high.

4. The search results do not provide specific cutoff details for BIT Sindri or NIT Mesra, but the general trend suggests your current ranks may not be sufficient for the CS branch in these institutes.

My advice would be to:

1. Check the latest cutoff ranks and admission criteria on the official websites of BIT Sindri and NIT Mesra.

2. Explore other options like state-level engineering colleges or NITs where your current ranks may have a better chance of securing admission.

3. Consider improving your performance in the next attempt of the entrance exam to increase your chances of getting into your desired BTech program.



For VARC, read daily from diverse sources (newspapers, novels, journals) to improve comprehension and vocabulary. Practice RC passages and verbal ability questions regularly. For DILR (Data Interpretation and Logical Reasoning) and QA (Quantitative Aptitude), solve previous years' papers and take mock tests to identify weak areas. Join a coaching institute or online courses for guidance and stay consistent with your study schedule. Review and analyze your performance in mocks to understand mistakes and improve. Maintain a positive mindset and stay disciplined in your preparation.

Hello aspirant,

Every year, IIMs conduct the Common Admission Test (CAT), a national MBA entrance exam, in rotation. For admission to over 1,200 institutions and premier B-schools in India, as well as PGDM, Executive MBA, PhD, and FPM programmes, the IIM CAT exam is regarded as one of the most difficult MBA entrance exams to pass. One of the best MBA schools in India, IIMs offers PGDM and MBA programmes for students who pass the CAT exam with scores in the 82nd to 99th percentiles.

For complete information you can visit our website by clicking on the link given below.

https://bschool-careers360-com.cdn.ampproject.org/v/s/bschool.careers360.com/exams/cat/amp?amp_gsa=1&amp_js_v=a9&usqp=mq331AQIUAKwASCAAgM%3D#amp_tf=From%20%251%24s&aoh=17204523672625&csi=1&referrer=https%3A%2F%2Fwww.google.com&ampshare=https%3A%2F%2Fbschool.careers360.com%2Fexams%2Fcat

Thank you

Hope this information helps you.

Hello!

The educational qualification required for CAT exam is bachelor's degree or its equivalent from a recognized university with minimum of 50% for the open category and 45% for the SC/ST/PwD category. Since you have secured more than the required percentage in your bachelor's degree, you are eligible for CAT exam.

For more information, please visit the website by clicking on the link given below:

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I hope you will find this information helpful. Best wishes ahead!

Hello Aspirant,

Yes, you can sit for the CAT exam with a CGPA of 8.5. However when you do crack the CAT exam and have to sit for the interview round or the Group discussion round, you will be asked the question about 4 years of graduation, in which case, carry your hospital records and medical certificates to prove to them that you actually had some health issues during your graduation. This shouldn't be a problem because you had a genuine reason for the one-year gap.

View All

1-radian measures 600. (True/False)

Option: 1

True


Option: 2

False


$111111^2$ = 

Option: 1

123456654321


Option: 2

123454321


Option: 3

123454321


Option: 4

12345654321


1111112 =___________ 

Option: 1

 123456654321


Option: 2

1234554321


Option: 3

123454321


Option: 4

12345654321


159702 is divisible by

Option: 1

7


Option: 2

9


Option: 3

11


Option: 4

6


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What best can be said about the number of satellites serving C? 

Option: 1

Must be between 450 and 725 

 


Option: 2

Cannot be more than 800 
 


Option: 3

Must be between 400 and 800 

 


Option: 4

Must be at least 100 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What is the minimum possible number of satellites serving B exclusively? 

Option: 1

100


Option: 2

200


Option: 3

500


Option: 4

250


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S? 

Option: 1

At most 475 

 


Option: 2

Exactly 475 
 


Option: 3

At least 475 

 


Option: 4

No conclusion is possible based on the given information 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

 If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE? 

Option: 1

The number of satellites serving C cannot be uniquely determined 

 


Option: 2

The number of satellites serving B is more than 1000 
 


Option: 3

All 1600 satellites serve B or C or S 

 


Option: 4

The number of satellites serving B exclusively is exactly 250 


2839155 is divisible by

Option: 1

2


Option: 2

7


Option: 3

55


Option: 4

None of the above


'a' for which x^{2}-ax+9= 0 can be written as square of a linear factor is

Option: 1

6


Option: 2

-6,6


Option: 3

\left ( 6,\infty \right )


Option: 4

\left ( -\infty,-6 \right )


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