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Decoding CAT Preparation: Exploring PnC, Selections, Syllogism Important PYQs, and Comparison- Day 37

Decoding CAT Preparation: Exploring PnC, Selections, Syllogism Important PYQs, and Comparison- Day 37

Edited By Irshad Anwar | Updated on Sep 20, 2023 09:35 AM IST | #CAT

Hello CAT 2023 candidates,

On November 26, the CAT exam 2023 for MBA admissions 2024–2026 will take place. In this CAT 2023 60-day preparation guide series of Careers360, we will discuss the strategies on permutation and combination problems for day 37 that can help you prepare well and crack the CAT entrance test 2023.

This article includes permutation and combination problems, syllogism questions with answers, and understanding comparison in VARC. Permutation and combination problems are considered a bit tough and aspirants find it difficult to solve these types of questions. In this article we have included permutation and combination examples with answers and also PYQs for the students to practice from.

Decoding CAT Preparation: Exploring PnC, Selections, Syllogism Important PYQs, and Comparison- Day 37
Decoding CAT Preparation: Exploring PnC, Selections, Syllogism Important PYQs, and Comparison- Day 37

CAT Preparation 2023 in 60 days

Part-1: Quantitative Aptitude for CAT exam (Permutation and Combination Aptitude)

CAT Exam Important Topic: Strategy to Prepare Permutations and Combinations (Selection, Grouping and Distribution) and permutation and combination problems.

Permutation and combination problems

  1. The number of permutations of n distinct items taking r items at a time is

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nPr = n!/n-r!

  1. nPn = n!

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  1. nCr = nCn-r

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  1. Out of n given things, the number of ways of selecting any number = 2n -1.

  1. Dividing n items into two groups of p and q items

= n!/q! p!

  • If p =q and two groups are not identical; a number of groups will be n! /(p!)2

  • If p =q and two groups are identical; a number of groups will be n!/2! (p!)2

  1. The number of diagonals in an n-sided regular polygon = nC2 – n

  1. Divide questions of distributions into the following categories while solving:

  • Identical Objects Identical Places

  • Identical Objects Distinct Places

  • Distinct Objects Identical Places

  • Distinct Objects Distinct Places

  1. Learn all the formulas and understand their applications.

  1. Practice all kinds of permutation and combination problems.

CAT Exam:

Previous Year CAT Questions on Permutations and Combinations (Selections and Groupings, Distributions):

Q1. The number of ways of distributing 15 identical balloons, 6 identical pencils and 3 identical erasers among 3 children, such that each child gets at least four balloons and one pencil, is [TITA, CAT 2021 Slot-2]

Permutation and combination examples with answers: 1000 ways

Given that, there are 15 identical balloons, 6 identical pencils, and 3 identical erasers.

We need to distribute these items among 3 children, such that each child gets at least four balloons and one pencil.

First, distribute 4 balloons and 1 pencil to each child. Now, we have 3 balloons, 3 pencils, and 3 erasers left with us after distribution.

Remaining balloons can be distributed in following possible combination;

(3, 0, 0), (2, 1, 0), (1, 1, 1)

(3, 0, 0) can be arranged in three ways.

(2, 1, 0) can be arranged in six ways.

(1, 1, 1) can be arranged in only one way.

The total ways of distributing the remaining balloons are 6+ 3+ 1= 10 ways.

Similarly, we can arrange 3 pencils in 10 ways and 3 erasers in 10 ways.

Therefore, the total number of ways is 10 x 10 x 10 = 1000 ways

Permutation and Combination Aptitude

Q2. In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser. Still, nobody gets more than 3 erasers? [CAT 2017]

  1. 16

  2. 20

  3. 14

  4. 15

Permutation and combination examples with answers

Ans: A

We have to find by how many numbers of ways the erasers are distributed such that each kid gets at least one eraser but nobody gets more than 3 erasers.

4 kids are getting a, b, c, d erasers such that a + b + c + d = 7.

a = p+1

b = q+ 1

c = x+ 1

d = z+1 since each should have at least 1 eraser.

So, p + q+ x+ y = 3

number of ways of distribution = n+rCr-1; here n =3, r = 4(number of variables)

So, the number of ways of distribution = 6C3 = 20 ways

If one kid a, gets 4 erasers the other kids b, c, and d can get each one respectively such that 4, 1, 1, 1 or 1, 1, 1, 4 or 1, 4, 1, 1 or 1, 1, 4, 1 so there are chances of 4 ways.

So, required ways = 20 – 4 = 16 ways

CAT entrance exam: Pre-requisite to permutation and combination problems

CAT permutation and combination questions

  1. Vedic Maths

  2. Factorial

  3. Fundamental Principle of counting

CAT study material: References to Study (Theory)

Permutation and Combination problems:

  1. NCERT Class 11 Maths

  2. CAT Funda (YouTube, Link: https://www.youtube.com/watch?v=509qwiX-3qY)

  3. https://www.youtube.com/watch?v=QsKl5GbBcHU

Study material: References to Practice CAT Permutation and Combination Questions (Syllogism)

  1. How to prepare quantitative Aptitude for CAT by Arun Sharma.

  2. CAT Funda (YouTube, Link: https://www.youtube.com/watch?v=RAOTFT1_Ynk)

Part-2: CAT 2023 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)

CAT 2023 Syllabus Topic: Strategy to prepare “Syllogism through PYQs” (Part-2) and syllogism reasoning questions and Syllogism examples with answers

CAT Exam:

Previous Year CAT Questions on Syllogism from CAT/ MBA Entrance Exam:

Q1. The following question is given by 3 statements and 2 conclusions numbered I and II. Choose the right answer from the given options. [MAHCET MBA 2023]

Statements:

I. No Box is a Book.

II. Few cups are books.

III. Only a few knives are Boxes.

Conclusions:

I. Some Knives being a book is a possibility.

II. All Cups being a Book is a possibility.

  1. If only conclusion I follows

  2. If only conclusion II follows

  3. If either I or II follows

  4. If neither I nor II follows

  5. If both conclusions follow

Solution: [E]

Cat Tips for syllogism 1: Draw Venn Diagram first

Cat Tips for syllogism 2: ‘A few’ means ‘some’

Cat Tips for syllogism 3: Go through Conclusions.

Conclusion 1: Some Knives being a book is a possibility.

Some Knives are there which are not certain to be either Boxes or Books. Therefore, Some knives can be book. So, first will follow.

Conclusion 2: All Cups being a Book is a possibility.

All cups can be inside Book. So, this is a possibility. Therefore, II will follow.

Syllogism examples with answers

Q2.

Statements

i) Some Cubes are Circles.

ii) No Circle is a Triangle.

iii) No line is a Cube.

Conclusions:

i) All Cubes can never be triangles.

ii) Some lines are Circles.

iii) No triangle is a cube.

iv) No line is a circle.

  1. All follows

  2. I, II and III follow

  3. I, IV and III follow

  4. II, IV and III follow

  5. None of these

Solution: (E)

Cat Tips for syllogism 1: Draw Venn Diagram first

Cat Tips for syllogism 2: Go through Conclusions.

i) All Cubes can never be triangles: Some cubes are Circles. So, definitely, some cubes are there which can never be Triangle.

Therefore, (i) will follow.

ii) Some lines are Circles: Not a definite conclusion; it will not follow.

iii) No triangle is a cube: Not a definite conclusion; it will not follow.

iv) No line is a circle: Not a definite conclusion; it will not follow.

Clearly, the third statement will follow.

CAT entrance exam: Prerequisite to syllogism reasoning questions

  1. Set Theory

  2. Venn Diagram

  3. Concept of Syllogism

References to Study (Theory syllogism questions for CAT

  1. Verbal and Non-Verbal Reasoning by B S Sijwali

  2. CAT Handa (YouTube link: https://www.youtube.com/watch?v=4N8qsbClYpA)

References to Practice syllogism questions for CAT

  1. Verbal and Non-Verbal Reasoning by R S Agrawal.

  2. MBA Entrance Exams Previous years Papers.3. ELITES GRID (YouTube; Link: https://www.youtube.com/watch?v=sn_k4q6BHxk)

Part-3: CAT Exam Preparation 2023: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)

CAT Exam Important Topic: Strategy to Prepare “Comparison (Comparatives and Superlatives)” for CAT-2023.

CAT Important Concepts

  • Comparative Adjectives and Superlative Adjectives Fast?Faster (Comparative)?Faster (Superlative)

  • Comparative Adverbs and Superlative Adverbs

  • Negative Comparatives

CAT Previous Years' Questions on Comparison (Comparatives and Superlatives).

Q1: My daughter is__________ than my wife

  1. more taller

  2. more tall

  3. taller

  4. tall

Ans: [C]

Here is a comparison between two persons.

Q2. This is the ____________chocolate I have ever had.

  1. best

  2. better

  3. good

  4. well

Ans: [A]

‘best’ is best suited because comparison is with all time.

CAT 2023:Prerequisite

  1. Sentence Structure

  2. Adjectives and Adverbs

  3. Comparative and Superlative Degrees

Tips and Tricks for CAT Exam

  1. Learn comparative and superlative adjectives.

  2. Learn the pronunciation of these comparatives and superlatives:

  • long /lɒŋ/ longer /lɒŋgə(r)/ longest /lɒŋgəst/

  • strong /strɒŋ/ stronger /strɒŋgə(r)/ strongest /strɒŋ gəst/

  • young /jʌŋ/ younger /jʌŋgə(r)/ youngest /jʌŋgəst/Put structurally equivalent verbs in the same form.

  1. Some one-syllable adjectives have irregular comparative and superlative forms:

  • bad, worse, worst far, farther/further, farthest/furthest

  • good, better, best old, older/elder, oldest/eldest

  1. Two-syllable adjectives

Two-syllable adjectives ending in -y change y to i and take the -er and -est endings:

  • busy, busier, busiest

  • happy, happier, happiest

  • easy, easier, easiest

  • funny, funnier, funniest

  1. Comparative adjectives: using much, a lot, far, etc.

  1. Comparative adjectives: using than

  1. Comparative adjectives: -er and -er, more and more

  1. Comparative adjectives: the -er, the -er and the more …, the more …

  1. Use than, not that or as to introduce a clause after a comparative adjective or adverb

CAT exam: References to Study (Theory)

  1. Wren and Martin

  2. (https://www.youtube.com/watch?v=cpQbmdKkNFs)

CAT exam: References to Study (Practice)

  1. Verbal Ability for CAT by Arun Sharma and Meenakshi Upadhyay.

  2. CAT Previous years Papers and Sample Papers.

  3. (youTube; Link: https://www.youtube.com/watch?v=pm9fq1MbR_I)

Day 37 will be posted tomorrow, so practice and stay focused.

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.

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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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