Decoding CAT 2025 Preparation: Exploring PnC, Selections, Syllogism Important PYQs, and Comparison - Day 37

CAT Preparation 2025 in 60 days

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

CAT Exam Important Topic: Strategy to Prepare Permutation and Combination (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

nPr = n!/n-r!

2. nPn = n!

3. nCr = nCn-r

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

5. 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

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

7. 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

8. Learn all the formulas and understand their applications.

9. 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 2025 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)

CAT 2025 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 2024]

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 2025: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)

CAT Exam Important Topic: Strategy to Prepare “Comparison (Comparatives and Superlatives)” for CAT-2025.

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 2025: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.

3. 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

4. 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

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

6. Comparative adjectives: using than

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

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

9. 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!

Free PDFs for CAT Preparation 2025