Cracking CAT 2025: Your Guide to Understanding Factors, Tables, Conjunctions, and Interjections - Day 5

Part-1: Quantitative Aptitude for CAT 2025

Topic: CAT Number System-4 (Factors and Trailing Zeroes)

Factors

CAT number system questions based on factors are regularly asked in the CAT exam and other MBA entrance examinations.

Questions about factors are of the form of

• To find the number of all factors

• To find the number of even factors

• To find the number of odd factors

• To find the number of factors of multiple of some value (Value will be given)

• To find the number of factors which are perfect squares/perfect cubes etc

• To find the number of Co-prime factors

• To find the sum of factors

• To find products of all factors etc.

• Number of ways of writing a number N as a product of two numbers?

Important Formula for CAT number system questions

Number of factors:

Do Prime factorization first

N = pa × pb × rc × … where p, q, r are prime numbers; a, b, c are positive integers

The number of factors of N= (a+1)(b+1)(c+1)…

Sum of factors

Do prime factorisation first.

N = pa × qb × rc × … where p, q, r are prime numbers; a, b, c are positive integers

Sum of factors = (pa+1-1/p-1) (qb+1-1/q-1) (rc+1-1/r-1)

Trailing Zeroes and Exponent of a prime number:

Trailing zeroes give the number of zeroes at the end of the number.

For example, 54600 has two trailing zeroes.

In a product, a pair of 2 and 5 forms one trailing zero. This concept is used to find the number of trailing zeroes.

From this topic following types of questions were asked:

• Find the trailing zeroes in 54! etc

• Find the trailing zeroes in x3b x5c etc

• Find the highest power of 7 in 200! etc

Previous Year CAT questions on number system

The two previous year CAT questions as per the number system CAT Syllabus are given below:

Q1. How many factors of 24 × 35 × 104 are perfect squares which are greater than 1? [TITA- CAT Question Paper 2019]

Solution:

N = 24 × 35 × 104 = 24 × 35 × 24 x 54 = 28 × 35 × 54

Perfect square factors will be formed only for even (including 0) powers of prime factors.

Powers of 2 for which perfect square factors will be found for = 0, 2, 4, 6, 8 (5 ways)

Powers of 3 for which perfect square factors will be found for = 0, 2, 4 (3 ways)

Powers of 5 for which perfect square factors will be found for = 0, 2, 4 (3 ways)

Total number of perfect square factors will be = 5 x 3 x 3 = 45

Total number of perfect square factors greater than 1 will be = 45 – 1= 44

So, the answer is 44.

Q2. What is the highest power of 12 that divides 54!

[Based On CAT Question Paper ]

1. 25

2. 26

3. 30

4. 4

Solution: A

12 = 22 x3, so we need to count the highest power of 2 and highest power of 3 that will divide 54!

The highest power of 2 divides 54! = [54/2] + [54/4] + [54/8] + [ 54/16] + [54/32]

= 27 + 13 + 6 + 3 + 1 = 50, where [x] ? greatest integer function.

Highest powers of 4 that divides 54! = 50/2 = 25

Highest power of 3 that divides 54! = [54/3] + [54/9] + [54/27] = 18 + 6 + 2 = 26, where [x] ? greatest integer function.

So, the highest power of 12 that divides 54! = min (25, 26) = 25.

Prerequisite:

To prepare for the number system for CAT exam according to the number system CAT syllabus, a student must have knowledge of

• Prime, Composite and Co-primes

• Even and Odd numbers

• Sum of Geometric Progression

• Exponents

• Factorials

Tips On CAT Preparation For Number System (Factors and Trailing Zeroes)

1. Find the number of 5s to find the trailing zeroes is n! as the number of 2s is always greater than the number of 5s.
   Eg: number of trailing zeros in 100! = [100/5] + [100/25] = 20 + 4 =24 where, [x] is the greatest integer function.
   So, we can write the number of trailing zeroes in n! = [n/5] + [n/25] + [n/125] + ……….

2. Product of all factors of N = N (no of factors/2)

3. To find the even factors, divide the given number by 2 and find the number of total factors of the quotient.

4. Apply the concepts to practice Number System questions.

5. Practice previous year CAT questions on number system

References to Study (Theory):

1. 1. Learn the concept of factors and Multiples from class 9 Mathematics NCERT (For Theory)

2. Arun Sharma: A Quantitative Approach for CAT (6th Edition)

3. Kailasha Online Learning Classroom

References to Study (Practice):

1. MASTER Number System for CAT and GMAT by Nishit K Sinha.

2. Sample Papers

3. CAT previous year papers

Part-2: Data Interpretation And Logical Reasoning For CAT 2025

Topic: Data Interpretation (Table)

In previous articles, we have covered DI based on Bar graphs, Pie charts and Line graphs. In this article, we will deal with data represented in the form of a table for the CAT exam. Data interpretation is a must-come topic in the CAT Exam and other management entrance exams.

DI on Table Chart

In this section, we will discuss the basics of a table chart. The boxes of the table consist of different types of information such as the population of a town, marks of a student, expenses of a company, production data of any industry etc. Table Chart questions are extremely important and have a good weightage as well. Many students sometimes find it difficult to solve these types of questions. Therefore, its recommended for students to practice these questions rigorously.

Sample:

Average marks of students of class 10 of different schools of a city are represented subject wise as shown in table:

Questions On the Line Graph From CAT Previous Year Papers

Answer the questions on the basis of the information given below. A study was conducted to ascertain the relative importance that employees in five different countries being assigned to five different traits in their Chief Executive Officers. The traits were compassion (C), decisiveness (D), negotiation skills (N), public visibility (P), and vision (V). The level of dissimilarity between two countries is the maximum difference in the ranks allotted by the two countries to any of the five traits. The following table indicates the rank order of the five traits for each country. [ CAT Question Paper 2015]

Q1. Which of the following pairs of countries are most dissimilar?

1. China and Japan

2. India and China

3. Malaysia and Japan

4. Thailand and Japan

Ans: (4)

Difference in ranks skills-wise is shown as below:

Thailand and Japan should be the answer since these countries show the maximum difference in ranks (i.e., 4) on the basis of decisiveness.

No other countries show a difference of 4.

Q2. Which of the following countries is least dissimilar to India?

1. China

2. Japan

3. Malaysia

4. Thailand

Ans: (1)

Difference between the ranks on the basis of given traits of other countries with India is calculated.

India and China show a maximum difference of 2 for 1 time.

India and Japan show a difference of greater than 2 (Compassion), so it cannot be least dissimilar and we need not to calculate differences for other traits.

Similar is the case with Malaysia.

With Thailand, the difference of 2 appeared twice. Therefore it can not be least dissimilar. The answer is China.

Q3. Which amongst the following countries is most dissimilar to India?

1. China

2. Japan

3. Malaysia

4. Thailand

Solution: (2)

since China is the least dissimilar, as discussed in the previous question. So, China cannot be the answer, and we will not find the differences for China in this case.

Clearly, Japan shows the maximum difference in ranks, So Japan is most dissimilar in ranks with India

Prerequisite:

To prepare Data Interpretation (Line Graph) for the CAT exam, a student must learn

• Percentage (Basic)

• Averages

• Calculations based on ratios

• Approximation

Tips On CAT Preparation For DI (Table Chart):

1. Use Approximation.

2. Observe the data carefully.

3. Solve small calculations mentally.

References to Study (Theory):

1. LRDI for CAT and GMAT by Nishit K Sinha.

2. To learn the basics of bar graph read statistics of class 9 and Class 10 Mathematics from NCERT (For Theory)

3. Kailasha Online Learning Classroom YouTube Channel

References to Study (Practice):

1. Sample Papers

2. Question bank from CAT-Holic

3. How to Prepare for Data Interpretation for CAT by Arun Sharma

4. CAT previous year papers

Part-3: VARC for CAT 2025

Topic: Conjunction and Interjection and its uses:

Conjunctions are used to connect more than two words or phrases. It defines the connection between the joined sentences.

Examples:

He likes to eat both Noodles and Pizza.

The tulips and orchids are flowers.

Until next month, I can’t afford to travel.

Conjunctions are useful as well as convenient. Conjunctions are extremely common.

There are three types of English conjunctions:

Coordinating: for, not, yet, so etc

Subordinating: Although, though, while, if, until etc.

Correlative: Neither/ Nor, Whether/ Or, Either/ Or etc.

Interjections are used to express emotions in a sentence. Also, interjections are grammatically independent of the words around them.

Examples:

Greeting: Hey! After such a long time, I am seeing you.

Joy: Oh my gosh! What is happening there?

Surprise: Ah! Finally you clear your CAT Exam!

Approval: Yes! you are hired!

Attention: Listen, you are fired.

Sorrow: Oh dear, I really wanted to marry you.

Questions On Conjunction and Interjection from CAT Previous Year Papers/ CAT practice questions on conjunctions

Direction: Choose the part which requires correction. [Based on Previous Years Questions]

Q.1 As soon as (1) / he got the (2) / courier, at once (3) / he started. (4) / No Error (5)

1. (1)

2. (2)

3. (3)

4. (4)

Ans: C

The conjunction 'as soon as is used to show two simultaneous actions. So, in the third part, the use of ‘at once’ is incorrect

Q2. I will either (1) / go for an interview (2) / else play (3) / Cricket. (4) / No Error (5)

1. 1

2. 2

3. 3

4. 4

5. 5

Ans: C

With “Either’, ‘Or’ comes.

So, (3) contains error. ‘else’ should be replace by ‘or’.

Q3. Be kind (1)/ not only in words (2) / and also (3) / in behavior. (4) / No Error (5)

1. 1

2. 2

3. 3

4. 4

5. 5

Ans: C

The correct conjunction to be used is ‘but’ in place of ‘and’.

Prerequisite:

• Knowledge of sentence formation

• Basic Knowledge of Sentence Formation

• Use of Nouns, Pronouns and Verbs.

CAT Preparation Tips for Verbal Ability (Conjunction and Interjection)

Use of the comma when a coordinating conjunction is joining two independent clauses.

When a conjunction joins two words in a sentence, then the sentence cannot be separated in two independent sentences.

Learn all the conjunctions and their uses separately with the help of examples.

References to Study (Theory):

1. Advanced English grammar by Wren and Martin

2. 2iim YouTube Channel

References to Study (Practice):

1. Question Bank from iquanta.com

2. CAT previous year papers

3. How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)

Tips and Tricks to Solve Factor and Table Questions

Mastering factors and multiplication tables is essential for quick and accurate math problem-solving. With the right strategies, identifying factors and solving table-based questions becomes easier. Practice, recognition of patterns, and smart shortcuts significantly improve speed and confidence in exams.

Tip 1: Learn Tables Up to 20 Thoroughly

Example: To solve 14 × 7 quickly, recall the table of 14: 14, 28, 42, 56, 70, 84, 98.

Memorising multiplication tables up to 20 boosts your ability to solve problems swiftly. Knowing answers instantly reduces the time needed for calculations and supports better factor recognition. Use songs, flashcards, or apps to reinforce memory.

Tip 2: Use Factor Pairs

Example: Factors of 36: (1,36), (2,18), (3,12), (4,9), (6,6)

Writing numbers as factor pairs helps in identifying all possible factors efficiently. Start with 1 and go up to the square root of the number. For 36, check from 1 to 6; each valid division gives a complete pair.

Tip 3: Apply Divisibility Rules

Example: 72 is divisible by 3 because 7 + 2 = 9 (which is divisible by 3).

Divisibility rules help identify factors quickly without full division. Learn rules for 2, 3, 5, 6, 9, and 10. These rules simplify spotting common factors and validating whether one number is a factor of another.

Tip 4: Break Numbers into Prime Factors

Example: 60 = 2 × 2 × 3 × 5

Prime factorisation breaks a number down into its simplest building blocks. This is especially helpful in finding LCM, HCF, or solving word problems. Use factor trees or the division method for clarity and systematic calculation.

Tip 5: Use Multiples to Identify Common Factors

Example: Multiples of 6: 6, 12, 18, 24...; Multiples of 8: 8, 16, 24... ⇒ Common multiple: 24

Listing multiples can identify the least common multiple (LCM) or help in comparing tables. It’s useful when solving time-based or event problems where something repeats at different intervals.

Tip 6: Recognise Square and Cube Numbers

Example: 49 is 7²; 27 is 3³

Recognising square and cube numbers helps quickly determine factors and simplify root-based problems. Memorise squares up to 30 and cubes up to 12 to improve speed and pattern recognition in exams and mental math tasks.

We will be back with Day-6 strategy. Do practice and be focused.

Thank You

All the best.

Free PDFs for CAT Preparation 2025