Be a CAT Expert: Ace Sequences and Series, Coin Puzzle and Critical Reasoning Questions

Part 1: Quantitative Aptitude for CAT Exam

To solve sequence and series questions in CAT 2025, focus on arithmetic and geometric progressions, nth term formulas, and sum of terms. Mastering these core concepts helps improve speed and accuracy in the Quant section.

Concepts and Formulas used in sequence and series problems and solutions are given below:

1. Arithmetic Progression (AP)

nth term of A.P. given by an = a+ (n-1)d

Sum of n terms of an AP

Sn = n/2 {2a + (n-1) d} or n/2 {first term + last term}

Arithmetic mean is (a+ an)/2.

Here, a is the first term, d (=a2- a1) is a common difference and n is the number of terms in AP.

2. Geometric Progression (GP)

nth term of the G.P. is an = ar(n-1)

Sum of n terms of a GP

Sn = a{(1- rn)/(1-r)}

sum of an infinite G.P. is given by

S = a/1-r

Geometric Mean of a & b is (ab)1/2.

Here, a is the first term, r (=a2/a1) is the common ratio and n are numbers of terms in GP.

3. Harmonic Progression (HP)

If a, b, c are in AP, then 1/a, 1/b, 1/c are in HP.

Solve HP with the help of AP.

CAT Sequence And Series Previous Year Questions

Q1. Sequence and Series Questions for CAT Exam are given below:

Three positive integers x, y and z are in arithmetic progression. If y − x > 2 and xyz = 5(x + y + z), then z − x equals [CAT 2021, slot 2]

1. 8

2. 10

3. 14

4. 12

Sequence and series questions and answers are given below:

Solution: [3]

If x, y and z are in AP, then

y- x = z- y > 2 (Given)

So, y > x +2 and z > y+ 2; z > x+ 4

Also, x+ z = 2y

It is given that

xyz = 5(x + y + z)

⇒ xyz = 5(3y)

⇒ xz = 15 and z > x+ 4

If z = 15, x = 1 (z > x+ 4, true)

If z = 5, x =3 (z > x+ 4, false)

Therefore z =15 and x= 1 will be taken and the difference is 14.

Q2. Sequence and Series Questions for CAT are given below:

For a sequence of real numbers x1, x2, ..., xn, if x1 - x2 + x3 - ... + (-1)n + 1xn = n2 + 2n for all natural numbers n, then the sum x49 + x50 equals [CAT 2021, Slot 2]

1. 2

2. -2

3. 200

4. -200

CAT questions on sequence and series are given below:

Answer: [2]

Sn = if x1 - x2+ x3 - ... + (-1)n + 1xn = n2 + 2n

If n = 50; S50 = 502+ 2 x 50 = 2600 = x1 - x2 + x3 - ... + x49 -x50

S49 = 492+ 2 x 49 = 2499 = x1 - x2 + x3 - ... + x49

So, S50 = S49 - x50

⇒ x50 = S49 - S50 = 2499 – 2600 = -101

S48 = 482+ 2 x 48 = 2400

Similarly, x49 = S49 – S48 = 2499 – 2400 = 99

So, x49 + x50 = -101 + 99 = -2

Tricks and Tips for sequence and series questions for CAT

Find the tips and tricks of sequence and series questions for CAT exam below:

1. An AP of an odd number of terms is to be assumed as

…, a-2d, a-d, a, a+ d, a+ 2d, … [common difference ‘d’]

2. An AP of an even number of terms is to be assumed as

…, a-3d, a-d, a+ d, a+ 3d, … [common difference ‘2d’]

3. A GP of an odd number of terms is to be assumed as

…, a/r, a, ar, … [common ratio ‘r’]

4. GP of an even number of terms is to be assumed as

…, a/r3, a/r, ar, ar3, … [common ratio ‘r2’]

5. AM x HM = GM2

6. AM≥ GM≥ HM

7. Practice sequence and series previous year questions to get an idea of questions in CAT 2025.

Key Concepts in Quadratic Equations

Quadratic equations play a vital role in the CAT Quantitative Aptitude section. Understanding the basics helps in solving problems quickly and accurately. Here are the key concepts every aspirant should master:

1. Standard Form:
A quadratic equation is written as ax² + bx + c = 0, where a, b, and c are real numbers, and a ≠ 0.

2. Discriminant (D):
The discriminant D = b² - 4ac helps determine the nature of roots—real and distinct, real and equal, or complex.

3. Nature of Roots:

• If D > 0: Two real and distinct roots

• If D = 0: Two real and equal roots

• If D < 0: Complex conjugate roots

4. Methods to Solve:

• Factorisation: Split the middle term and rewrite the equation as a product of two simpler expressions. This method works best when the roots are integers.

• Quadratic Formula: Plug the values into the formula x = (-b ± √D) / 2a to find the roots. It's reliable for all types of quadratics.

• Completing the Square: Rewrite the equation into a perfect square form and then solve. This method helps when the other two aren’t easy to apply.

5. Sum and Product of Roots:

In any quadratic equation of the form ax² + bx + c = 0, the sum and product of the roots follow these simple formulas:

• Sum of roots = -b/a

• Product of roots = c/a

These shortcuts save time, especially in MCQs where you don’t need to find the exact roots.

Example:
Take the equation 2x² - 5x + 3 = 0
Here, a = 2, b = -5, and c = 3

• Sum of roots = -(-5)/2 = 5/2

• Product of roots = 3/2

You can now answer questions related to the relationship between roots without solving the full equation.

CAT Study Material: References to Study (Theory) Sequence and Series for CAT

1. NCERT Mathematics Class 11.

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

3. Mission CAT (https://www.youtube.com/watch?v=efy0XXnmIpE)

CAT Study Material: References to Practice CAT Sequence and Series questions

Study sources of Sequence and Series questions for CAT are given below:

1. Quantitative Aptitude by R S Agrawal.

2. Rodha: YouTube (https://www.youtube.com/watch?v=XrbkOHqFQqA&list=PL2pKbEwLDvEOwgnhXiKM-I3plDVEQpdMQ

3. (https://www.youtube.com/watch?v=FKFwQG0TvKA&list=PL2pKbEwLDvEOwgnhXiKM-I3plDVEQpdMQ&index=2)

4. (https://www.youtube.com/watch?v=7D84xjcyxrE&list=PL2pKbEwLDvEOwgnhXiKM-I3plDVEQpdMQ&index=3)

5. Practice Sample Papers on sequence and series questions

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

Logical Reasoning and Data Interpretation (DILR) is often considered the most unpredictable section in CAT. To prepare effectively, focus on understanding various puzzle types, data sets, and logic-based problems. Practice is key to solving diverse question sets regularly to improve pattern recognition and speed. Analyse CAT mock tests to identify weak areas. Build a strategy to manage time, select the right sets, and avoid lengthy traps.

CAT 2025 Syllabus Topic: Strategy to prepare “Picking of Coins” for CAT

Important Concept/Formula Used in questions on coins

1. These problems are basically a special type of D.I. problems which require a high level of understanding.

2. There are basically two types of scenarios in these Questions.

3. The first case is who picks last wins the game

4. The second case is who picks last loses the gam

5. For the first case, the person who picks last wins must left (MINIMUM PICK MAXIMUM PICK) *k coins on the table to ensure it wins.

6. In the second case, the person who picks last loses. So, the person who picks first must left(MINIMUM PICK MAXIMUM PICK) *k+ 1) coins on the table to ensure it’s winning.

CAT Previous Years Questions on Coins

Q1. Two smart players A and B are playing a coin game in which they can pick up 1, 2, 3, or 4 coins. They have 78 coins and the player who picks the last coin will lose the game. A and B play alternately and A plays the first move. How many coins should A pick at first so his win is independent of the number of coins B picks in his first move?

[CAT PYQ]

Solution:

As the question explained, A is the first picker so he needs to maintain a such number of coins on the table that after his first pick his winning doesn't depend on the coins picked up by B.

So, in such cases, the trick is to maintain (multiple of a sum of minimum pick + maximum pick on the table)

So, the person who has the chance to pick first must pick as many numbers of coins so on the table the coins left on the table must be

(Multiple of the sum of minimum pick + maximum pick on the table)

So if this question the sum of minimum pick + maximum pick would be (1+4)k=5k

must leave on the table so the first person will pick 3 coins from the table and left 75 coins on the table for another person so he will ensure his win.

Q2. An old woman had the following assets: [CAT 2017]

Rs. 70 lakh in bank deposits

1 house worth Rs. 50 lakh

3 flats, each worth Rs. 30 lakh

a certain number of gold coins, each worth Rs. 1 lakh

She wanted to distribute her assets among her three children; Neeta, Seeta and Geeta. The house, any of the flats or any of the coins were not to be split. That is, the house went entirely to one child; a flat went to one child and similarly, a gold coin went to one child.

The value of the assets distributed among Neeta, Seeta and Geeta were in the ratio of 1:2:3, while the gold coins were distributed among them in the ratio of 2:3:4. One child got all three flats and she did not get the house. One child, other than Geeta, got Rs. 30 lakh in bank deposits.

How many gold coins did the old woman have?

1. 72

2. 90

3. 180

4. 216

Ans: [B]

Let the old woman have ‘x’ gold coins.

herefore, total asset base = Rs. 70 lakhs + Rs. 50 lakhs + Rs. 3 * 30 lakhs + x = Rs 210 lakhs + x

The assets were distributed in the ratio of 1:2:3. So, 210 +x should be multiple of 6.

Since there are “x” gold coins, then the total 210 + x is a multiple of 6.

210 is a multiple of 6. So, x is a multiple of 6.

Also, the gold coins were distributed in the ratio of 2:3:4. So, gold coins should be multiple of 9 also. Therefore, from the above two conclusions, we can say that gold coins are multiple of 18.

Therefore, x is a multiple of 18.

The total value of assets can be taken as 210 + 18k.

Dividing this in the ratio of 1:2:3 among Neeta, Seeta and Geeta.

Neeta = 1/6 x (210 + 18K) = 35 + 3k = 35 – k + 4k

Seeta gets = 2/6 x (210 + 18K) = 70 + 6k

Geeta gets = 3/6 x (210 + 18K) = 105 + 9k = 105+ k + 8k

Discuss for Geeta, the one only who can get three flats worth Rs 90 lakhs

Geeta will have a house of worth Rs 50 lakh, So, she cannot get Rs 30 lakh Cash.

Neeta will get 30 lakhs bank deposits, she will get (5+ 3k) gold coins.

Neeta got a total (35 – k) + 4k worth of assets. So, k = 5.

Neeta = 30 lakhs deposit and 20 gold coins

Seeta = One house + Rs. 20 lakh in bank deposits + 30 gold coins.

Geeta = 3 flats + Rs. 20 lakh in bank deposits + 40 gold coins.

Therefore, the total no. of gold coins = 20 + 30 + 40 = 90.

Tips/Tricks for CAT questions on coins

• These are special types of problems, so these must be practised before exams.

• All different types of cases needed to be covered by aspirants because every case required a unique approach to solve this question.

CAT entrance exam: Pre-requisite

1. Puzzle

2. Understanding of Division Process

3. Understanding of Linear Equations

References to CAT Study (Theory)

1. LRDI by Nishit K. Sinha

2. Handa Ka Funda

References to Study (Practice) problems on coins

1. MBA Entrance Previous years Papers and Sample Papers.

2. Elite Grid’s youtube Channel

3. Cat Preparation-iquanta

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

CAT Exam Important Topic: Strategy to Prepare “Statement and Arguments” (What is Critical Reasoning in CAT) for CAT-2025

Important Concept used in Statement and Arguments questions

• Statement: A statement is defined as that which is

• expressible by a sentence and is either true or false.

• Argument: An argument is a dispute or debate. In logic, the term has a more technical meaning.

CAT Previous Years' Questions on Statements and Arguments

Practising CAT's previous years' questions on Statements and Arguments is essential for mastering this critical Logical Reasoning topic. These questions test your ability to evaluate the strength and relevance of arguments based on given statements. Analysing past questions helps you understand the logic pattern, common traps, and the examiner’s perspective. Regular practice enhances your reasoning skills, improves accuracy, and builds familiarity with the question style commonly seen in the CAT 2025 exam.

Q1. Statements and Arguments are given below:

Statement: Should military training be made compulsory in our country? [PYQ]

Arguments:

1. Yes, every child should go through this training

2. No, it is not compulsory in USA

1. If only argument I is strong.

2. If only argument II is strong.

3. If either I or II is strong.

4. If neither I nor II is strong.

5. If both I and II are strong.

Statements and Arguments questions with solutions are given below:

Ans. Option D

Explanation:

Argument 1: Not every child is strong enough physically. So, it is not a strong argument.

Argument 2: USA is a different country at different levels. Comparison is done here so it is also a weak argument.

Q2. Statements and Arguments (critical reasoning questions for CAT) are given below:

Statement: Should powerful nations attack relatively weaker nations which pose a probable danger to world peace? [IPMAT 2020]

Arguments:

1. Yes. War is justified for the noble purpose of peacekeeping.

2. No. War/violence should never be resorted to.

3. If only 1 is implicit

4. If only 2 is implicit

5. If either assumption 1 or 2 is implicit

6. If neither assumption 1 nor 2 is implicit

Ans: [A]

Explanation:

If someone is dangerous to humankind, it should get eliminated by a stronger person. So, Argument I seem to be implicit.

Tips and Tricks for CAT questions on Statement and Arguments

1. The criterion of being either true or false is one thing that served to identify the informative use of language.

2. An argument is a set of at least two statements, one of which is the conclusion of the argument, and the rest of which are premises offered in support of the conclusion.

3. An argument will often contain indicator words that help identify the premises and conclusion.

• Some conclusion indicators are:

So/, therefore,/consequently/ as a result/thus/hence/accordingly/it follows that

• Some Premise indicators are:

Since/because/for/in light of/in view of/as shown by.

4. Identify strong arguments and weak arguments

Strong Arguments Includes:

• Facts based on experience

• Educational development

• Universal truth etc

Weak Arguments Include:

• over exaggeration

• Involves Comparison

• Half explained arguments

• Contains words like Each, Nothing, Very, All, only etc

CAT 2025: Pre-requisite to Statement and Arguments

1. Knowledge of basic components of statements and arguments.

2. Sentence Structure.

References to Study (theory) what is critical reasoning in CAT

1. How to Prepare for Verbal Ability and Reading Comprehension for CAT | 9th Edition

2. Book by Arun Sharma and Meenakshi Upadhyay

3. CareerRide (YouTube: https://www.youtube.com/watch?v=u8FGPJzW140)

References to Study (Practice)Statement and Arguments questions

1. Verbal Reasoning by Disha Experts (kindle)

2. https://www.youtube.com/watch?v=7wiYAxzteI8

CAT 2025 Ebooks by Careers360

CAT 2025 eBooks by Careers360 are digital study guides that you can read anytime on your phone or laptop. They cover all key topics from Quant, VARC, and DILR and help to score high marks in the exam. These eBooks make focused preparation easier, smarter, and more flexible.

Practice and stay focused; Day 52 will be posted tomorrow.

Thank you! All the Best!