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Be a CAT Expert: Ace Sequences and Series, Coin Puzzle and Critical Reasoning Questions
Edited By Irshad Anwar | Updated on Jul 19, 2025 01:18 PM IST | #CAT
Ongoing Event
CAT Application Date : 01 Aug' 2025 - 13 Sep' 2025
As part of the ongoing 60-day CAT preparation guide by Careers360, Day 51 focuses on crucial topics like Sequence and Series, Picking Up Coins, and Critical Reasoning. These areas play a significant role in your overall performance. For those aiming for MBA admission from 2025-27, mastering such topics is essential. Critical Reasoning helps strengthen logical thinking, a key skill for the exam. The CAT preparation 2025 in 60 days, the plan is equally effective for CAT 2025 aspirants. Sequence and Series, in particular, includes three key question types and carries notable weightage in the exam. Aspirants should thoroughly practice these concepts. You can also download the Arithmetic Sequence Questions and Answers PDF to aid your preparation.
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:
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.
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.
Harmonic Progression (HP)
CAT 2025: VARC, DILR, and Quant MCQs & Weightages
Comprehensive CAT prep guide with focused practice on Verbal Ability, Data Interpretation & Logical Reasoning, and Quantitative Aptitude.
Download NowIf 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]
8
10
14
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]
2
-2
200
-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:
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’]
An AP of an even number of terms is to be assumed as
…, a-3d, a-d, a+ d, a+ 3d, … [common difference ‘2d’]
A GP of an odd number of terms is to be assumed as
…, a/r, a, ar, … [common ratio ‘r’]
GP of an even number of terms is to be assumed as
…, a/r3, a/r, ar, ar3, … [common ratio ‘r2’]
AM x HM = GM2
AM≥ GM≥ HM
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
NCERT Mathematics Class 11.
How to Prepare Quantitative Aptitude by Arun Sharma (7th Edition)
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:
Quantitative Aptitude by R S Agrawal.
Rodha: YouTube (https://www.youtube.com/watch?v=XrbkOHqFQqA&list=PL2pKbEwLDvEOwgnhXiKM-I3plDVEQpdMQ
(https://www.youtube.com/watch?v=FKFwQG0TvKA&list=PL2pKbEwLDvEOwgnhXiKM-I3plDVEQpdMQ&index=2)
(https://www.youtube.com/watch?v=7D84xjcyxrE&list=PL2pKbEwLDvEOwgnhXiKM-I3plDVEQpdMQ&index=3)
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
These problems are basically a special type of D.I. problems which require a high level of understanding.
There are basically two types of scenarios in these Questions.
The first case is who picks last wins the game
The second case is who picks last loses the gam
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.
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?
72
90
180
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
Understanding of Division Process
Understanding of Linear Equations
References to CAT Study (Theory)
LRDI by Nishit K. Sinha
References to Study (Practice) problems on coins
MBA Entrance Previous years Papers and Sample Papers.
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
If only argument I is strong.
If only argument II is strong.
If either I or II is strong.
If neither I nor II is strong.
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:
Yes. War is justified for the noble purpose of peacekeeping.
No. War/violence should never be resorted to.
If only 1 is implicit
If only 2 is implicit
If either assumption 1 or 2 is implicit
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
The criterion of being either true or false is one thing that served to identify the informative use of language.
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.
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.
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
Knowledge of basic components of statements and arguments.
Sentence Structure.
References to Study (theory) what is critical reasoning in CAT
How to Prepare for Verbal Ability and Reading Comprehension for CAT | 9th Edition
Book by Arun Sharma and Meenakshi Upadhyay
CareerRide (YouTube: https://www.youtube.com/watch?v=u8FGPJzW140)
References to Study (Practice)Statement and Arguments questions
Verbal Reasoning by Disha Experts (kindle)
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.
eBook Title | Download Links |
CAT 2025 Quantitative Aptitude Questions with Answers | |
CAT DILR Questions with Solution, Download LRDI Questions for CAT | |
CAT 2025 Verbal Ability and Reading Comprehension (VARC) Study Material | |
CAT 2025 Important Formulas | |
Past 10 years CAT Question Papers with Answers | |
CAT 2025 preparation tips with 30-day study material by Experts | |
CAT 2025 Quantitative Aptitude Study Material PDF - Geometry and Mensuration |
Practice and stay focused; Day 52 will be posted tomorrow.
Thank you! All the Best!
Frequently Asked Questions (FAQs)
1. Why are Sequences and Series important for CAT 2025 Quant section?
Sequences and Series test your pattern recognition and formula application. They often appear in CAT 2025 Quant with moderate to high difficulty.
2. How can I approach Coin Puzzle questions in CAT 2025 Logical Reasoning?
In CAT 2025 LR, coin puzzles require a step-by-step approach. Use diagrams or tables to track coin flips or movements clearly.
3. What’s the role of Critical Reasoning in CAT 2025 VARC section?
Critical Reasoning helps assess your ability to evaluate arguments. In CAT 2025 VARC, it improves accuracy in reading comprehension and paragraph-based questions.
4. Do these topics appear frequently in CAT 2025?
Yes, all three, Sequences and Series, Coin Puzzles, and Critical Reasoning, are commonly featured in past CAT papers and are expected in CAT 2025 as well.
5. How should I prepare for Sequences, Puzzles, and Reasoning in CAT 2025?
Divide your prep time across all three topics daily. Start with concept clarity, then solve targeted CAT 2025-level practice sets to build speed and confidence.
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Aug 21, 2025
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Have a question related to CAT ?
Hello Aspirant,
-
I saw a cat. The cat found an old map inside a drawer of the king's palace.
Here's why:
-
"a cat": It's the first time we mention the cat, so it's indefinite.
-
"The cat": Now we're talking about that specific cat we just mentioned, so it's definite.
-
"an old map": It's the first time we mention a map, and "old" starts with a vowel sound, so "an."
-
"a drawer": It's one of possibly many drawers, not a specific one known to us yet.
-
"the king's palace": This is a specific, unique place, so "the."
SHUBHRADIP ROY 20 August,2025
Hello Kapish
You can find the last 5 year questions of DILR for CAT at Careers360 website. Moreover, you can find the previous year papers of all the subjects i.e. DILR, Quants and VARC. I am attaching the link through which you would be able to access the same.
Here's the link:
CAT Previous Year Papers by CAREERS360
Sample paper of DILR:
CAT Sample Paper (DILR) by CAREERS360
Thank You!!!
Yash Teotia 18 August,2025
Hello Divya,
Yes, candidates with an online BBA can sit for both CAT and GMAT provided that the degree is from a recognized (UGC approved in India or accredited abroad) institution. The leading B-schools in both India and abroad do not look down upon online degrees as long as the degree is from a recognized body, they will mostly be looking at your test scores, academic performance, work experience, and profile holistically. What matters is the legitimacy of the institution and how you showcase your abilities, not whether your degree was obtained online or in-person.
gopi 17 August,2025
Yes, someone with an online BBA can sit for both CAT and GMAT, provided the degree is from a UGC recognized university. Top B-schools in India (like IIMs) and abroad generally accept online degrees if they are valid, and you won’t be marked down just because it’s online. What matters more is your entrance exam score, academic record, work experience, and overall profile.
Chelsie G 17 August,2025
In situations like yours, where the CAT 2025 payment has been successfully debited from your bank account but the portal shows the transaction as failed, it is usually due to a technical delay in updating the system. Such discrepancies can sometimes take more than 48 hours to be resolved automatically. It is important to retain all proof of payment, including bank statements, transaction IDs, and any receipts. You should contact the CAT helpdesk again, providing full details of your application and payment. Additionally, keep checking your email for any automated confirmation or ticket numbers. If there is no response within a few days, you can escalate the issue by contacting the IIM Kozhikode admissions office directly through official contact details.
Chelsie G 18 August,2025
Popular CAT Questions
Directions for question :
M/s Deloitte Touche Tohmatsu Limited, one of the top four audit and accounting firms in the world with headquarters at London, UK, and with an operational presence in 153 countries, hires Management Trainees (MT) from all the premier management institutes of India thrice every year, in the months of January, May and September.
Each new group of Management Trainees (MT) have to go through a four month rigorous training schedule, after which they have to pass through a test consisting of a written assessment and a case-analysis. The top hundred ranked Management Trainees (MT) based on the performance in the test are confirmed as Management Executives (ME). The rest are given the opportunity of undergoing the training for four months one more time along with the next batch of Management Trainees (MT) and then passing through the subsequent test consisting of the written assessment and case-analysis. The Management Trainee (MT) who fails to get confirmed as a Management Executive (ME) the second time is fired.
The scatter-graph below depicts the number of Management Trainees (MT) at Deloitte taking the tests from January 2020 till May 2022, and the vis-à-vis hired Management Trainees (MT) at Deloitte who were fired :
It is also known that for the month of September 2019 at Deloitte, 96 hired Management Trainees (MT) failed to be confirmed as a Management Executive (ME) the first time, and that 36 hired Management Trainees (MT) were fired.
Question :
In which test did the minimum number of Management Trainees (MT) get confirmed as a Management Executive (ME) in the second attempt ?
Option: 1
September 2020
Option: 2
May 2021
Option: 3
January 2021
Option: 4
January 2022
Directions for question:
The bar-graph given below shows the foreign exchange reserves of Nepal (in million Rupees) from 2014 to 2021. Answer the following questions based on the graph :
Question:
What was the percentage increase (rounded to the nearest integer, if deemed necessary) in the foreign exchange reserves in 2020 over 2016 ?
Option: 1 None
Option: 2 None
Option: 3 None
Option: 4 None
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