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Be a CAT Expert: Conquering Sequences and series, Coin Puzzle questions, and Introduction to Critical Reasoni
Edited By Irshad Anwar | Updated on Sep 19, 2024 10:25 AM IST | #CAT
Hello, aspiring CAT 2024 candidates, The CAT exam 2024, scheduled for November 24 in preparation for MBA admissions from 2025-27, In the continuation of the CAT 2024 60 days preparation guide series of Careers360, on day 51 we will discuss the strategies for sequence and series questions for CAT exam, picking up of coins, and Critical Reasoning for CAT 2024 that can help you prepare well and crack the CAT entrance test 2024. Students can download the arithmetic sequence questions and answers pdf.
Free Study Material: VARC | DILR | Quant | Chapter-wise Practice MCQs
CAT 2024: 60-day study material | CAT'23 Official Question with Solutions (Slot 1, 2, 3)
Test: 20 Free Mock Test | 10 Year PYQs | Most Scoring Concepts
Sequence and Series questions are of utmost importance and have 3 question types as well for the same. Aspirants need to practice it well and be thorough with the same. sequence and series questions for CAT carry a good amount of weightage and cannot be entirely neglected. CAT Preparation 2024 in 60 days
Part-1: Quantitative Aptitude for CAT exam
CAT Exam Important Topic: Strategy to Prepare “Sequence and Series” for CAT. Aspirants can also download the sequences and series questions and answers pdf.
Important Concept/Formula Used in sequence and series questions for CAT
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.
CAT 2024 Most Scoring Concepts- VARC, DILR & QUANT
Start your CAT journey today and download CAT 2024 most scoring concepts PDF, including study materials based on CAT previous year papers, CAT question papers, and CAT exam sample questions.
Download EBooknth 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)
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]
- 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 2024.
CAT entrance exam: Prerequisite to CAT Sequence and Series
Vedic Maths
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 2024 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)
CAT 2024 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
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 from the CAT Exam (Coins LRDI questions for CAT):
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 Preparation 2024: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)
CAT Exam Important Topic: Strategy to Prepare “Statement and Arguments” (What is Critical Reasoning in CAT) for CAT-2024
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 (critical reasoning questions for CAT)
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 2024: 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
Practice and stay focused; Day 52 will be posted tomorrow.
Thank you! All the Best!
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Nov 15, 2024
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Questions related to CAT
Have a question related to CAT ?
The student cannot join the postgraduate MA program directly in the second year of the MA after completing the MBA.
Universities generally expect students to begin the first year of a masters' program even though they had qualifications at the level of a bachelor's degree. The university's curriculum along with the courses are planned to give an in-depth knowledge of the subjects.
But you could opt for:
Postgraduate Studies:
Research Career: In case research interests you, then you can pursue a Ph.D. in your specific interest.
Specialized Master's Programs: Find any specific master's course that supports the career goal.
Professional Certifications:
Make a professional certification in CFA, CA, or FRM to enhance the professional skills and better opportunities in the career field.
Job Entry via MBA
After gaining an MBA from a renowned institution, it's possible to get entry into the corporate world where the diversity in the career field is assured.
In the end, it would depend on what you would like and what you are particularly interested in. It will be better if you take a suggestion from your academic advisor or career counselor.
Samprikta Mondal 13 November,2024
Hello Pratik,
If your family income exceeds 8 LPA, it will affect your eligibility for the NC-OBC category under the CAT reservation rules. The NC-OBC category requires that the family income should be below 8 LPA to qualify. If you anticipate that your income will exceed this threshold, you should update your status and notify the CAT authorities .
Here's what you can do:
-
Email the CAT authorities : Inform them about the potential change in your income status and request to be considered under the General category, if applicable. You should do this before the examination or any further processing, as your eligibility for the OBC category depends on the income criteria.
-
Documents and Proof : Make sure you have a valid OBC certificate and any relevant documentation regarding your family income, in case they require verification. Also, be aware that if your income exceeds 8 LPA, you might need to apply under the General category, as the OBC-NC reservation is no longer applicable.
-
General Category Consideration : If your application is accepted as General, you will be evaluated based on the General category criteria, including cutoffs and ranking.
To summarize, notifying the CAT authorities is the correct approach to avoid discrepancies later, and if your income is above the threshold, you will be treated as a General candidate for the admissions process.
For more details about CAT exam you can check out an article by Careers360 whose link is given below:
Link: https://bschool.careers360.com/exams/cat
I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.
Thank you and wishing you all the best for your bright future.
kumardurgesh1802 08 November,2024
Hi Shreya ,
Having a tattoo on your wrist should not create a problem during the CAT exam as long as it does not contain any content that violates exam rules , such as communication-related symbols , unauthorised messages or any text resembling formulas or answers .
For a safe side , it is recommended :
1. Inform the Invigilators : Let them know about your tattoo during the identification check , so there are no misunderstandings .
2. Follow the Guidelines : Ensure you follow all instructions regarding permissible items and dress code on the exam day .
Hope this helps you .
ALL THE BEST .
Mitali Sharma 09 November,2024
To know about this please prefer our college predictor
Sumit Mishra 07 November,2024
Hello,
Yes, you can also join IIMs two years after graduation, depending upon the justification in interviews and your performance in entrance exams. If you are not sure about CAT, try those other management exams less hard:
Common Management Admission Test: Easier than CAT; 4-5 months of continuous preparation will suffice.
MAT : Much easier and takes place thrice a year.
SNAP (Symbiosis National Aptitude Test): A bit easier than CAT, apt for Symbiosis Institutes.
Xavier Aptitude Test or XAT : Hence, easier than CAT but the unique decision-making section.
Use exams like CMAT and MAT as a challenge to be competitively prepared. This can be given about 4-5 months, along with a few rounds of mock tests and smart studying.
Deepti Singh 06 November,2024
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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