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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.
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 College Predictor
Know Your Chances for getting Calls from IIMs & other Top MBA Colleges through CAT Percentile, based on your category, academic profile, work-ex & CAT result.
Use Nownth 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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Questions related to CAT
Have a question related to CAT ?
Top MBA colleges based on CAT, XAT, SNAP, and NMAT scores include some of India’s best institutions. For CAT, the IIMs (Ahmedabad, Bangalore, Calcutta) and FMS Delhi are highly regarded. XAT results in prestigious colleges like XLRI Jamshedpur and XIMB. SNAP is known for Symbiosis Institutes, such as SIBM Pune and SCMHRD. NMAT scores open doors to NMIMS Mumbai, SPJIMR Mumbai, and ISB Hyderabad. Each exam has unique eligibility requirements, and their cutoffs vary, so it's important to research the specific criteria and select based on your preferences and strengths.
Ankit 17 January,2025
Hello,
Here are important points regarding your query :-
- Opportunity for candidates: IIM Kashipur might be inviting candidates for further consideration, regardless of initial CAT scores.
- Broadening applicant pool: They may aim to review diverse profiles beyond just percentile.
- Different criteria: Other factors like academic performance, work experience, and diversity may contribute to the decision.
- Possibility of screening: The email could be a formality, and actual shortlisting will depend on various selection criteria.
- No guarantee of shortlist: The invitation doesn’t ensure selection; many institutes offer preliminary applications before filtering through comprehensive evaluations.
Hope it helps !
Prachi Kumari 13 January,2025
Hi,
Based on the previous year analysis, According to your CAT 2024 percentile some of the colleges in which you have chances to get a seat includes:
- ISBR Business School
- SOIL Institute of Management
- Birla Institute of Management Technology
- GD Goenka University
- The ICFAI University
- Great Lake Institute of Management
- Jaipur National University
You can predict more colleges using the CLAT 2024 college predictor tool .
Hope this information will help you
Devraj 12 January,2025
Hello Greetings
With a CAT 2024 percentile of 68.28%, you may face a challenging time getting into IIT Delhi, as their cutoffs are typically higher. However, being an SC female student, you may be eligible for relaxation in the cutoff criteria .
To give you a better idea, here are some general CAT cutoff percentiles for IITs and other top B-schools:
- *IIT Delhi*: Typically above 90 percentile for general category students.
- *Newer IIMs*: Such as IIM Vishakapatnam, IIM Shillong, and IIM Udaipur, may have lower cutoffs, around 80-90 percentile.
- *Other top B-schools*: Like IMT Ghaziabad, XIM Bhubaneswar, and TAPMI, may also consider students with lower percentiles.
It's essential to note that CAT cutoffs can vary from year to year, and other factors like your academic background, work experience, and performance in the personal interview (PI) and written ability test (WAT) also play a significant role in the admission process.
To explore more options and predict your chances of getting into various colleges, you can use online CAT college predictor tools .
Have a great day
Sakshi Badoni 09 January,2025
Hello Greetings
Considering your 82.58 percentile in CAT and 22 months of industry experience in IT and Financial analysis, you have several options for General Management PGDM or PGPM programs.
*Decent Colleges Accepting Low CAT Percentile:*
- _SPJIMR_: Offers PGDM and PGPM programs, accepting CAT scores, with a minimum eligibility criterion of 50% aggregate in graduation ¹ ².
- _SOIL_: Provides PGPM and PGDM programs, considering CAT scores, with a focus on experiential learning ³.
- Other institutes like _IMT Ghaziabad_, _XIMB_, and _IRMA_ might also accept candidates with lower CAT percentiles, but this may vary depending on the program and intake.
*Key Factors to Consider:*
- _Work Experience_: With 22 months of experience, you might be eligible for PGPM programs, which typically require more work experience than PGDM programs ¹.
- _Career Gap_: Explain your career gap effectively in your application, highlighting any relevant activities or skills gained during that period.
- _Profile-Based Selection_: Some institutes consider profiles, including work experience, academic background, and extracurricular activities, in addition to CAT scores ¹.
*Next Steps:*
1. Research the institutes mentioned above and their programs.
2. Review the eligibility criteria, admission process, and fees for each program.
3. Prepare your application, ensuring you effectively communicate your strengths, work experience, and career goals.
4. Be prepared for interviews, focusing on your profile, experience, and motivation for pursuing a PGDM or PGPM program.
Remember, a lower CAT percentile doesn't necessarily limit your options. Focus on showcasing your strengths, experience, and fit with the program to increase your chances of admission.
Have a great day
Sakshi Badoni 09 January,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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