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Be a CAT Expert: Conquering Sequences and series, Coin Puzzle questions, and Introduction to Critical Reasoni

Be a CAT Expert: Conquering Sequences and series, Coin Puzzle questions, and Introduction to Critical Reasoni

Edited By Irshad Anwar | Updated on Oct 12, 2023 09:42 AM IST | #CAT

Hello, aspiring CAT 2023 candidates, The CAT exam 2023, scheduled for November 26 in preparation for MBA admissions from 2024-2026, has released its admit cards. In the continuation of the CAT 2023 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 2023 that can help you prepare well and crack the CAT entrance test 2023. Students can download the arithmetic sequence questions and answers pdf.

Be a CAT Expert: Conquering Sequences and series, Coin Puzzle questions, and Introduction to Critical Reasoni
Be a CAT Expert: Conquering Sequences and series, Coin Puzzle questions, and Introduction to Critical Reasoni

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 2023 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:

  1. Arithmetic Progression (AP)

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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.

  1. Geometric Progression (GP)

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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.

  1. Harmonic Progression (HP)

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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’]

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

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

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

…, a/r, a, ar, … [common ratio ‘r’]

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

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

  1. AM x HM = GM2

  2. AM≥ GM≥ HM

  3. Practice sequence and series previous year questions to get an idea of questions in CAT 2023.

CAT entrance exam: Prerequisite to CAT Sequence and Series

  1. Average

  2. Vedic Maths

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 2023 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)

CAT 2023 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. 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 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?

  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. Puzzles

  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

  1. Cat Preparation-iquanta

Part-3: CAT Exam Preparation 2023: 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-2023

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

  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.


  1. If only 1 is implicit

  2. If only 2 is implicit

  3. If either assumption 1 or 2 is implicit

  4. 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.

  1. 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.

  1. 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.

  1. 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 2023: 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

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 ?

Hello aspirant,

A bachelor's degree from an accredited university with a CGPA of at least 50% (or an aggregate of 45% for the SC, ST, and PwD/DA categories) is required in order to appear in the CAT exam in 2024. Duration and manner of degree: The course needs to last three years. The mode might be online, distant, or regular.

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Hello student

As a self-employed individual with your own cafe, you'll need to provide documents that establish your business and work experience. Here are some documents you can prepare for your CAT application:


1. *Business Registration Documents*:

- Partnership Deed (already have)

- Business PAN Card (already have)

- FSSAI License (already have, though it's in your partner's name)

2. *Proof of Business Ownership*:

- Affidavit or declaration stating your ownership and role in the cafe

- Business registration certificate (if you have one)

3. *Proof of Work Experience*:

- A letter or certificate from your partner or co-owner confirming your work experience and role in the cafe

- A detailed resume highlighting your entrepreneurial journey and responsibilities

4. *Financial Documents*:

- Income Tax Returns (ITRs) for the last 2-3 years (if applicable)

- Balance Sheets and Profit & Loss statements for your cafe (if audited)

5. *Rental Agreement*:

- Already have, but ensure it's updated and signed


Additional tips:


- Ensure all documents are scanned and uploaded in the required format (usually PDF or JPEG)

- Keep your documents organized and easily accessible for the application process

- Be prepared to provide additional information or clarification if requested by the admission authorities


Remember to check the specific requirements for each B-school you're applying to, as they may vary. Good luck with your CAT application!

Hello aspirant,
The CAT exam syllabus is not officially prescribed, but it generally includes topics from the following sections:

1. Verbal Ability and Reading Comprehension (VARC)
2. Data interpretation and logical reasoning
3. Quantitative ability

  • Arithmetic

  • Algebra

  • Geometry and Mensuration

  • Number System

  • Modern Math

It seems unlikely that you would be able to get admission in the BTech CS branch at BIT Sindri or Mesra with a CML rank of 2058 and category rank of 433.

Key points:

1. The search results indicate that a CML (Common Merit List) rank of 2058 is quite low for admission to premier engineering colleges like BIT Sindri or NIT Mesra.

2. The cutoff ranks for BTech CS branch at these institutes are usually much higher, often in the range of 1000-2000 for the general category.

3. With a category rank of 433, you may have a better chance of getting admission in the reserved category quota, but the competition is still quite high.

4. The search results do not provide specific cutoff details for BIT Sindri or NIT Mesra, but the general trend suggests your current ranks may not be sufficient for the CS branch in these institutes.

My advice would be to:

1. Check the latest cutoff ranks and admission criteria on the official websites of BIT Sindri and NIT Mesra.

2. Explore other options like state-level engineering colleges or NITs where your current ranks may have a better chance of securing admission.

3. Consider improving your performance in the next attempt of the entrance exam to increase your chances of getting into your desired BTech program.



For VARC, read daily from diverse sources (newspapers, novels, journals) to improve comprehension and vocabulary. Practice RC passages and verbal ability questions regularly. For DILR (Data Interpretation and Logical Reasoning) and QA (Quantitative Aptitude), solve previous years' papers and take mock tests to identify weak areas. Join a coaching institute or online courses for guidance and stay consistent with your study schedule. Review and analyze your performance in mocks to understand mistakes and improve. Maintain a positive mindset and stay disciplined in your preparation.

View All

1-radian measures 600. (True/False)

Option: 1

True


Option: 2

False


$111111^2$ = 

Option: 1

123456654321


Option: 2

123454321


Option: 3

123454321


Option: 4

12345654321


1111112 =___________ 

Option: 1

 123456654321


Option: 2

1234554321


Option: 3

123454321


Option: 4

12345654321


159702 is divisible by

Option: 1

7


Option: 2

9


Option: 3

11


Option: 4

6


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What best can be said about the number of satellites serving C? 

Option: 1

Must be between 450 and 725 

 


Option: 2

Cannot be more than 800 
 


Option: 3

Must be between 400 and 800 

 


Option: 4

Must be at least 100 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What is the minimum possible number of satellites serving B exclusively? 

Option: 1

100


Option: 2

200


Option: 3

500


Option: 4

250


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S? 

Option: 1

At most 475 

 


Option: 2

Exactly 475 
 


Option: 3

At least 475 

 


Option: 4

No conclusion is possible based on the given information 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

 If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE? 

Option: 1

The number of satellites serving C cannot be uniquely determined 

 


Option: 2

The number of satellites serving B is more than 1000 
 


Option: 3

All 1600 satellites serve B or C or S 

 


Option: 4

The number of satellites serving B exclusively is exactly 250 


2839155 is divisible by

Option: 1

2


Option: 2

7


Option: 3

55


Option: 4

None of the above


'a' for which x^{2}-ax+9= 0 can be written as square of a linear factor is

Option: 1

6


Option: 2

-6,6


Option: 3

\left ( 6,\infty \right )


Option: 4

\left ( -\infty,-6 \right )


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