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CAT Exam: Maxima & Minima Solved questions, Algebra Quant, LR & DI - Day 19

CAT Exam: Maxima & Minima Solved questions, Algebra Quant, LR & DI - Day 19

Edited By Irshad Anwar | Updated on Sep 28, 2023 10:29 AM IST | #CAT

Based on the CAT syllabus 2023, we have created a study schedule to ace the CAT Exam. We discussed a plan for every day from Day 1 through Day 18 in advance.

On the basis of the CAT syllabus 2023, we discussed strategies on how to prepare for functions and graphs (Algebra), puzzles on the linear arrangement and conditionals in the previous article - Day 18 of CAT preparation.

We're back with a strategy for the Day 19 of our preparation for the CAT 2023. In this article, we will be discussing strategies for the following topics: Maxima and Minima Questions for CAT, problem-solving questions in maths, puzzle-solving questions, Logical Reasoning puzzles for CAT exam and questions from CAT previous year papers.

With the 60-day CAT exam preparation schedule we created for you, you can ace the CAT 2023 and get a flow, plan, and schedule for your preparation.

CAT Exam Part-A: Quantitative Aptitude for CAT 2023

Topic: Algebra and Maxima and Minima Questions for CAT Exam

Maxima Minima CAT Questions are used to find the maximum or minimum possible value of a function. Depending on the function, there are several ways to find the maximum and minimum value of a function.

In maxima minima aptitude questions, the function given can be:

  • Quadratic function

  • Linear function

  • Polynomial function etc.

For such functions, we need to find the maximum or minimum values.

CAT Exam: Tips And Approaches To Solve The Maxima and Minima Questions for CAT

Here are some tips and tricks to solve maxima minima aptitude questions:

  1. If the sum of positive numbers is constant then their product is maximum when all numbers are equal.

Example:

a + b + c = 36, find maximum value of a.b.c

The answer is (36/3)3 = 1728.

  1. Arithmetic Mean ≥ Geometric Mean

a + b + c = 11; find Maximum value of a3 x b4 x c5

a + b + c = a/3 + a/3 + a/3 + b/4 + b/4 + b/4 + b/4 + c/5 + c/5 +c/5 + c/5 + c/5 = 11

Now, AM ≥ GM

So, (a/3 + a/3 + a/3 + b/4 + b/4 + b/4 + b/4 + c/5 + c/5 +c/5 + c/5 + c/5)/12 ≥ (a/3 .a/3 .a/3 .b/4 .b/4 .b/4 .b/4 .c/5 .c/5 .c/5 .c/5 .c/5)1/12

⇒ (11/12)12 ≥ (a/3)3 .(b/4)4 . (c/5)5

⇒ a3.b4. c5 ≤ 33x 44 x 55 x (11/12)12

Trick: To solve Maxima and Minima Questions, we can use the following trick

Divide 11 in the ratio 3: 4: 5

i.e. a = (11/12)3; b = (11/12)4; c = (11/12)5

So, a3.b4. c5 = 33x 44 x 55 x (11/12)12 (After putting the values of a, b and c)

  1. For a quadratic equation:

If the minimum value is to be found, convert the equation in the form of (a – b)2 + k.

(Minimum value is k)

Example: find the minimum value of a2 + 26 – 4a

a2 + 26 – 4a = (a-2)2 + 22; Minimum value is 22

  1. To find the maximum value of a function f(x) can be calculated with the help of a method of derivative.

Step 1: find f’(x) i.e. the first derivative.

Step 2: Put f’(x) = 0, and find values of x for which function is either maximum or minimum. Let the values of x be x1 and x2.

Step 3: Find f’’(x) i.e. the second derivative.

If f’’(x) > 0 at x = x1 then the function gives minimum value at x= x1.

If f’’(x) < 0 at x = x2 then the function gives minimum value at x= x2.

These are local maxima and local minima.

  1. Learn the above concepts well and apply them to solve questions.

  1. Learn basic rules of differentiation.

CAT Exam: Maxima Minima Questions for CAT exam From CAT Previous Year Papers

Q1. If three sides of a rectangular park have a total length of 400 ft, then the area of the park is maximum when the length (in ft) of its longer side is [CAT Exam 2017]

Ans:

Let one side be a and the other side be b.

So, a + 2b = 400 ⇒ 2b = 400-a

Area = ab = a (400-a)/2 = (400a – a2)/2

To find maximum value of (400a – a2); differentiate with respect to a

dA/da = 400 – 2a = 0 (For maxima)

So, a = 2006; b = 100

Therefore, the longer side will be 200 ft for maximum area.

Q2. An elevator has a weight limit of 630 kg. It is carrying a group of people of whom the heaviest weighs 57 kg and the lightest weighs 53 kg. What is the maximum possible number of people in the group? [CAT exam 2017, TITA]

Ans:

Each person must weigh 53 Kg or more.

So, remaining weight = 630 – 53 – 57 = 520

Therefore, no of remaining persons n ≤ 520/53

So, n ≤ 10 (For maximum value n =9)

Therefore, total persons in the elevator = 9+ 2 =11

CAT Exam: Prerequisite to Maxima Minima Questions Maths

Before practising Maxima and Minima Questions for CAT, students must be well versed with

  • Function and Graph

  • Derivatives

  • Arithmetic and Geometric Mean

  • Basic arithmetic identities,

CAT Exam: References to Study (Theory)

  • NCERT Class 12 (Chapter: Functions, Derivative, Maxima and Minima)

  • Functions and Graph (Arihant Publication)

  • 2IIM CAT Preparation

CAT Exam: References to Practise Maxima and Minima Questions for CAT

  • R D Sharma

  • https://bodheeprep.com/maxima-minima

  • Previous Years Question Papers

Part-B: CAT Logical Reasoning And Data Interpretation

Topic: circular arrangement questions for CAT

The topic covered for the day and logical reasoning puzzles for CAT exam are given below:

Topic: Problem Solving Questions in Maths/ Puzzles Solving Questions (Circular Arrangement questions or CAT Part-1)

Placing objects or persons in a circular table following a specific rule is Circular arrangement.

According to a given set of rules or instructions, persons are to be arranged circularly.

Aspirants can also download the following circular arrangement questions for CAT pdf. for further references

Concepts Involved and Importance of Circular Arrangement

Puzzles Solving Questions of Circular Arrangements involve the concept of ranking, Blood Relation, Direction Sense etc.

It carries a good weightage in CAT exam/SNAP and other MBA entrance Exams as seen in previous years.

Problem solving questions in maths are generally based on:

  1. Facing towards centre

  2. Facing outward the centre

  3. Facing in two different directions.

Knowledge of solving problems enables you:

  1. To identify the unique position of a person in an arrangement.

  2. To identify respective positions of persons.

  3. Relations among the persons/ objects.

Questions on Circular Arrangement from CAT Previous Year Papers

Based on the information given below, answer the questions: (SNAP)

Ten friends Matt, Sam, Pat, Tom, Sid, Alex, Kat, Jim, Jane and John are having dinner on a rectangular table. Eight face each other along the length of the table while two face each other along the smaller side of the table. Pat is sitting diagonally opposite to Kat, Alex is facing Jim, John is to the right of Jane, Tom is sitting between Sam and Jim, Pat is to the extreme left of Jane who is sitting on the extreme right along the length of the table. Sid is facing Tom and Matt is on the right of Sam.

Q1) Who do you think is sitting in front of each other along the small sides of the table? (CAT exam)

  1. Matt and John

  2. Matt and Sam

  3. Matt and Kat

  4. John and Sam

Ans: 1

Q2) Sid is sitting between which of the following two? (CAT exam)

  1. Sam and Kat

  2. Pat and Alex

  3. Alex and Jane

  4. Kat and Jane

Ans: 2

Q3) Who are sitting diagonally opposite to each other? (CAT exam)

  1. Sid and Tom

  2. Sam and Jane

  3. Alex and Jim

  4. Jane and Kat

Ans: 2

Q4) Who is sitting to the immediate right of Jim (CAT exam)

  1. Sam

  2. Jane

  3. Alex

  4. Tom

Ans: 4

Q5) Who is sitting two places left to Jane? (CAT exam)

  1. Pat

  2. Alex

  3. Sid

  4. Sam

Ans: 3

Solution:

Based on the information given above; the following arrangement be formed

1695875994414

For this read every piece of information very carefully and place the persons.

Prerequisite to Logical Reasoning Puzzles for CAT Exam

  1. Knowledge of Ranking, Direction Sense and Blood Relation.

  2. Knowledge of Linear Arrangement.

Tips and Tricks for Puzzle Solving Questions of Circular Arrangement

Following are some tips and tricks to solve the problems on circular arrangement:

  1. There is no specific formula to solve CAT Circular arrangement questions.

  2. First, find the number of persons in the arrangement and draw a circle or rectangle (as per the given condition) and mark their positions.

  3. If the persons are facing away from the centre, the left of the persons/ objects will be in the anticlockwise direction and the right of the persons/ objects will be in the clockwise direction.

  4. If the persons are facing towards the centre, the right of the persons/ objects will be in the anticlockwise direction and the left of the persons/ objects will be in the clockwise direction.

  5. Questions on rectangular arrangements are to be solved in the same way.

  6. Remember the information by short notations.

  7. Students can also refer to this link: circular arrangemen questions for CAT

CAT Exam: References to Study Theory (CAT circular arrangement questions)

  • Verbal and Non-Verbal Reasoning by R S Agrawal

  • cetking (YouTube Channel)

  • MBAP CAT EBook (Concept Theory)

CAT Exam: References to Practise Problem Solving Questions in Maths

  • LRDI for CAT and GMAT by Nishit K Sinha. (Advance)

  • https://cetking.com/circular/

  • Previous Years Question Papers

Part-C: CAT Exam VARC

Topic: Sentence Improvement Based on Articles

Correct Use of Articles is one of the most significant skills one should be aware of. The article is commonly used with an uncountable or countable noun, indefinite or definite noun, and plural or singular noun.

Importance of Sentence Improvement Based on Articles And Uses For CAT and In Real life Sentence improvement based on Articles is effective in the following manner:

If you want to rack your skills up in the verbal ability domain, then practise for sentence improvement based on Articles that should be a ‘not to be missed’ topic in your life.

Correct use of articles gives precise specifications about the noun.

With the knowledge of articles, one can easily enhance the quality of a sentence.

Adding articles to your sentence can help you to speak fluently.

CAT Exam: Practice Questions on Articles

Direction: Write the correct form of the underlined phrase.

Q1. Union Carbide Corporation (UCC) was asked to build a plant for manufacture of Sevin, a pesticide commonly used throughout Asia.

  1. of manufacturing the Sevin,

  2. As to manufacture of the Sevin,

  3. for the manufacture of Sevin,

  4. None of these

Ans. C

‘the’ should be used before manufacture.

Q2. CAT exam candidates are not allowed to use calculators during their examinations, although they are permitted to do so if certain models meet the requirements.

  1. are not allowed using calculator

  2. do not allowed using the calculator

  3. are not allowed to use a calculator

  4. No correction required

Ans: C

‘a’ should be used before the calculator.

Q3. After Geeta fought with Seeta, she moved to a second apartment.

  1. had moved to second apartment

  2. moved to the second apartment

  3. had been moved to the second apartment

  4. No correction required

Ans: B

The’ should be used before second

Q4. The prime necessity, as the Director of ICRIER said, is to neutralise the amount of imports and exports in the country in a non-discriminatory manner.

  1. neutralising amount of the imports and the exports

  2. neutralise the amount of the imports and exports

  3. neutralise the amount of imports and exports

  4. No correction required

Ans: C

‘The’ should be used before amount

CAT Exam: Prerequisite

  • Basic Knowledge of Sentence Structure.

  • Basic Knowledge of the Usage of Articles.

Tips to Prepare Sentence Improvement on Articles and Uses

  1. Make sure you pay close attention to words whose first letters are vowels, but when they are pronounced, they have the sound of a consonant or vice versa. This is the case with words like university, an honest person, etc. For more details, you can head over to the Day-6 strategy.

  2. Practice error-based questions daily.

  3. Read newspapers, and listen to Ted Talks so that you will get more clarity about the uses of articles.

CAT Exam: References to Study (Theory)

  • How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)

  • Mastering A, An, The - English Articles Solved by Douglas Porter.

  • A' and 'The' Explained: A learner's guide to definite and indefinite articles by Seonaid Beckwith.

CAT Exam: References to Study (Practice)

  • The Article Book: Practice Toward Mastering a, an, and the by Tom Cole.

  • Oxford Practice Grammar (sixth edition)

  • engvid.com (Web)

Tomorrow we'll be back with a strategy for Day 20, so practice and stay focused.

We appreciate you.

Best wishes.

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Questions related to CAT

Have a question related to CAT ?

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.

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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.

Hello aspirant,

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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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