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Mastering Quadrilaterals and Polygons, Games and Tournaments Puzzles, Antonyms, and PYQs- Day 42

Mastering Quadrilaterals and Polygons, Games and Tournaments Puzzles, Antonyms, and PYQs- Day 42

Edited By Irshad Anwar | Updated on Sep 28, 2023 10:48 AM IST | #CAT

Hello CAT 2023 aspirants, On November 26, the CAT exam 2023 will be given for MBA admissions 2024-2026. In this CAT 2023 60-day preparation guide series of Careers360, we will discuss the strategies on Quadrilateral and Polygons questions for CAT exam for day 42 that can help you prepare well and crack the CAT entrance test 2023. As you prepare for CAT 2023, don't forget to focus on mastering quadrilaterals & polygons CAT questions and answers, as they are integral to the Quantitative Aptitude section. Students can download the geometry questions and answers pdf. CAT Preparation 2023 in 60 days

Mastering Quadrilaterals and Polygons, Games and Tournaments Puzzles, Antonyms, and PYQs- Day 42
Mastering Quadrilaterals and Polygons, Games and Tournaments Puzzles, Antonyms, and PYQs- Day 42

Part-1: Quantitative Aptitude for CAT exam

Important Concept/Formula Used in Quadrilateral and Polygons questions

Quadrilateral and Polygons

  • Types of Quadrilaterals.
  • Areas related to different quadrilaterals.
  • Properties
  • Basics of Polygons (Regular).
  • Area related to the polygon.
  • Polygon Formula:
  • The sum of interior angles of a polygon with “n” sides =180°(n-2)

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All the aspirants need to solve quadrilaterals & polygons cat questions and answers to have a good command on this topic. Here, we have provided the quadrilaterals & polygons cat questions and answers for the practice in the form of previous year questions which will be really helpful for the students. Apart from these questions, To excel in CAT, it's essential to practice a variety of questions, especially quadrilaterals & polygons CAT questions and answers, to strengthen your geometry skills.

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CAT Previous Years Questions on Quadrilateral and Polygons:

Q1. Problems on quadrilaterals with answers are given below:

In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P be a point on CD such that AP is perpendicular to CD. Then the area, in sq cm, of triangle APD is [CAT 2018]

  1. 18√3

  2. 32√3

  3. 12√3

  4. 24√3

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Solution: (B)

1695877475353

Area of parallelogram ABCD = 72 = CD ×AP

9AP=72

AP = 8 cm

In right-angled triangle APD, AP2 + PD2 = AD2

On solving, we get

PD=8√3

Thus, Area of triangle APD = 1/2 AP×PD = 1/2×8×8√3 = 32√3

Q2. Regular Polygon Questions

The number of sides in a regular polygon is ‘m’ times the number of diagonals in it. What is the interior angle of this polygon in terms of m? [TITA, based on CAT PYQ]

Solution:

Measure of an interior angle of a regular polygon = [(n-2)1800]/n

Number of diagonals in an n-sided regular polygon = [n(n-3)/2]

Also, n = m times number of diagonals

n/m = number of diagonals

So, n/m = n(n-3)/2

On solving, we get

n = (2+ 3m)/m

Therefore,

Interior angle = (n-2)180/n = ((2+ 3m)/m-2)180/(2+ 3m)/m = ((2+ m)/m)180/(2+ 3m)/m= (2+ m)180/(2+ 3m) degrees

CAT Exam Important Topic: Strategy to Prepare for “ CAT Geometry (Quadrilateral and Polygons)

Quadrilateral questions strategy:

  1. Learn Important Properties of Quadrilaterals

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Area = 1/2 (product of diagonals) × (sine of the angle between, them)

A parallelogram circumscribed about a circle is a rhombus.

Median (For a trapezium) = 1/2 × sum of the parallel sides (median is the line equidistant from the parallel sides).

  1. Learn Properties related to diagonals

1695877475461

  1. Properties of a Regular Polygon

  • Number of diagonals in an n-sided regular polygon = [n(n-3)/2]

  • Measure of an interior angle of a regular polygon = [(n-2)1800]/n

  • Measure of an exterior angle of a regular polygon = 3600/n

  1. Practise CAT previous years questions to know the pattern of the questions and concepts involved.

  1. Practise Similar problems on quadrilaterals with answers and polygons questions and answers.

In the final stages of CAT preparation, revisiting quadrilaterals & polygons CAT questions and answers can boost your confidence and accuracy in geometry-related topics.

CAT entrance exam: Prerequisite to Quadrilateral and Polygons

  1. Lines and Angles

  2. Basics of trigonometry

  3. Basics of Triangles

CAT study material: References to Study (Theory)Quadrilateral and Polygons

  1. NCERT Mathematics Class 9 and 10

  2. Rodha (YouTube, Link: https://www.youtube.com/watch?v=TZadcVDti64 )

  3. CAT Funda (https://www.youtube.com/watch?v=0Pu_bQjot1M )

CAT study material: References to Practice quadrilateral questions and answers and Regular Polygon Questions

  1. How to prepare quantitative Aptitude for CAT by Arun Sharma.

  2. Rodha (https://www.youtube.com/watch?v=Dy4_ESXGjeY )

  3. CAT Questions on Polygon (Link: https://www.youtube.com/watch?v=_l0wPqRgfy04 )

Part-2: CAT 2023 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)

Games And Tournament Questions In CAT is a topic that demands a strategic approach and logical thinking to solve complex problems in the CAT exam. CAT aspirants should allocate time for extensive practice of Games And Tournament Questions In CAT to enhance their logical reasoning skills. In the CAT exam, Games And Tournament Questions In CAT often challenge candidates with intricate scenarios that require careful analysis.

CAT 2023 Syllabus Topic: Strategy to prepare “Games and Tournaments (Part-1)” for CAT

Important Concepts/ Formula Used in Games and Tournaments

  1. Round Robin Format:

Total number of matches in a single round robin = nC2, where N is a number of teams.

total wins + (total ties/2) = total number of matches.

  1. Knock-Out Format:

Total number of matches = Number of teams – 1

The player ranked the highest plays the player ranked the lowest. The second-ranked player plays the second-last-ranked player and so on.

The CAT exam often includes challenging CAT games and tournaments questions, which test your logical and analytical skills. To perform exceptionally in the CAT DILR section, you must practise a variety of CAT games and tournaments questions to hone your problem-solving abilities.

Previous Years Questions on Games and Tournaments from CAT/ MBA Entrance Exam:

Six players – Tanzi, Umeza, Wangdu, Xyla, Yonita and Zeneca competed in an archery tournament. The tournament had three compulsory rounds, Rounds 1 to 3. In each round, every player shot an arrow at a target. Hitting the centre of the target (called bull’s eye) fetched the highest score of 5. The only other possible scores that a player could achieve were 4, 3, 2 and 1. Every bull’s eye score in the first three rounds gave a player one additional chance to shoot in the bonus rounds, Rounds 4 to 6. The possible scores in Rounds 4 to 6 were identical to the first three.

A player’s total score in the tournament was the sum of his/her scores in all rounds played by him/her. The table below presents partial information on points scored by the players after the completion of the tournament. In the table, NP means that the player did not participate in that round, while a hyphen means that the player participated in that round and the score information is missing. [CAT 2019]

1695877475610

The following facts are also known.

  1. Tanzi, Umeza and Yonita had the same total score.
  2. Total scores for all players, except one, were in multiples of three.
  3. The highest total score was one more than double the lowest total score.
  4. The number of players hitting the bull’s eye in Round 2 was double that in Round 3.
  5. Tanzi and Zeneca had the same score in Round 1 but different scores in Round 3.

Q.1 What was Zeneca's total score?

  1. 23

  2. 24

  3. 21

  4. 22

Ans: [2]

Q2. What was the highest total score?

  1. 24

  2. 21

  3. 23

  4. 25

Ans: [4]

Q3. Which of the following statements is true?

  1. Xyla’s score was 23.

  1. Xyla was the highest scorer.

  1. Zeneca was the highest scorer.

  1. Zeneca’s score was 23.

Ans: [2]

Q4. What was Tanzi's score in Round 3?

  1. 3

  2. 5

  3. 4

  4. 1

Ans: [4]

Solution:

Player

Bull’s Eye Scored till 3rd round

T

1 (Played round 4)

U

2 (Played round 4 and 5)

W

0 (Played till round 3)

X

3 (Played all rounds)

Y

1 (Played round 4)

Z

2 (Played round 4 and 5)

Information given in the question and above information can be tabulated as

1695877475774

Total Hit bull’s Eye score till round 3 should be 9 (After counting R4, R5 and R6 played)

Total Hit bull’s eye score in round 2 can be either 1 or 2.

If Hit bull’s Eye scores in R3 =1, then R2 must have 2, and R1 should have 6 which is not possible since W has not scored any hit bull’s eye.

So, the total Hit Bull’s score in R3 = 2, R4= 4, R3 = 3; x =5 (only possibility)

All empty spaces must have a value of 5. (Since R2 have 4 hit bull’s eye score)

After this value of y and z cannot be 5. So, U must have 5 in R3.

The table will look like this

1695877476078

Total of T, U and Y must be multiple of 3.

Possible values for A = 15, 18

If A =18; Value of T in R3 = 4; Value of U in R1 = 5(Not possible)

If A =15; Value of T in R3 = 1; Value of U in R1 = 2; Value of Y in R1 = 2 (Correct)

Also, W must have a minimum score (Let it is m) and X must have maximum possible score let it be n (must be greater than 22).

As n= 2m + 1

m = 12; n = 25

But if m = 11, m = 23 (which is not possible as only one of the all-total scores is not multiple of 3)

Thus n = 25 and m = 12

As Z has four scores of 5 so his 5th score will be either 1 or 4. But it cannot be 1 as T’s score was 1.

Now the complete table will be as

1695877476134

Tips and Tricks for CAT Games and Tournaments

  • Develop creative thinking through games and creative activities.
  • Do solve puzzles every day.
  • Learn new skills.
  • Number of Teams/Players in knockout tournaments will be in multiple of 4.
  • There can not be any tie matches in Knock-out tournaments.

CAT 2023 candidates must familiarise themselves with different types of CAT games and tournaments questions to adapt to the exam's unpredictability.

CAT entrance exam: Prerequisite

  1. Puzzles

  2. Basic Knowledge of Sports

References to CAT Study (Theory)

  1. LRDI by Nishit K. Sinha

  2. Crack U (YouTube link: https://www.youtube.com/watch?v=fZIx-bnpNO0)

References to Study (Practice)

  1. Verbal and Non-Verbal Reasoning by R S Agrawal.

  2. MBA Entrance Previous years Papers and Sample Papers.

  3. Rodha (YouTube: https://www.youtube.com/watch?v=Oy9ERJEboWY)

  4. https://www.youtube.com/watch?v=1t4e0EpU12A

Part-3: CAT Exam Preparation 2023: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)


Sample Problems based on CAT/MBA Entrance Exams:

Directions: Choose the word opposite in meaning from the given options for highlighted phrase/word.

Q1: Due to the recent fallen prices of petrol, the common class has to deal with a lot of budget issues.

  1. Raised

  2. Increased

  3. Slanted

  4. Upright

Ans. Option (B)

Explanation: according to the context of the sentence, the most suitable word or antonym word can be increased.

Q2: Find the opposite word of FRAUDULENT

  1. Candid

  2. Direct

  3. Fortnight

  4. Genuine

Ans. Option (D)

Explanation: the only possible word that means opposite to the given word is an option (d). Other words do not fit in the context.

CAT Exam Important Topic: Strategy to Prepare “Antonyms (Part-1)” for CAT-2023

  1. Antonyms are contextual.
  2. Focus on the root words.
  3. Learn antonyms by logically associating a word with a sentence or a situation.
  4. Elimination of wrong options.
  5. Eliminate answer choices that have no clear antonym.
  6. Observe positive and negative words. It is possible to discern every word with a positive, negative, or neutral meaning.
  7. It is preferable to choose the word which matches the degree of the word in the sentence.
  8. Practise more and more exercises.

CAT 2023: Pre-requisite to Antonyms

  1. Vocabulary

  2. Parts of Speech

CAT exam: References to Study (Theory)

  1. Made Word Power Easy

  2. CATking

  3. (https://www.youtube.com/watch?v=qXw3syyd_Ak&t=6s )

CAT exam: References to Study (Practice)

  1. Newspaper readings (The Hindu/ Times of India)

  2. CAT Previous years Papers and other MBA Entrance Exams.

  3. (YouTube; Link: https://www.youtube.com/watch?v=PiN521XFNd0 )

We will be back with Day 43 tomorrow. Do practice and be focused.

Thank you! All the Best!

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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.

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.

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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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