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)

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.

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

Solution: (B)

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

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).

2. Learn Properties related to diagonals

3. 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

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

5. 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 Tournaments 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.

2. 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]

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.

2. Xyla was the highest scorer.

3. Zeneca was the highest scorer.

4. 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:

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

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

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

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. Puzzle

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!