CAT Exam Success guaranteed through Circles, Games, and Tournaments problems and more PYQs on Antonyms- Day 43

Part-1: Quantitative Aptitude for CAT exam

Important Concept/Formula Used in circle questions for CAT exam

Circle questions and answers are based on:

1. Sector and Segment

2. Areas related to Sector and Segment

• Area of sector = (Angle of sector/360) x Area of Circle
• Area of Segment = Area of Circle – Area of corresponding Sector

3. Tangent, Secant and Chord

4. Congruency of Circles

5. Cyclic Quadrilateral

CAT Previous Year Questions On Circle (Geometry):

CAT circle questions with solutions are given below:

Q1. CAT Questions on Circles:

AB is a diameter of a circle of radius 5 cm. Let P and Q be two points on the circle so that the length of PB is 6 cm, and the length of AP is twice that of AQ. Then the length, in cm, of QB is nearest to [CAT 2019]

1. 9.1
2. 7.8
3. 9.3
4. 8.5

Ans: [1]

APB and AQB are semicircular Arc

Angle APB = angle AQB = 90o

Using Pythagoras

AP² = 10² - 6²

⇒ AP = 8cm

⇒ AQ = AP/2 = 4cm

Again, Using Pythagoras

QB² = 10² – 4²

⇒ QB = 9.1 cm (Approx)

Q2. CAT Questions on Circles are given below:

ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then the value of ∠BCD (in degrees) is [TITA, CAT 2017]

Solution: 90 degrees

See the diagram above (As per question)

angle (BDC) = angle (BAC) = 300 (angles made by same arc on same side of the arc are equal)

Also, OD = OC (Radius of circle)

So, angle (ODC) = angle (OCD) = 300

Now, angle (BOC) = 1800 - angle (DOC) = 1800 – 1200 = 600 (Linear pair angles)

angle (BCO) = angle (OBC) (since OB= OC; radii)

angle (BCO) = (1800 – 600)/2 = 600

Also,

angle (BCD) = angle (OCD) + angle (OCB) = 300 + 600 = 900

Answer: 90 degrees

CAT Exam Important Topic: Strategy to Prepare “Geometry (Circles questions and answers)” for CAT-2024

Tips to solve circle questions:

1. Learn Important Properties of Circle

Area = πr2, r is the radius of circle

Circumference = 2πr

Length of Arc = θ/360× 2πr; θ is the angle made by arc at the centre.

Two circles are congruent if they have equal radii.

2. Learn Properties related to Chord

• The perpendicular from the centre of a circle to a chord bisects the chord. The converse is also true.
• There can be one and only one circle passing through three or more non-collinear points.
• If two circles intersect in two points then the line through the centres is the perpendicular bisector of the common chord.
• Equal chords of a circle or congruent circles are equidistant from the centre.
• The degree measure of an arc of a circle is twice the angle subtended by it at any point on the alternate segment of the circle.

3. Properties related to Cyclic Quadrilateral

Sum of opposite angles is 180 degrees.

4. Properties related to Tangents and Secants

• If a circle touches all four sides of a quadrilateral, then the sum of the two opposite sides is equal to the sum of the other two
• Tangents to a circle form an external point are equal.
• Radius is perpendicular to the tangent at the point of contact.
• Tangent-Secant Theorem

5. Practice CAT previous years questions to know the pattern of the questions and concepts involved.

6. Practice Similar questions.

CAT entrance exam: Pre-requisite to circle reasoning questions

1. Lines and Angles , triangles, polygons
2. Basics of trigonometry

CAT study material: References to Study (Theory) Geometry: Circle reasoning questions

1. NCERT Mathematics Class 9 and 10
2. Rodha (YouTube, Link: https://www.youtube.com/watch?v=EAz4sd6svzo
3. https://www.youtube.com/watch?v=nZR9cijpmkQ
4. https://www.youtube.com/watch?v=BAlO-DvSWic)

References to Practice circle questions for CAT exam

Circle questions and answers

1. How to prepare quantitative Aptitude for CAT by Arun Sharma.
2. Crack U (https://www.youtube.com/watch?v=IqfBailsqTk)
3. Practice Sample Papers

Part-2: CAT 2024 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)

CAT 2024 Syllabus Topic: Strategy to prepare “Games and Tournaments (Part-2)” for CAT

Tips and Tricks for CAT Games and Tournaments through Previous Years Questions from CAT/ MBA Entrance Exam:

Passage: In an 8 X 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row, or in the same column or in any diagonal position in any possible 4 directions, provided there is no other piece in between in the path from the queen to that piece.

The columns are labelled a to h (left to right) and the rows are numbered 1 to 8 (bottom to top). The position of a piece is given by the combination of column and row labels. For example, position c5 means that the piece is in cth column and 5th row. [CAT 2017]

Question1: If the queen is at c5, and the other pieces are at positions c2, g1, g3, g5 and a3, how many are under attack by the queen? There are no other pieces on the board.

1. 2

2. 3

3. 4

4. 5

Ans: [c]

CAT Tip 1: Draw an 8x8 matrix and Arrange Queen first.

CAT Tip 2: Arrange the other pieces and try to join them diagonally, vertically or horizontally.

Clearly, four pieces are under attack.

Passage: Ten players, as listed in the table below, participated in a rifle shooting competition comprising 10 rounds. Each round had 6 participants. Players numbered 1 through 6 participated in Round 1, players 2 through 7 in Round 2,…, players 5 through 10 in Round 5, players 6 through 10 and 1 in Round 6, players 7 through 10, 1 and 2 in Round 7 and so on. The top three performances in each round were awarded 7, 3 and 1 points respectively. There were no ties in any of the 10 rounds. The table below gives the total number of points obtained by the 10 players after Round 6 and Round 10

The following information is known about Rounds 1 through 6:

• Gordon did not score consecutively in any two rounds.
• Eric and Fatima both scored in a round.

The following information is known about Rounds 7 through 10:

• Only two players scored in three consecutive rounds. One of them was Chen. No other player scored in any two consecutive rounds
• Joshin scored in Round 7, while Amita scored in Round 10.
• No player scored in all four rounds.

[CAT 2019]

Q.1 What were the scores of Chen, David, and Eric respectively after Round 3?

1. 3, 3, 0

2. 3, 3, 3

3. 3, 6, 3

4. 3, 0, 3

Answer: 2

Q.2 Which three players were in the last three positions after Round 4?

1. Hansa, Ikea, Joshin

2. Bala, Chen, Gordon

3. Bala, Ikea, Joshin

4. Bala, Hansa, Ikea

Answer: 1

Q.3 Which player scored points in a maximum number of rounds?

1. Ikea

2. Chen

3. Amita

4. Joshin

Answer: 1

Q.4 Which players scored points in the last round?

1. Amita, Chen, Eric

2. Amita, Bala, Chen

3. Amita, Eric, Joshin

4. Amita, Chen, David

Answer: 1

Solution:

CAT Tip 1: Tabulate given information

CAT Tip 2: Analyze the total after round 6 and round 10 (Easy Finings)

B must be scored 1and 1 in R1 and R2 respectively

G must have scored 0 in R7

D must score 0 in R9 and R10

E must score 7 in R10

J must score 7 and 7 in R5 and R6 both

CAT Tip 3: Use Additional Information and fill the table simultaneously(shown in red colour)

Top 3 performaces awarded 7, 3 and 1 in each round.

In R1; only A can get 7. So, in R6 A will get 1.

I will get 1 in each of the round R4 and R5 (Since in R6, A get 1)

H will get 1 in R3

G must score 7 in R2 and R4. Also scored 3 in R6. ( Since G can not score in consecutive rounds)

F scored 7 in R3. E scored 3 in the same round.

F scored a 3 in R5 and D scored a 3 in R4 (Solving puzzle)

A scored 3 in R10 since 7 is scored by E

C must score 1 in each of rounds R8, R9 and R10

I should have scored 1, 7 and 7 in R7, R8 and R9 respectively. So, A will score 7 in R7.

J score 3 in R7; H scored 3 in R8; B scored 3 in R9.

The final Table will look as shown above.

CAT entrance exam: Prerequisite

1. Puzzles
2. Basic Knowledge of Sports
3. Basics of Games and Tournaments

CAT References to Study (Theory)

1. LRDI by Nishit K. Sinha
2. Crack U (YouTube link: https://www.youtube.com/watch?v=fZIx-bnpNO0)

CAT 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 2024: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)

CAT Exam Important Topic: Strategy to Prepare “Antonyms (Part-2)” for CAT-2024

Sample Problems on Antonyms from CAT/MBA Entrance Exams:

Q1: In the following question, out of the four alternatives, select the word opposite in meaning to the given word.

Intriguing

1. Banal

2. Riveting

3. Comforting

4. Absorbing

Answer: A

Explanation:

‘Intriguing’ meaning is “arousing one's curiosity or interest, fascinating”

Tip for CAT Antonyms: The word is an adjective so the answer should be an adjective.

Comforting (adj.): serving to alleviate a person's feelings of grief or distress

Riveting (adj.): completely engrossing

Absorbing (adj.): intensely interesting

Banal (adj.): so, lacking in originality as to be obvious and boring.

So, the correct answer is option A.

Q2: In the following question, out of the four alternatives, select the word opposite in meaning to the given word.

Revive

1. Defibrillate

2. Torpefy

3. Recuperate

4. Dead

Answer: B

Explanation:

Revive (v.): to restore consciousness.

Torpefy (v.): to make (someone or something) lifeless.

Recuperate (v.): recover from illness.

Defibrillate (v.): to restore the heart to a normal rhythm.

Dead (Noun): unconsciousness or apparent death.

Tip for CAT Antonyms: The word is a verb. So, the answer should be option B (Dead is not a verb)

So, the correct answer is option B.

CAT 2024: Pre-requisite

1. Vocabulary
2. Parts of Speech

CAT Exam: References to Study (Theory) Antonyms

1. Made Word Power Easy

2. BodhBridge

3. (https://www.youtube.com/watch?v=idFKTCWQihI&t=35s)

CAT Exam: References to Practice Antonyms questions

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

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

3. Knowation (YouTube; Link: https://www.youtube.com/watch?v=zIsFke7zJqs

Practice, stay focused, and we'll be back tomorrow with Day 44.

Thank you. All the best!