CAT Geometry Question on Triangles, Data Sufficiency Questions, PYQs on Synonyms - Day 41

Part-1: Quantitative Aptitude for CAT exam

Important Concept/Formula Used in CAT questions on triangles. Concepts used in Triangles questions are given below:

• Similarity of Triangles
• Congruence of Triangles
• Types of Triangles
• Area of Triangles/ Heron's Formula
• The intersection of Medians/ Altitudes/ Perpendicular bisectors/ Angle bisectors
• Pythagoras Theorem

Previous Year CAT Geometry Questions on Triangles

Question 1: From a triangle, ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is. [CAT 2017]

1. 500/√3

2. 225/√3

3. 275/√3

4. 250√3

Geometry solved questions for CAT are given below:

Solution: (A)

Medians divides a triangle into 6 equal areas.

Area of triangle GBC = Two parts

Area of triangle ABC = 6 parts

Area of remaining portion = 6 parts – 2 parts = 4 parts

Area of Triangle ABC Using Heron's Formula: [s = (40+ 25+ 35)/2 = 50]

A = ss-as-bs-c = 5050-4050-2550-35,

A = 250√3

Area of remaining portion = 4 (250√3)/6= 500/√3.

Question 2: Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with a diameter of BC. Let BPC be an arc of a circle centred at A and lying between BC and BQC. If AB has a length of 6 cm then the area, in sq cm, of the region enclosed by BPC and BQC is [CAT 2017]

1. 9π- 18

2. 18

3. 9

4. 9π

Geometry test for CAT: Triangle Questions for CAT with Solutions are given below:

Solution: (B)

We need to find the area of the shaded region.

Area of shaded region = Area of Semicircle BCQC - Area of segment BPCP

Also BC = 6√2 (using Pythagoras)

Area of Semicircle BCQC = [π (3√2)2]/2 = 9π

Area of segment BPCP = Area of quadrant ACPBA - Area of triangle ABC = 6π2/4 - 6 x 6/2 = 9π- 18

Area of shaded region = 9π - (9π- 18) = 18

CAT Exam Important Topic: Strategy to Prepare Triangles (Geometry CAT Questions) and triangles questions

1. Learn Important Properties of Triangle

   • Sum of the length of any two sides > third side.

   • Difference between the lengths of any two sides of a triangle < third side.

   • Side opposite to the greatest angle will be the largest and the side opposite to the least angle is the smallest.

   • The sine rule: a/sin A = b/sin B = c/sin C = 2R (Where, R = circumradius.)

   • The cosine rule: a2 = b2 + c2 – 2bc cos A

   • This is true for all sides and respective angles.

   • The exterior angle is equal to the sum of two opposite interior angles.

   • Centroid divides medians in the ratio of 2:1.

   • A median divides a triangle into two parts of equal area.

2. Learn Properties related to area of triangle

   • Area = 1/2 base × height

   • Area = ss-as-bs-c, where S = (a+b+c)/2

   • Area = rs (where r is in radius)

   • Area = 1/2 × product of two sides × sine of the included angle

   • Area = abc/4R, where R = circum radius

3. Practice on Congruence and Similarity of triangles.

4. Learn Pythagoras Triplets (helps in saving time)

Eg: [3, 4, 5], [ 24, 10, 26], [7, 24, 25] etc

5. Divide the Triangle into different Sections based on the concepts used and practice accordingly.

CAT entrance exam: Prerequisite to triangles questions

1. Lines and Angles
2. Basics of trigonometry ( trigonometry CAT questions pdf)

CAT study material: References to Study (Theory)

1. NCERT Mathematics Class 9 and 10
2. Rodha (YouTube, Link: https://www.youtube.com/watch?v=rUI1bbCvk7E&list=PLG4bwc5fquziUvO3dlzG0MW9vqi3epud4)
3. https://www.youtube.com/watch?v=25P2O9r3AfM&list=PLG4bwc5fquziUvO3dlzG0MW9vqi3epud4&index=2

CAT study material: References to Practice Geometry: Triangles Questions

Geometry aptitude questions on triangles

How to prepare quantitative Aptitude for CAT by Arun Sharma. Below are the given youtube videos links to practice CAT questions on triangles:

1. Rodha (CAT PYQs; https://www.youtube.com/watch?v=hKyCT4T4Q4M&list=PLG4bwc5fquziUvO3dlzG0MW9vqi3epud4&index=10)
2. https://www.youtube.com/watch?v=c_Abx1YkGbE&list=PLG4bwc5fquziUvO3dlzG0MW9vqi3epud4&index=11
3. https://www.youtube.com/watch?v=GJu0L7KeXAg&list=PLG4bwc5fquziUvO3dlzG0MW9vqi3epud4&index=12
4. CAT geometry questions with solutions pdf

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

CAT 2024 Syllabus Topic: Strategy to prepare “Data Sufficiency in LR (Part-2)” for CAT

Tips and Tricks to Prepare for Data Sufficiency (LR) through PYQs from CAT/ MBA Entrance Exam:

Direction:

1. Statement I alone is sufficient to answer this question but statement II is not sufficient to answer this question.

2. Statement II alone is sufficient to answer this question but statement I is not sufficient to answer this question.

3. None is sufficient to answer this question.

4. Both statements together are sufficient to answer this question.

Questions 1: Five students Amit, Bhanu, Chetna, Devendra and Elena were the only ones who participated in a debate competition. They were ranked based on their scores in the contest. Devendra got a higher rank as compared to Elena, while Bhanu got a higher rank as compared to Chetna. Chetna’s rank was lower than the median. Who among the five got the highest rank?

I. Amit was the last rank holder.

II. Bhanu was not among the top two rank holders. [Based on CAT 2007]

Solution: [D]

CAT Tip 1: Collect the information from the problem paragraph

D> E

B> C

Rank of C is either 4 or 5 (Chetna’s rank was lower than the median)

CAT Tip 2: Is Statement I alone sufficient?

Amit is last.

Either D or B can be on top.

Two possible answers are there. So, the statement I alone is not sufficient.

CAT Tip 3: Is Statement II alone sufficient?

Bhanu is not among the top 2.

Bhanu is either 3 or 4.

Either A or D can be on top.

Two possible answers are there. So, statement II alone is not sufficient.

CAT Tip 4: Are Statement I and Statement II together sufficient?

Amit is last; Either D or B can be on top.

Bhanu is not among the top 2; Bhanu is either 3 or 4.

Either A or D can be on top.

From these two, we can say D is at the top.

Therefore, we can find answers using both statements together.

Questions 2: “On which day of the week did Akash reach Goa?”

Statement (1): Akash’s brother Sumit reached Goa a day before Akash.

Statement (2): Akash’s father reached Goa on Thursday which was two days later than the Sumit. [Based on PYQs]

Solution:

Tip 1: Is Statement I alone sufficient?

S reached a day before A.

No certain information is given.

So, the statement I alone is not sufficient.

Tip 2: Is Statement II alone sufficient?

A’s father = Thursday

S = Tuesday

No information about A can be deduced. So, statement II alone is not sufficient.

Tip 3: Are Statement I and Statement II together sufficient?

S reached a day before A.

A’s father = Thursday

S = Tuesday

A will reach on Monday.

Therefore, we can find answers using both statements together.

CAT entrance exam: Prerequisite

1. Blood Relation, Direction Sense, Ranking, Coding-Decoding, Inequality, Cubes, and various other basic topics of LR.

2. Basics of Data Sufficiency.

References to CAT Study (Theory)

1. LRDI by Nishit K. Sinha

2. (YouTube link: https://www.youtube.com/watch?v=LkvOu3oUymg )

References to Study (Practice)Data Sufficiency Questions

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

2. MBA Entrance Previous years Papers and Sample Papers.

3. https://www.youtube.com/watch?v=v3lDOtlFzL4&t=1016s

Part-3: CAT Exam Preparation 2024: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)

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

Sample Problems on Synonyms

Directions: Choose a similar word from the given options for the highlighted phrase/word.

Question 1: Find a similar word to EMBEZZLE

1. Misappropriate

2. Balance

3. Remunerate

4. Clear

Ans. Option (A)

Explanation: embezzle comes with the suffix ‘bezzle’ which means the act of stealing.

Also, we need negative connotations as misappropriation has a negative connotation. And from the given options, option (a) has a negative connotation. Rest 3 words have a positive connotation.

Question 2: Find a similar word to WILE

1. Destroy

2. Ruse

3. Urge

4. Comply

5. None of these

Ans. Option (B)

Explanation: wile means a trick or stratagem meant to fool, trap or entice.

Ruse means a trick or clever plan

Tips and Tricks to Solve CAT Questions on Synonyms:

• Break down the typical word into two. This will lead to the relevant option.

• Familiarize yourself with tricky words.

• Distinguish a word in positive, negative, or neutral connotation. This will lead to making the right choice.

• Associate a word with a previously known similar type of word. This will also give an idea of its connotation.

• Sometimes similar type of words is given. Make the right choice according to the context in which it is used.

• It is essential to observe which word is contextually right and why. This will help in the elimination of the wrong options.

CAT 2024: Prerequisite

1. Vocabulary

2. Parts of Speech

CAT exam: References to Study (Theory)

1. Made Word Power Easy

2. Study Buzz: YouTube

3. (https://www.youtube.com/watch?v=QBqXNgJzhz8 )

CAT exam: References to Study (Practice)

1. Big Book of Synonyms and Antonyms – English (Maple Press)

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

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

Practice, stay focused, and we'll be back tomorrow with CAT Preparation Day 42. Thank you!

All The best