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

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

Edited By Irshad Anwar | Updated on Sep 14, 2023 06:57 PM IST | #CAT

Hello CAT 2023 aspirants, On November 26, the CAT exam 2023 will be given for MBA admissions from 2024-2026. In this CAT 2023 60 days preparation guide series of Careers360, we will discuss the strategies for triangle questions for day 41 that can help you prepare well and crack the CAT entrance test 2023. Students can download the geometry questions and answers pdf.

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

This article includes triangle questions, geometry questions for CAT, Data sufficiency questions for CAT, and PYQs on synonyms. Geometry is a very vast topic and includes many concepts and formulas. Students can refer to geometry and mensuration questions for CAT pdf. CAT Preparation 2023 in 60 days

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

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Geometry solved questions for CAT are given below:

Solution: (A)

Medians divides a triangle into 6 equal areas.

1694696464853

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

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

Solution: (B)

1694696465152

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.

    • 1694696878547

    • 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.

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  1. 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

  1. Practice on Congruence and Similarity of triangles.

  1. Learn Pythagoras Triplets (helps in saving time)

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

  1. 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 2023 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)

CAT 2023 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 2023: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)

CAT Exam Important Topic: Strategy to Prepare “Synonyms (Part-2)” for CAT-2023

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 2023: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

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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.

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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