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Exploring Pyramids, PYQs for Binary Logical Reasoning Questions, Parajumbles Problem & Strategies, Day 46

Exploring Pyramids, PYQs for Binary Logical Reasoning Questions, Parajumbles Problem & Strategies, Day 46

Edited By Irshad Anwar | Updated on Oct 11, 2023 12:21 PM IST | #CAT

Aspirants for the CAT exam in 2023, The CAT exam 2023 will be offered on November 26 in preparation for MBA admissions from 2024 to 2026. The strategies on mensuration: pyramid questions for CAT exam for day 46 will be covered in this 60-day preparation guide series for the CAT 2023 exam by Careers360. These strategies can help you prepare effectively and pass the CAT entrance exam 2023. Students can download the mensuration questions and answers pdf.

Exploring Pyramids, PYQs for Binary Logical Reasoning Questions, Parajumbles Problem & Strategies, Day 46
Exploring Pyramids, PYQs for Binary Logical Reasoning Questions, Parajumbles Problem & Strategies, Day 46

Pyramids questions for CAT exam are also an important part of mensuration and thus students should be thorough with the topic as well. CAT Preparation 2023 in 60 days

Part-1: Quantitative Aptitude for CAT exam

Important Concept/Formula Used in Pyramid Questions for CAT (mensuration )

CAT Mensuration: Pyramids Formulas

  1. Figures under Pyramid

  • Any solid which can have any polygon as its base and its edges converge to a single apex.
  • Cone
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  1. Important formulae related to Prism:

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  • Slant surface of a pyramid = 1/2 * Perimeter of the base* slant height
  • Whole surface of a pyramid = Slant surface + area of the base
  • Volume of a pyramid = area of base * height/3
  1. Frustum of a Pyramid

  • When a pyramid is cut from the top, the lower remaining part is called the frustum of the pyramid.
  • Slant surface of the frustum = 1/2 * sum of perimeters of end * slant height.
  • Volume of the frustum of a pyramid = Volume of Pyramid – volume of removed part

Previously Asked Questions from Mensuration (Pyramid) in the CAT Exam:

Q1. CAT geometry mensuration questions on pyramids are given below:

The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, the length of each side being 20 cm. The vertical height of the pyramid, in cm, is [CAT 2019, Slot 2]

  1. 10√2
  2. 8√3
  3. 12
  4. 5√5

Ans: [1]

For better understanding, see the below diagram

1697004799001

Side of square = side of equilateral triangle = 20 cm.

Slant height (L) of pyramid = altitude or perpendicular bisector of the base of equilateral triangle

L = √(202+102) = 10√3 cm

So, from the diagram

L2 = h2 + 102

⇒ h2 = L2 - 102

⇒ h2 = 300 - 100

⇒ h = 10√2 cm

Q2. CAT menstruation questions on pyramids are given below:

A right circular cone, of height 12 ft, stands on its base which has a diameter of 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With π = 22/7, the volume, in cubic ft, of the remaining part of the cone is: [CAT 2018, TITA]

Solutions for Pyramid questions for MBA entrance exams are given below:

Ans:

Volume of frustum = Volume of larger cone – Volume of smaller cone

Using the concept of similar triangle

(Radius of smaller cone)/(Radius of larger cone)= (height of smaller cone)/(height of larger cone)

⇒ Radius of smaller cone (3412)

⇒ Radius of smaller cone = 1 ft

So, Volume of frustum = π/3 (42 x 12 – 12 x 3) = 198 cubic ft

CAT Exam Important Topic: Strategy to Prepare “CAT Geometry Mensuration (Pyramids)” for CAT

  • In a pyramid with a base of n sides, number of vertices = n + 1.
  • Number of faces including the base = n + 1.
  • Attempt online CAT mock test/CAT model tests
  • Do not waste time trying to solve the question if got stuck. (During Exam)
  • Look for symmetry and take advantage of that.

CAT entrance exam: Prerequisite to mensuration: pyramids questions for MBA entrance exams

  1. Geometry
  2. Basics of trigonometry
  3. Percentage

CAT study material: References to Study Theory for pyramids (mensuration)

  1. NCERT Mathematics Class 9 and 10
  2. MBA Pathshala (YouTube, Link: https://www.youtube.com/watch?v=tA3ofmDtg1A)

References to Practice CAT mensuration questions on pyramids

  1. How to prepare quantitative Aptitude for CAT by Arun Sharma.
  2. 2IIM CAT Preparation (https://www.youtube.com/watch?v=X7F6Lnouppk)
  3. Practice Sample Papers

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

CAT 2023 Syllabus Topic: Strategy to prepare “Binary Logic (Part-2)” and binary logical reasoning CAT questions pdf.

Tips and Tricks for Binary Logic CAT Questions through Previous Years Questions from the CAT/ MBA Entrance Exam

Q1. Binary Logic Examples with Questions and Answers are given below:

The EDI rounded up Riya, Aryan, and Shovik yesterday because one of them was suspected of keeping drugs. The 3 suspects gave the following statements after intensive questioning:

Riya: I’m innocent.

Aryan: I’m innocent.

Shovik: Aryan is the guilty one.

Who kept the drugs among the three persons, if only one of the statements will be true?

  1. Riya
  2. Aryan
  3. Shovik
  4. None of these
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Solutions: [1]

Binary Logic Tip 1: Assume any of the given statements is truth and check the validity of the statement

Assume Shovik is a true-teller.

So, we can see that Shovik's statement of Shovik is correct. It also makes the statement given by Riya is also a truth and the statement made by Aryan is false.

So, 2 statements are correct which is a violation of the given condition.

Binary Logic Tip 2: Statement which was earlier assumed to a truth, consider it a false statement and check the validity of the statement

Statement of Shovik is considered a false statement.

It makes the statement of Aryan a true statement and the statement given by Riya is a false statement. Two statements are wrong in this case.

and the statement made by Aryan is false.

Therefore, Riya is the one who kept drugs.

Q2. CAT Binary Logic Questions and Answers are given below:

Mohan went to an Island on which there were three tribes of people. People from one of the tribes always spoke the truth. People from the second tribe always lied. People who belonged to the third tribe spoke the truth and lied alternately. The Island had only 3 fruits i.e. apple, mango and banana. Mohan found three people X, Y and Z asked them about their favourite fruits.

Their responses were as follows:

X: I like apples. Y likes mango

Y: Z likes mango. X likes bananas

Z: I like apples. X likes bananas

If it is known that X, Y and Z belonged to different tribes and each one of them liked a different fruit, then answer the following questions.

Who likes apples?

  1. X
  2. Y
  3. Z
  4. cannot be determined

Solution: [b]

CAT Binary Logic Tip 1: Assume any of the persons is a truth teller and check the validity

Assume Y is a truth-teller (always speaks the truth).

Conclusion: Z likes mango; X likes bananas, so Y must like apples.

CAT Binary Logic Tip 2: let’s see if the statements by the other people validate or contradict our assumption.

X says I like apples (wrong) since we know that Y likes apples.

His second statement is that Y likes mangoes (wrong) since Y likes apples.

Since both statements of X are wrong, he must be a liar.

Now, see whether Z is an alternator or not:

Z’s first statement is wrong since Y likes apples.

Z’s second statement is that X likes bananas. This is true.

Hence our assumption is correct.

Final Conclusion:

Y (Likes Apple) is the truth-teller

Z (like mango) is the alternator

X (like bananas) is the liar.

CAT entrance exam: Prerequisite

  1. Puzzles

  2. Boolean Algebra

  3. Concept of truth-teller, liar and alternator

References to CAT Study (Theory)

  1. LRDI by Nishit K. Sinha

  2. gofudu (YouTube link: h https://www.youtube.com/watch?v=EeJ25Wd2lH0&t=583s)

References to Study (Practice) Binary Logic

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

  2. MBA Entrance Previous years Papers and Sample Papers.

  3. Shankar’s Aptitude (YouTube: https://www.youtube.com/watch?v=eSgM3GZQbM8&list=PLo0WP7XtW0AjhsxpLj2Z7TvJex118ibUC&index=2)

  4. (https://www.youtube.com/watch?v=WwAUypn8SZg&list=PLo0WP7XtW0AjhsxpLj2Z7TvJex118ibUC&index=3)

  5. (https://www.youtube.com/watch?v=fshqYb9kX04&list=PLo0WP7XtW0AjhsxpLj2Z7TvJex118ibUC&index=4)

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

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

Sample/ Practice Questions on Para Jumbles for CAT/MBA Entrance Exams:

Direction: The four sentences (labelled A, B, C, D) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:

Q1: CAT Parajumbles Questions with Solutions are given below:

  1. The study suggests that the disease did not spread with such intensity, but that it may have driven human migrations across Europe and Asia.

  2. The oldest sample came from an individual who lived in southeast Russia about 5,000 years ago.

  3. The ages of the skeletons correspond to a time of the mass exodus from today's Russia and Ukraine into western Europe and central Asia, suggesting that a pandemic could have driven these migrations.

  4. In the analysis of fragments of DNA from 101 Bronze Age skeletons for sequences from Yersinia pestis, the bacterium that causes the disease, seven tested positive.

  5. DNA from Bronze Age human skeletons indicate that the black plague could have emerged as early as 3,000 BCE, long before the epidemic that swept through Europe in the mid-1300s.


  1. 54123

  2. 51243

  3. 12345

  4. 12435

Ans. Option A

Explanation: CAT Parajumbles Trick: Try to find starting statement (About phrase) and conclusion statement (Last statement)

Sentence 5 can be the best opening sentence. Sentence 5 talks about a DNA study and Sentence 4 explains the findings of the study. So, sentence 4 follows sentence 5. Sentence 1 also relates to the study—its conclusion. So, sentence 1 follows sentence 4. Both sentence 2 and sentence 3 relate to the ages of the skeletons tested. Sentence 3 is more general and a better concluding sentence than sentence 2, so sentence 3 follows sentence 2.

Q2: CAT Para jumbles Questions with Solutions are given below:

1. But now we have another group: the unwitting enablers.

2. Democracy and high levels of inequality of the kind that has come to characterize the United States are simply incompatible.

3. Believing these people are working for a better world, they are, actually, at most, chipping away at the margins, making slight course corrections, ensuring the system goes on as it is, uninterrupted.

4. Very rich people will always use the money to maintain their political and economic power.

  1. 2314

  2. 1234

  3. 2413

  4. 2431

Ans. Option C

Explanation:

CAT Parajumbles Trick: Statement 1 cannot be an opening statement (since starting with ‘but’)

Sentence 2 can be the best opening sentence. Sentence 4 explains sentence 2 and so sentence 4 follows sentence 2. Sentence 4 talks of ‘very rich people as a group, while sentence 1 talks of ‘another group’, the unwitting enablers. Hence, sentence 1 follows sentence 4. The reference to ‘these people in 3 could only be to the unwitting enablers. So, 3 can be the concluding sentence.

Q3: CAT Questions on Para jumbles with Solutions are given below:

  1. Complex computational elements of the CNS are organized according to a “nested” hierarchic criterion; the organization is not permanent and can change dynamically from moment to moment as they carry out a computational task.

  2. Echolocation in bats exemplifies adaptation produced by natural selection; a function not produced by natural selection for its current use is exaptation -- feathers might have originally arisen in the context of selection for insulation.

  3. From a structural standpoint, consistent with exaptation, the living organism is organized as a complex of “Russian Matryoshka Dolls” -- smaller structures are contained within larger ones in multiple layers.

  4. The exaptation concept, and the Russian-doll organization concept of living beings deduced from studies on the evolution of the various apparatuses in mammals, can be applied to the most complex human organ: the central nervous system (CNS).


  1. 2431

  2. 2341

  3. 4321

  4. 2143

Ans. Option B

Explanation:

CAT Para jumbles Questions Trick: Statement 3 cannot be an opening statement (Starting with ‘From’, seems the statement must lie somewhere in the middle of a passage)

Sentence 4 talks of various concepts being applied to the central nervous system. Sentence 1 is about the central nervous system. 4, however, is not the opening sentence of the paragraph, as it talks of the 'exaptation' concept and 'Russian doll organisation' concept, the meaning of which is not clear from 4. 2 explains what exaptation is and 3 what Russsian doll organisation is. So, 2341 is the right order.

CAT 2023: Prerequisite

  1. The basic idea of sentence structure.
  2. Knowledge of basic grammar rules.
  3. Reading speed should be good and should be able to understand the idea of the passage.

References to Study (Theory)para jumbles for CAT

  1. How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)
  2. Mission CAT (YouTube: https://www.youtube.com/watch?v=Cil9A0tQDIA)

References to Practice CAT Para jumbles Questions

  1. Jumbles Sentences and Paragraphs (Arihant)
  2. Bodhee Prep CAT Preparation (https://www.youtube.com/watch?v=av6O1Ub1fbg&list=PLhsX_kQ8ISVZsgGigUd3YPkub37DV6MmE&index=2)
  3. CAT Previous years Papers and Sample Papers.

Tomorrow we'll be back with Day 47, so practice and pay attention.

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Questions related to CAT

Have a question related to CAT ?

Hello,

In the context of Karnataka's reservation categories, Vishwakarma is classified under Category 2A . Specifically:

  • Category 2A : This category includes communities that are identified as Vishwakarma , along with others such as Panchamasali , Nayaka , Goud , and others.

Hope it helps !

Hello aspirant,

A bachelor's degree from an accredited university with a CGPA of at least 50% (or an aggregate of 45% for the SC, ST, and PwD/DA categories) is required in order to appear in the CAT exam in 2024. Duration and manner of degree: The course needs to last three years. The mode might be online, distant, or regular.

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Hope this information helps you.

Hello student

As a self-employed individual with your own cafe, you'll need to provide documents that establish your business and work experience. Here are some documents you can prepare for your CAT application:


1. *Business Registration Documents*:

- Partnership Deed (already have)

- Business PAN Card (already have)

- FSSAI License (already have, though it's in your partner's name)

2. *Proof of Business Ownership*:

- Affidavit or declaration stating your ownership and role in the cafe

- Business registration certificate (if you have one)

3. *Proof of Work Experience*:

- A letter or certificate from your partner or co-owner confirming your work experience and role in the cafe

- A detailed resume highlighting your entrepreneurial journey and responsibilities

4. *Financial Documents*:

- Income Tax Returns (ITRs) for the last 2-3 years (if applicable)

- Balance Sheets and Profit & Loss statements for your cafe (if audited)

5. *Rental Agreement*:

- Already have, but ensure it's updated and signed


Additional tips:


- Ensure all documents are scanned and uploaded in the required format (usually PDF or JPEG)

- Keep your documents organized and easily accessible for the application process

- Be prepared to provide additional information or clarification if requested by the admission authorities


Remember to check the specific requirements for each B-school you're applying to, as they may vary. Good luck with your CAT application!

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.



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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