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

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

2. Important formulae related to Prism:

• 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

3. 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

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

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.