Ace the CAT Exam with Mensuration, Binary Logic, and PYQs on Parajumbles Proficiency - Day 45

Part-1: Quantitative Aptitude for CAT exam

Important Concept/Formula Used in Mensuration CAT Questions

CAT Geometry Mensuration (Prism)

1. Figures under Prism

• Cubes
• Cuboids
• Right Circular cylinder
• Symmetric figures with top and bottom identical

2. Important formulae related to Prism:

• Volume = Area of base x height
• Lateral Surface Area = Perimeter of base x height
• Total Surface Area = LSA + 2x Area of base

CAT Previous Years Questions on Mensuration (Prism).

Q1. CAT Mensuration Geometry Questions with Solutions are given below:

A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1: 1: 8: 27: 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to: [CAT 2017]

1. 10
2. 50
3. 60
4. 20

Ans: [2]

Let the Volumes of smaller cubes be 1, 1, 8, 27 and 27; their respective sides will be 1, 1, 2, 3, and 3.

Therefore, Total Surface Area of these five smaller cubes = 6(12+ 12+ 22+ 32+ 32) = 144.

The volume of Original Cube = 1+ 1+ 8+ 27+ 27 = 64 and side will be 4.

Surface Area of Cube = 6x 16 = 96

Percentage increase in the area = (48/96) x 100= 50%

Q2. Geometry and mensuration questions for CAT pdf can be downloaded. The question is given below:

A room has floor size of 15*6 sq.cm. What is the height of the room, if the sum of the areas of the base and roof is equal to the sum of the areas of the four walls? [IPMAT 2020]

1. 1.12cm

2. 3.24cm

3. 4.29cm

4. 2.5cm

Ans: [1]

Let height be ‘h’

According to given condition:

Area of base+ roof = Area of four walls

2(15x 6) = 2h (15+ 6)

⇒ h = 90/21= 4.29 cm

CAT Exam Important Topic: Strategy to Prepare Mensuration (Prism) and mensuration CAT questions on prism.

CAT Mensuration (Prism)

• Understand the difference between 2-D and 3-D figures.
• For any regular solid; Number of faces + Number of vertices = Number of edges + 2
• Length of the longest rod that can be kept inside a rectangular room is = √(L2 + B2 + H2)
• Practice previous years questions to know the pattern of the questions and concepts involved.

CAT entrance exam: Prerequisite to Mensuration CAT Questions

• Geometry
• Basics of trigonometry

CAT study material: References to Study (Theory) Mensuration (prism)

• NCERT Mathematics Class 9 and 10
• Rodha (YouTube, Link: https://www.youtube.com/watch?v=HhtLt2JZKu4)

References to Practise Mensuration CAT Questions

• How to prepare quantitative Aptitude for CAT by Arun Sharma.
• Mission CAT (https://www.youtube.com/watch?v=HKecEB0PF3U)
• Practice Sample Papers

Part-2: Logical Reasoning and Data Interpretation:

Binary Logic questions for CAT

Important Concept/Formula Used

Truth-teller: always speak the truth and all the statements spoken by him/her are true.

Lie-teller: always tells lies and all the statements spoken by him/her are false.

Switcher/Alternator: keeps on shifting between lies and truth that keep on changing on an alternate basis which means if his first statement is true, second is false and vice versa.

After understanding the concept/formula used, we can attempt Binary logic CAT questions and make their concepts stronger. Aspirants can also refer to binary logical reasoning CAT questions pdf

Binary Logical Reasoning Questions for CAT/ MBA Entrance Exam:

Q1. Three persons A, B and C gave these statements:

A said, either Freedom Party or Green Party won the elections.

B said, Freedom Party won.

C said, neither Freedom Party nor Green Party won the elections.

Of these persons, only one person is wrong. [SNAP 2019]

Who won the elections?

1. Freedom Party

2. Green Party

3. Data Inadequate

4. None of these

Ans: [1]

Assume that A is telling lies, then statements made by him will be false which implies that neither Freedom Party nor Green Party won the election.

It will make B’s statement false. It violates the condition of being only one person wrong.

Our Assumption is wrong.

A is telling the truth and hence B is also telling the truth. It implies that the Freedom Party won the election.

Q2. Ramesh, Suresh and Mahesh are three people who belong to three different tribes of people. The three tribes are known as knights (those who always speak the truth), Knaves (who always lie) and switchers (those who alternatively speak the truth and lie). Ramesh said that Suresh is not a switcher. Mahesh said that Ramesh is a switcher. [SNAP 2015]

Who among the following is Knave?

1. Suresh
2. Ramesh
3. Mahesh
4. Cannot be determined

Ans: [A]

R: Suresh is not a switcher

M: Ramesh is a switcher

Case 1: If R is a Knight;

S must be a Knave and M is a switcher.

M is saying ‘Ramesh is a switcher’ is a wrong statement here which is a possibility.

Case 2: If R is a Knave

S is a switcher which implies that M is also a Knave.

This case of having two Knaves is a false case.

Case 3: If R is a switcher;

M is telling the truth which implies that S is a Knave.

From the three cases, it is clear that Suresh is a Knave.

Topic: Strategy to prepare “Binary Logic (Part-1)” for CAT

• Divide the questions in levels of difficulties
• Learn the concept of binary logics (Boolean Algebra)
• Binary Logics are all about making assumptions and dealing with conflicts/ Contradictions
• Find trigger statement to start the question with

Like: I am a liar; I am a truth teller, I am an alternator etc.

• A person who declares himself a ‘not a truth teller’ is always an ‘alternator’ and the statement ‘I am not a truth teller’ is always a true statement.
• A person who declares himself a ‘Liar’ is always an ‘alternator’ and the statement ‘I am a liar’ is always a false statement.
• A person who declares himself an ‘alternator’ can never be a ‘truth teller’.
• A person who declares himself ‘not an alternator’ can never be a ‘liar’.

Pre-requisite:

1. Puzzles
2. Boolean Algebra

References to Study (Theory)

1. LRDI by Nishit K. Sinha
2. CAT Funda (YouTube link: https://www.youtube.com/watch?v=z69ElNGKPFs)
3. Shankar’s Aptitude (https://www.youtube.com/watch?v=hZOe3FaoM1w&list=PLo0WP7XtW0AjhsxpLj2Z7TvJex118ibUC)

References to Study (Practice)

1. Verbal and Non-Verbal Reasoning by R S Agrawal.
2. MBA Entrance Previous years Papers and Sample Papers.
3. Riya Agrawal (YouTube: https://www.youtube.com/watch?v=dFYBSEVH6GE)
4. https://www.youtube.com/watch?v=EeJ25Wd2lH0

Part-3: VARC

Topic: Strategy to Prepare “Para-jumbles” for CAT-2023 (Part-1)

Sample Problems based on CAT/MBA Entrance Exams/ Parajumbles questions with solutions:

Q1-CAT Sentence Rearrangement: The French Revolution

A. The French Revolution created a vision for a new moral universe: that sovereignty resides in nations; that a constitution and the rule of law govern politics; that people are equal and enjoy inalienable rights; and that church and state should be separate.

B. The French Revolution invented the modern revolution —the idea that humans can transform the world according to a plan—and so has a central place in the study of the social sciences.

C. It ushered in modernity by destroying the foundations of the “Old Regime”—absolutist politics, legal inequality, a “feudal” economy (characterized by guilds, manorialism, and even serfdom), and an alliance of church and state.

D. That vision is enshrined in the Declaration of the Rights of Man and Citizen of 1789, whose proclamation of “natural, imprescriptible, and inalienable” rights served as the model for the 1948 United Nations Universal Declaration of Human Rights.

1. ADBC

2. BADC

3. ACBD

4. BCAD

Ans. Option (D)

Explanation: Sentences C and D start with "it" and "that" respectively and can be hence ruled out as starting sentences for the paragraph.

Sentence A talks of a vision. Sentence D starts with “That vision?. So D should follow A. Only options (a) and (d) have this arrangement.

Sentence B is a general premise that the French Revolution invented the modern revolution.

Sentence C talks of how the revolution brought in modernity by destroying the foundations of the Old Regime. We can see that there is a link between sentences B and C- both talk of "modernity". C follows B.

Sentence A talks of a “new moral universe? while Sentence C talks of the old regime. So again, A follows C.

Q2- CAT Parajumbles: Indian Village Culture and Polity

1. Patrilineal ownership of lands and the culture of dowry attached to it have turned daughters into bad debts.

2. The control of such castes on local politics aggravates masculine hubris.

3. The bigotry of our village culture and polity is intrinsically linked to a control of land and agriculture.

4. Land makes certain castes ‘kingly’ in rural communities

1. DBCA

2. DABC

3. CDBA

4. ADBC

Ans. Option (c)

Explanation: Sentence C talks of the intolerance that marks the village culture and polity. We see that this is the main idea of the paragraph.

Sentence D talks of some castes being considered “kingly? in rural communities. Sentence C talks of the control of “these castes? on local politics and how it aggravates masculine pride. So, C comes after D. Both of these sentences substantiate the idea of bigotry that is made by sentence C.

Sentence A talks of the patrilineal system of passing ownership of lands and system of linking dowry to land ownership turning daughters to be regarded as “bad debts”. This sentence substantiates the point made by sentence C.

Hence according to the given question option (c) is correct.

Tips and Tricks for CAT

1. Find the central theme of the passage by reading all the sentences quickly to understand the flow of the paragraph.
2. Look for the opening and closing sentence.
3. A closing scene is the one that has a conclusion and most of the time starts with therefore, thus, hence etc.
4. Opening sentence usually starts with a person’s name or establishes a scene.
5. Try to weave the sentences together by taking hints from time/ chronology/ events etc.
6. Sentences with full forms come first, followed by the sentence with abbreviations.
7. Ideas always precedes the examples. Sentences that start with a connective or a transition word are almost never introductory sentence
8. Transition words are words used by the author to shift one idea in a sentence to another.

Pre-requisite

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

References to Study (Theory)

1. How to Prepare for Verbal Aptitude for CAT by Arun Sharma (9th Edition)

2. Affairscloud

References to Study (Practice)

1. https://bodheeprep.com/cat-parajumbles-questions-solutions-practice
2. CAT Previous years Papers.
3. CAT Sample Papers.

We will be back with Day-46 tomorrow. Do practice and be focused.

Thank You. All the best.