CAT Masterclass: Understanding Spheres, Logical Connectives, and Some Important PYQs of Para jumbles - Day 47

CAT Preparation 2024 in 60 Days

Part-1: Quantitative Aptitude for CAT Exam

CAT Exam Important Topic: Strategy to Prepare “Mensuration (Sphere)” and CAT mensuration questions on sphere. Sphere questions and answers for CAT exam pdf download are available at the top of the page.

Important Concept/Formula Used in Mensuration Questions For CAT exam

Important formulae related to CAT Geometry Mensuration: Sphere and Hemisphere are given below:

1. A sphere is solid in the form of a ball with radius r.

2. Surface Area of a sphere = 4πr²

3. Volume of a sphere =4/3 πr³

4. Curved Surface Area of a Hemisphere = 2πr²

5. Total Surface Area of a Hemisphere = 3πr²

6. Volume of a Hemisphere =2/3 πr³

CAT Previous Year Mensuration Geometry Questions on Sphere:

Q1. Previous Year CAT Mensuration Questions are given below:

A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is 9 π cm³. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is [TITA, CAT 2017]

Mensuration Geometry Questions with Solution are given below:

Given that the height of the cylinder is 3 cm, while its volume is 9π cm3

⟹ πr²h = 9π

⟹ r = √3 cm

See the diagram below:

x² = 2² – (√3)²

x = 1 cm

Height of the top point of the sphere from the bottom of the cylinder = Height of cylinder + radius of sphere + x = 3+ 1+ 2 = 6 cm

Q2. Questions on CAT Geometry Mensuration are given below:

A spherical-shaped Laddoo has been placed inside an open box of the cubical shape of side 10 cm such that the sweet fit the box. A fly is sitting on one of the vertices of the cube. What is the shortest distance the fly must travel to reach the sweet? [Based on CAT PYQ]

1. 5 cm

2. 5(√3 – 1) cm

3. 5(√2 – 1) cm

4. 2.5(√3 – 1) cm

CAT Geometry Mensuration questions with solutions are given below:

Ans: [2]

Edge of cube = diameter of sphere = 10 cm

Top view of the situation:

CD = Minimum distance required

CD = AD- BC- AB = AD – BC – CD (since AB = CD; by symmetry)

CD = (AD – BC)/2 = (10√3 – 10)/2 = 5 (√3 – 1)

[Here AD = diagonal of cube = √3 x side of cube]

Tricks and Tips for CAT Geometry Mensuration and Sphere

Tricks and tips for Sphere Questions for CAT are given below:

1. Imagine a ball/football as a sphere and do make the analysis

2. See the pattern of asked Sphere Questions for CAT

3. Practice Hybrid questions on the sphere with cone, a sphere with cylinder, sphere inside a cube etc.

4. Do not confuse curved surface area and Total Surface Area.

CAT entrance exam: Prerequisite to mensuration Problems: Sphere Questions for CAT

1. Geometry

2. Basics of trigonometry

3. Percentage

CAT study material: References to Study Theory for Sphere (Mensuration)

1. NCERT Mathematics Class 9 and 10

2. 2IIM (YouTube Channel)

References to Practice CAT mensuration questions on Sphere

Mensuration Questions For CAT exam

1. How to prepare quantitative Aptitude for CAT by Arun Sharma.

2. Concept Tree: YouTube (https://www.youtube.com/watch?v=3FRFRG_GUpw)

3. Practice Sample Papers and previous year mensuration questions

Part-2: CAT 2024 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation) (h2)

CAT 2024 Syllabus Topic: Strategy to prepare “Logical Connectives” for CAT

Important Rules/ Tips and Tricks to solve the questions on Logical Connectives

1. Rules

2. Rewrite the given statement by putting a logical connective at the beginning of the statement if it is not already there and reverse the conditions to check the validity of the new statement.

3. Also check whether the negatives of both conditions still hold true.

4. Practice the varieties of questions based on patterns of CAT and other MBA entrance Exams.

CAT/ MBA Entrance Exam Previous Years Questions on Logical Connectives

Q1. Examine the following statements:

I. I listen to 91.9 FM only if I am in a happy mood.

II. I am never in a happy mood when I have my brother’s company.

III. Whenever I go shopping I take my brother along.

Which one of the following conclusions can be drawn from the above statements?

1. If I am in a happy mood, I listen to 91.9 FM.

2. If I am in a happy mood, I seek my brother’s company.

3. If I am not with my brother, then I’ll listen to the 91.9 FM.

4. If I am not happy I do not listen to the 91.9 FM. [Based on PYQ]

Solution: D

Only (d) can be drawn from the above statements.

If I am in a happy mood does not conclude that I will listen to 91.9 FM.

It is given that if I am in my brother’s company, I can never be in a happy mood. So, this conclusion is totally wrong.

No such relation is given

Q2. If Amit walks slower than Sumit, and Sumit walks as fast but not faster than Bhanu; then, as compared to Amit, Bhanu walks: [Based on PYQ]

1. slower than Amit

2. faster than Amit

3. with the same speed as Amit

4. Given data is not sufficient to determine

Solution: (b)

From the given information, we get the following.

Bhanu = Sumit > Amit

Bhanu walks faster than Amit.

CAT entrance exam: Prerequisite to Logical Connectives

1. Analytical Approach

2. Basics of Syllogism ism and Logical Deduction

References to CAT Study (Theory) for Logical Connectives

1. A new approach to Reasoning (B.S. Sijwali & S. Sijwali Arihant)

2. FundaMakers-CAT Preparation (YouTube link: https://www.youtube.com/watch?v=wVjpq7db4JI)

References to Practice CAT Logical Connectives

1. Analytical Reasoning by M. K. Pandey.

2. MBA Entrance Previous years Papers and Sample Papers.

3. PrepLadder CAT (YouTube: https://www.youtube.com/watch?v=PyJAWeMDJvg)

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

CAT Exam Important Topic: Strategy to Prepare “Para jumbles” (Part-3) for CAT-2024

Previous Years' Questions on Para Jumbles from the CAT Exam

Q1. CAT Para jumbles Questions with Solutions are given below:

The four sentences (labelled 1, 2, 3, 4) 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: (CAT 2021)

1. But today there is an epochal challenge to rethink and reconstitute the vision and practice of development as a shared responsibility – a sharing which binds both the agent and the audience, the developed world and the developing, in a bond of shared destiny.

2. We are at a crossroads now in our vision and practice of development.

3. This calls for the cultivation of an appropriate ethical mode of being in our lives which enables us to realize this global and planetary situation of shared living and responsibility.

4. Half a century ago, development began as a hope for a better human possibility, but in the last fifty years, this hope has lost itself in the dreary desert of various kinds of hegemonic applications.

Ans: 2-4-1-3

Explanation: Sentence 2 indicates the main idea of the paragraph therefore it can be used as the best opening sentence. Sentence 4 describes the development process and how it has been lost his way. Sentence 1 tells the view of today’s development. Sentence 3 contains the complete idea which has been discussed in 2. So, 2413 is the correct order.

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

The five sentences (labelled 1, 2, 3, 4, 5) 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: (CAT 2017)

1. One of the most dramatic examples in nature of ill wind that blows goodness is lightning.

2. In its aerial form nitrogen is insoluble, unusable and in need of transformation.

3. Lightning starts the series of chemical reactions that need to happen to nitrogen, ultimately helping it nourish our earth.

4. Nitrogen — an essential food for plants — is an abundant resource, with about 22 million tons of it floating over each square mile of earth.

5. Before plants can take life from the atmosphere, nitrogen must undergo transformations similar to the ones that food undergoes in our digestive machinery.

Ans: 5-3-4-2-1

Explanation: In the above passage, 5 is assigned as the best second opening statement. As it talked about the major idea of the passage. Then, 3 explains why it happens. 4 elaborate on this. So,5-3-4-2-1 is the right order.

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

The four sentences (labelled 1, 2, 3) below, when properly sequenced would yield a coherent paragraph. As the position of the opening sentence is already fixed (A), decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer: (CAT 2018)

1. Impartiality and objectivity are fiendishly difficult concepts that can cause all sorts of injustices even if transparently implemented.

2. It encourages us into bubbles of people we know and like while blinding us to different perspectives, but the deeper problem of ‘transparency’ lies in the words “and much more”.

3. Twitter’s website says that “tweets you are likely to care about most will show up first in your timeline based on accounts you interact with most, tweets you engage with, and much more.”

4. We are only told some of the basic principles, and we can’t see the algorithm itself, making it hard for citizens to analyse the system sensibly or fairly or be convinced of its impartiality and objectivity.

Ans: 3-2-4

Explanation: 324 is a clear sequence: all three sentences signify Twitter’s rules. 2 comes after 3, as the pronoun ‘it’ that starts 2 could only be pointed to the statement on Twitter’s website elaborated in 3.

Q4. The four sentences (labelled 1, 2, 3) below, when properly sequenced would yield a coherent paragraph. As the position of the closing sentence is already fixed (4), decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:

1. Including wearing a “hijab” or headscarf that is supposed to completely hide the hair.

2. Many Iranian women, especially in major cities, have long played a game of cat-and-mouse with authorities.

3. Iran’s Islamic Republic requires women to cover up in public.

4. With younger generations wearing loose scarves and outfits that push the boundaries of conservative dress.

Ans: 3-1-2

Explanation: 312 is the best sequence. 3 is the best opening statement. Then comes 1 as 1 completes the sentence that has been left unfinished in 3. 2 contains the full idea that has been discussed in 1.

CAT Pre-requisite

1. The basic idea of sentence structure.

2. Reading speed should be good and able to understand the idea of the passage.

3. Basics of Arranging the statements.

References to Study (Theory)para jumbles for CAT

1. Oxford Practice Grammar (sixth edition)

2. engvid.com (Web)

References to Practice CAT Para jumbles Questions

1. 2 IIM (Web and Youtube)

2. Bodhee Prep CAT Preparation (Web and YouTube)

3. CAT Previous years Papers and Sample Papers.

Do your practice and stay focused; Day 48 will be back tomorrow.

Thank you!

All the best!