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CAT Success : Expert Tips on Probability, Intro to Data Sufficiency, Synonyms & PYQs Discussion- Day 39

CAT Success : Expert Tips on Probability, Intro to Data Sufficiency, Synonyms & PYQs Discussion- Day 39

Edited By Irshad Anwar | Updated on Oct 11, 2023 10:17 AM IST | #CAT

Hello CAT 2023 candidates, On November 26, the CAT exam 2023 for MBA admissions in 2024–2026 will take place. In this CAT 2023 60-day preparation guide series of Careers360, we will discuss the strategies on probability questions for day 39 that can help you prepare well and crack the CAT entrance test 2023.

CAT Success : Expert Tips on Probability, Intro to Data Sufficiency, Synonyms & PYQs Discussion- Day 39
CAT Success : Expert Tips on Probability, Intro to Data Sufficiency, Synonyms & PYQs Discussion- Day 39

This article includes probability questions and other difficult aptitude questions on probability, Data sufficiency questions for CAT and Synonyms for CAT Exam. CAT Preparation 2023 in 60 days

Part-1: Quantitative Aptitude for CAT exam

Aspirants can also refer to the permutation combination and probability problems with solutions pdf.

CAT Exam Important Topic: Strategy to Prepare Probability Questions For CAT Exam, Permutations and Combinations

Important Concept/Formula Used in CAT Probability Practice Questions

  1. CAT Probability or Chance:

Probability is a quantitative measure of the chance of occurrence of a particular event.

PE=n(E)/n(S), n(E) = no of favourable events; n(S) = Sample Space.

  1. Random Experiment probability problems

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If all the possible outcomes of an experiment are known but the exact output cannot be predicted in advance.

Examples

(i) Tossing of a fair coin (Total Outcome 2)

(ii) Dice probability questions

Throwing an unbiased die (Total Outcome 6)

(iii) Cards game probability questions

Drawing a card from a pack of shuffled cards

A pack or deck of playing cards has 52 cards which are divided into four categories as given below

a. Spades (♠)

b. Clubs (♣)

c. Hearts (♥)

d. Diamonds (♦)

[13 Cards: 9 Number cards, 1 Ace, 1 Jack, 1 Queen and 1 King] in each type

  1. Sample Space: Sample Space is the set of all possible outcomes of an experiment. It is denoted by S.

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  1. Event: Any subset of a Sample Space is an event.

  1. Equally Likely Events: Events are said to be equally likely if there is no preference for a particular event over the other.

Examples

(i) When a coin is tossed, Head (H) or Tail is equally likely to occur.

  1. Mutually Exclusive Events: if the occurrence of one of the events excludes the occurrence of the other

Example

(i) Tossing of a coin: either Head or Tail.

(iii) Rolling of a die: Either odd or even.

  1. Independent Events: The occurrence or non-occurrence of one event does not influence the occurrence or non-occurrence of the other.

  1. Exhaustive Event is the total number of all possible outcomes of an experiment.

Examples

(i) When a coin is tossed, we get either Head or Tail. Hence there are 2 exhaustive events.

CAT Exam: Previous Year Cat Questions On Probability Permutations And Combinations

Q1. Difficult aptitude questions on probability

A coin of radius 3 cm is randomly dropped on a square floor full of square-shaped tiles of 10 cm each. What is the probability that the coin will land completely within a tile? In other words, the coin should not cross the edge of any tile.[XAT 2018]

  1. 0.91

  2. 0.5

  3. 0.49

  4. 0.36

  5. 0.16

Solution: (E)

The radius of the coin is 3 cm. Since the coin should not cross the edge, the centre of the coin should at least be 3 cm away from the edge of the tile.

If we left 3 cm from all the edges, then the centre can lie in a square of 4 x 4.

So, Probability = Area of square 4 x4/ Area of tile

= 16/100 =0.16.

Q2. A die is thrown three times and the sum of the three numbers is found to be 15. The probability that the first throw was a four is [IPMAT 2019]

  1. 1/6

  2. ¼

  3. 1/5

  4. 1/10

solution: [C]

We can get sum 15 if

Case 1: 6, 6, 3

Total outcome = 3!/2! = 3

Favourable outcome (getting 4 at first throw) = 0

Case 2: 6, 5, 4

Total outcomes = 3! = 6

Favourable outcome (getting 4 at first throw) = 2 (4, 5, 6 or 4, 6, 5)

Case 3: 5, 5, 5

Total outcome = 1

Favourable outcome (getting 4 at first throw) = 0

Probability = 2/10 = 1/5.

Tricks and Tips of CAT permutations and combinations, probability

  1. Learn Algebra of Events

(i) A ∪ B is the event that either A or B or Both occur. (i.e., at least one of A or B occurs)

(ii) A ∩ B is the event that both A and B occur

(iii) is the event that A does not occur

(iv) is the event that none of A and B occurs

  1. P(S) = 1

  1. 0 ≤ P (E) ≤ 1

  1. P(ϕ) = 0 (∵ Probability of occurrence of an impossible event = 0)

  1. Let x outcomes be favourable to E and y outcomes are not favourable to E, then

Odds in favour of E are x:y, i.e.,x/y and

Odds against E are y:x, i.e.y/x

PE=x/x+y

PE'=y/x+y

  1. Learn Conditional Probability.

  1. Binomial Distribution:”

P (r successes in n trials) =

1696998564626

  1. If n fair coins are tossed,

The Total number of outcomes in the sample space = 2n

The probability of getting exactly the r-number of heads when n coins are tossed =

1696998564415

  1. Practice sample papers and questions based on previous years CAT Questions.

  1. Solve Questions from easy to moderate levels and after that try hard questions.

CAT entrance exam: Prerequisite to probability questions

Know this before probability permutations and combinations

  1. Factorial

  2. Permutation and Combination

  3. Basics of Set Theory

CAT study material: References to Study (Theory)

For probability problems and concepts

  1. NCERT Class 11 Maths

  2. Mission CAT (YouTube, Link: https://www.youtube.com/watch?v=99zr_7OogIM)

CAT study material: References to Practice probability questions

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

  2. CAT Funda (CAT PYQs; YouTube:://www.youtube.com/watch?v=nTqInfzG5yw)

  3. CAT probability 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-1)” for CAT

CAT Exam: About Topic/ Formulas

  1. While the genre of Data Sufficiency is unique, the structure is not – all Data Sufficiency questions are structured the same, with three key elements:

  2. The question stem: may or may not contain important facts

  3. The statements: always two statements

  4. The answer choices: always the same.

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CAT Exam Preparation

Sample Question based on PYQs on Data Questions for CAT/ MBA Entrance Exam:

Q1. In a particular school, sixty students were athletes. Ten among them were also among the top academic performers. How many top academic performers were in the school?

I. Sixty per cent of the top academic performers were not athletes.

II. All the top academic performers were not necessarily athletes. [CAT 2007]

  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.

Solution: [A]

Statement I: 40% of top academic performers are athletes = 10.

Statement II: does not provide any relevant information.

So the answer is (1).

Tips and Tricks for CAT 2023

  1. Ask yourself the following questions (starting with the statement (1):

Is the information in the statement (1) alone enough to answer the question?

Is the information in a statement (2) alone enough to answer the question?

Can an answer be given if with the information from statements (1) and (2) both?

  1. A statement is sufficient when it guarantees exactly one (and only one) answer to the question.

  1. You do not have sufficient information if more than one answer is possible

  1. Do not solve the question after the moment you know the unique answer can be found thereafter.

  1. If the answer from one statement alone and by combining both statements can be found out then the answer will be from one statement alone.

  1. Stick to the basics.

CAT entrance exam: Prerequisite

  1. Blood

  2. Relation, Direction Sense, Ranking, Coding-Decoding, Inequality, Cubes, and various other basic topics of LR.

References to CAT Study (Theory)

  1. LRDI byNikhil K. Sinha

  2. (YouTube link: https://www.youtube.com/watch?v=Fw6oK3aWuXw)

CAT References to Study (Practice)

  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=blkzss4S0-0

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

Sample Questions:

Directions: Choose a similar word from the given options for highlighted phrase/word.

Q1. Public policy in regard to food in main economies around the world has not provided adequate incentive, and the response to emergencies like accidents is equally sad.

  1. Acceleration

  2. Surplus

  3. Baiting

  4. Encouragement

Ans: D

Explanation: The context of the sentence refers to Encouragement. Hence option D is correct.

Q2. We today can see a swing away from these stereotypes, or have they established a stranglehold on our perceptions.

  1. Asphyxiation

  2. Containment

  3. Prohibiting entry

  4. Overwhelming control

Ans: D

Explanation: Asphyxiation- it happens when someone is literally strangled. And here the context is different.

Containment: it cannot be established and hence can be eliminated.

It does not seem appropriate here.

Prohibiting entry is for physical context and not for abstract. Hence can be eliminated.

Overwhelming control is a perfect fit here. Hence option D is correct.

CAT Exam Important Topic: CAT preparation strategy on “ English Synonyms for CAT (Part-1)”.

  • One needs to be careful about the context.

  • Every word in the English language has a lot of different meanings.

  • To learn synonyms one can create word families

    • Beautiful- Gorgeous, Dazzling, Splendid, Magnificent

    • Important- necessary, vital, critical, Indispensable

  • One can also take reference from root words.

  • One can learn synonyms by logically associating a word with a sentence or a situation.

  • One needs to carefully observe the sentence's meaning as a whole.

  • Another method is to eliminate the other options.

  • Practise more and more exercises.

Prerequisite to CAT Exam Preparation

  1. Vocabulary

  2. Parts of Speech

References to Study (Theory)

  1. Wren and Martin

  2. Made Word Power Easy

  3. CATking.in (https://www.youtube.com/watch?v=qXw3syyd_Ak)

CAT preparation: 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. CATKing.in (YouTube; Link: https://www.youtube.com/watch?v=qXw3syyd_Ak&t=6s )

FAQS

Q1. How many questions come from probability in CAT?

A1. On average, in the quantitative aptitude section of the CAT exam, you might expect to see around 2 to 4 questions related to probability. This is a rough estimate based on historical data up until 2021.

We will be back with Day 40 tomorrow. Do practice and be focused.

Thank you! All the best!

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Questions related to CAT

Have a question related to CAT ?

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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Thank you

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.



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.

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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