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Miscellaneous topics for CAT exam for DILR, Partnership Ratios, Practice questions for RC & PYQs - Day 27

Miscellaneous topics for CAT exam for DILR, Partnership Ratios, Practice questions for RC & PYQs - Day 27

Edited By Irshad Anwar | Updated on Oct 09, 2023 11:59 AM IST | #CAT

Hello aspiring CAT 2023 candidates, On November 26, the CAT exam 2023 for MBA admissions 2024–2026 will take place. In this CAT 2023 60-day preparation guide series of Careers360, we will discuss the strategies for day 27 that can help you prepare well and crack the CAT entrance test 2023.

This article includes the following topics: ratio questions and answers, partnership CAT questions with solutions, Miscellaneous CAT questions and RCs strategies and PYQs of VARC.

Partnership questions with solutions is a very important topic and students should go through this topic thoroughly. CAT Preparation 2023 in 60-day

CAT Exam Important Topic: Algebra (Ratio and Partnership) and partnership questions with solutions

CAT Syllabus 2023: Important Concept/Formula Used in Ratio and Partnerships Problems

Problems on ‘to find profit Sharing

  • PA: PB: PC = IA x TA: IB x TB: IC x TC
  • PA, PB, PC are shared in profits of A, B and C respectively.
  • IA, IB, IC are investments made by A, B and C respectively.
  • TA, TB, TC are the time of investment of A, B and C respectively

CAT previous years Questions on Ratio and Partnership

Q1. Peter started a business with 20, 000. John joined him 4 months later with 30, 000. After 2 more months, Peter withdrew 5,000 of his capital and 2 more months later, John brought in 20, 000 more. At the end of the year what should be the ratio in which they should share the profits? [CAT exam]

Partnership problems with solutions:

Peter invested Rs 20000 and after 6 months (4 +2), he withdrew Rs 5000 and hence his investment remains Rs 15000.

John joins after 4 months i.e. for a total of 8 months with Rs 30, 000 for the initial 4 months and then invests Rs 20000 for the next 4 months.

Therefore, share of profit of Peter and John will be in the ratio

P: J = (20000 x 6 + 15000 x 6): (30000 x 4 + 50000 x 4)

P: J = 21: 32

Q2. Partnership questions with solutions:

A profit of Rs 144000 has to be divided among three partners Akram, Bipin and Chintan if their investments are in the ratio 3:2:7. How much Rs. Chintan get [CAT exam]

  1. 84000

Miscellaneous topics for CAT exam for DILR, Partnership Ratios, Practice questions for RC & PYQs - Day 27
Miscellaneous topics for CAT exam for DILR, Partnership Ratios, Practice questions for RC & PYQs - Day 27
  1. 24000

  1. 36000

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  1. 42000

Solution: [a]

Ratio of profit = ratio of investment = 3:2 :7 (Time of investment is equal)

Share of Chintan = 7 (144000)/12 = 84000

CAT entrance exam: Pre-requisite

  • Ratios
  • Percentage
  • Average

CAT 2023 QA Preparation Tips (Quantitative Aptitude)

In the partnership math question, If the time of investment is the same for all the partners, then the profit ratio is equal to the ratio of their respective investments.

For Passive or sleeping partners, the share is only for their investment.

Share of Active (Working) partners is for both i.e. investment as well as work.

CAT study material: References to Study Theory

  • Quantitative Aptitude by R S Agrawal
  • Mission CAT (YouTube: https://www.youtube.com/watch?v=QPAf9lxnPGo)

CAT study material: References to Study (Practice)

Part-2: CAT 2023 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation) (h2)

CAT preparation: Concepts Used

  1. Classification based Puzzles
  2. Comparison based Puzzles
CAT 2024 Syllabus PDF (Free Download)
This CAT exam 2024 syllabus pdf has detailed section-wise and subject-wise syllabus and important topics of CAT.
Download Now

CAT 2023 Syllabus Topic: Strategy to prepare Problem Solving/Puzzle (Miscellaneous CAT Questions) Part 1

CAT previous years questions

Comprehension:

Fuel contamination levels at each of 20 petrol pumps P1, P2, …, P20 were recorded as either high, medium, or low.

Contamination levels at three pumps among P1 – P5 were recorded as high.

P6 was the only pump among P1 – P10 where the contamination level was recorded as low.

P7 and P8 were the only two consecutively numbered pumps where the same levels of contamination were recorded.

High contamination levels were not recorded at any of the pumps P16 – P20.

The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded. [CAT exam 2018]

Q1. Which of the following MUST be true?

  1. The contamination level at P10 was recorded as high.
  2. The contamination level at P13 was recorded as low.
  3. The contamination level at P20 was recorded as a medium.
  4. The contamination level at P12 was recorded as high.
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Q2. What best can be said about the number of pumps at which the contamination levels were recorded as a medium?

  1. At most 9
  2. Exactly 8
  3. More than 4
  4. At least 8

Q3. If the contamination level at P11 was recorded as low, then which of the following MUST be true?

  1. The contamination level at P12 was recorded as high.
  2. The contamination level at P15 was recorded as a medium.
  3. The contamination level at P18 was recorded as low.
  4. The contamination level at P14 was recorded as a medium.

Q4. If the contamination level at P15 was recorded as a medium, then which of the following MUST be FALSE?

  1. Contamination levels at P11 and P16 were recorded as the same.
  2. Contamination level at P14 was recorded to be higher than that at P15.
  3. Contamination levels at P13 and P17 were recorded as the same.
  4. Contamination levels at P10 and P14 were recorded as the same.

Solution:

Tip 1: Write concrete information first

P6 was the only pump among P1 – P10 with a low contamination level.

Only P7 and P8 were the only two consecutively numbered pumps with the same levels of contamination.

Contamination levels at three pumps among P1– P5 were recorded as high i.e. P1, P3 and P5 have high Contamination levels whereas P2 and P4` will be with medium Contamination levels.

Tip 2: Draw all the possibilities

We get two possible cases for P1 to P10.

1696831669571

Tip 3: Eliminating the wrong possibilities

In Case I, Maximum number of H can be 8 (P1, P3, P5, P7, P8, P10, P12, P14) since high contamination cannot be in P16- P20

It is given that

H = 2L

8 = 2L

⇒ L = 4, therefore M must be 20- 8- 4 = 8

Thus H + L = 3L must be multiple of 3.

The possible arrangement will be

1696831669222

Also, 8 H can be at P1, P3, P5, P7, P88 P10, P13, P15, then

The possible arrangement will be

1696831669411

In case II, H can be 6 and L will be 3;

Number of pipes with medium contamination level = 11 which is not possible.

So, Case I is true with two possibilities.

Answers:

Q1. (1)

Q2. (2)

Q3. (4)

Q4. (1)

CAT entrance exam: Pre-requisite

  • Ranking
  • Selection and Arrangement-based Puzzles

CAT Tips and Tricks

  • Write Concrete information first
  • Draw all possibilities by assigning the right value
  • Eliminate the wrong possibilities

CAT Syllabus 2023: References to Study (Theory)

  • Verbal and Non-Verbal Reasoning by R S Agrawal
  • ADDA 247 (YouTube: https://www.youtube.com/watch?v=ONuoAGsIjDE)

CAT Syllabus 2023: References to Study (Practice)

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

CAT Exam Important Topic: Reading Comprehension Part-4 (Solving through CAT Previous Years Questions)

CAT Previous Years Question on RC:

Comprehension:

Read the passage and answer the question based on it.

Creativity is at once our most precious resource and our most inexhaustible one. As anyone who has ever spent any time with children knows, every single human being is born creative; every human being is innately endowed with the ability to combine

and recombine data, perceptions, materials and ideas, and devise new ways of thinking and doing. What fosters creativity? More than anything else: the presence of other creative people. The big myth is that creativity is the province of great individual

geniuses. In fact, creativity is a social process. Our biggest creative breakthroughs come when people learn from, compete with, and collaborate with other people.

Cities are the true fonts of creativity... With their diverse populations, dense social networks, and public spaces where people can meet spontaneously and serendipitously, they spark and catalyze new ideas. With their infrastructure for finance, organization and trade, they allow those ideas to be swiftly actualized.

As for what staunches creativity, that's easy, if ironic. It's the very institutions that we build to manage, exploit and perpetuate the fruits of creativity — our big bureaucracies, and sad to say, too many of our schools. Creativity is disruptive; schools and organizations are regimented, standardized and stultifying.

The education expert Sir Ken Robinson points to a 1968 study reporting on a group of 1,600 children who were tested overtime for their ability to think in out-of-the-box ways. When the children were between 3 and 5 years old, 98 percent achieved

positive scores. When they were 8 to 10, only 32 percent passed the same test, and only 10 percent at 13 to 15. When 280,00025-year-olds took the test, just 2 percent passed. By the time we are adults, our creativity has been wrung out of us.

I once asked the great urbanist, Jane Jacobs, what makes some places more creative than others. She said, essentially, that the question was an easy one. All cities, she said, were filled with creative people; that's our default state as people. But some cities had more than their shares of leaders, people and institutions that blocked out that creativity. She called them "squelchers."

Creativity (or the lack of it) follows the same general contours of the great socio-economic divide - our rising inequality – that plagues us. According to my own estimates, roughly a third of us across the United States, and perhaps as much as half of us in our most creative cities - are able to do work which engages our creative faculties to some extent, whether as artists, musicians, writers, techies, innovators, entrepreneurs, doctors, lawyers, journalists or educators - those of us who work with our minds. That leaves a group that I term "the other 66 percent," who toil in low-wage rote and rotten jobs — if they have jobs at all — in which their creativity is subjugated, ignored or wasted.

Creativity itself is not in danger. Its flourishing is all around us - in science and technology, arts and culture, in our rapidly revitalizing cities. But we still have a long way to go if we want to build a truly creative society that supports and rewards the creativity of each and every one of us.

Q1. In the author's view, cities promote human creativity for all the following reasons EXCEPT that they

  1. contain spaces that enable people to meet and share new ideas.
  2. expose people to different and novel ideas, because they are home to varied groups of people.
  3. provide the financial and institutional networks that enable ideas to become reality.
  4. provide access to cultural activities that promote new and creative ways of thinking.

Ans: D

CAT Tips and Tricks: Search each statement individually in the passage.

(A), (B) and (C) are mentioned in the second paragraph

A, refers to new ideas

B, refers to a diverse population

C, refers to the infrastructure of finance

Q2. The author uses 'ironic' in the third paragraph to point out that

  1. people need social contact rather than isolation to nurture their creativity

  1. institutions created to promote creativity eventually stifle it

  1. the larger the creative population in a city, the more likely it is to be stifled

  1. large bureaucracies and institutions are the inevitable outcome of successful cities

Ans: B

CAT Tips and Tricks: See only third paragraph (Search keywords) or eliminate the irrelevant options

Option A: did not discuss in the third paragraph

Option C: Contrary statement

Option D: Irrelevant

Option B: Explicitly mentioned in the paragraph

Q3. The central idea of this passage is that

  1. social interaction is necessary to nurture creativity

  1. creativity and ideas are gradually declining in all societies

  1. the creativity divide is widening in societies in line with socio-economic trends

  1. more people should work in jobs that engage their creative faculties

Ans: A

CAT Tips and Tricks: Go through options and search in the passage

Neither B nor C mentioned in the passage whereas D is a recommendation of the passage.

Q4. Jane Jacobs believed that cities that are more creative

  1. have to struggle to retain their creativity

  1. have to 'squelch' unproductive people and promote creative ones

  1. have leaders and institutions that do not block creativity

  1. typically, do not start off as creative hubs

Ans: C

CAT Tips and Tricks: Go through options and search in the passage

Key Words: Jane, Jacob, Creative

Q5. The 1968 study is used here to show that

  1. as they get older, children usually learn to be more creative

  1. schooling today does not encourage creative thinking in children

  1. the more children learn, the less creative they become

  1. technology today prevents children from being creative.

Ans: B

CAT Tips and Tricks: Go through options and search in the passage

Key Words: 1968 study

CAT 2023: Pre-requisite

  • Good reading skills (speed)
  • Understanding the comprehension

CAT 2023: References to Study (Theory)

  • How to Prepare for Verbal Ability and Reading Comprehension for CAT’- by Arun Sharma & Meenakshi Upadhyay
  • https://unstop.com/blog/reading-comprehension-for-cat

CAT 2023: References to Study (Practice)

  • Verbal Ability and Reading Comprehension for the CAT’ – by Nishit K Sinha
  • CAT Previous Years Question Papers RCs

Some Important FAQs:

  1. What is Miscellaneous in CAT?
    • Miscellaneous questions are designed to assess a candidate's analytical prowess and grasp of key concepts. These types of questions often integrate two or more topics through clear analogies or solutions. They are intended to challenge individuals who rely on deep understanding rather than rote memorization. Tackling such intricate questions demands concentration, logical thinking, and a firm grasp of the subject matter.
  2. What Topics come under miscellaneous in CAT exam?
    • Miscellaneous CAT questions are a common occurrence in the Arithmetic Section of the CAT Exam. Among the pivotal topics covered in the exam, a subset is dedicated to miscellaneous questions. Solving these queries demands unconventional thinking and adherence to specific guidelines for accurate answers. The CAT exam evaluates various sections, encompassing Logical Reasoning, Data Interpretation, Quantitative Aptitude, and Verbal Ability, all of which include a selection of miscellaneous questions. These intricate questions require careful consideration and precision in your responses.

  3. What is the formula for partnership in CAT?
    • There are mainly two types of partnership i.e. simple and compound partnerships. The formulas of both of them are given below:

Rule 1: Simple Partnership Formula

If P and Q contributed Rs. a and b respectively for one year in a business, their profit (or loss) at that time will be-

=> P’s benefit (or misfortune) : Q’s profit(or misfortune) = a : b

Rule 2: Compound Partnership Formula

=> P1 : P2 = C1 × T1 : C2 × T2

Here,

P1 = Partner 1’s Profit.

C1 = Partner 1’s Capital.

T1 = Time period for which Partner 1 contributed his capital.

P2 = Partner 2’s Profit.

C2 = Partner 2’s Capital.

T2 = Time period for which Partner 2 contributed his capital.

We will be back with Day 28 tomorrow of the CAT exam preparation guide 2023 for 60 days. 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,
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.

Hello aspirant,

Every year, IIMs conduct the Common Admission Test (CAT), a national MBA entrance exam, in rotation. For admission to over 1,200 institutions and premier B-schools in India, as well as PGDM, Executive MBA, PhD, and FPM programmes, the IIM CAT exam is regarded as one of the most difficult MBA entrance exams to pass. One of the best MBA schools in India, IIMs offers PGDM and MBA programmes for students who pass the CAT exam with scores in the 82nd to 99th percentiles.

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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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