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Mastering Mixtures and Intro to Selection: A Comprehensive CAT Exam Preparation Guide with RC & PYQs - Day 25

Mastering Mixtures and Intro to Selection: A Comprehensive CAT Exam Preparation Guide with RC & PYQs - Day 25

Edited By Irshad Anwar | Updated on Sep 14, 2023 11:01 AM IST | #CAT

Hello CAT 2023 aspirants,

CAT exam 2023 for MBA admission 2024-2026 will be held on November 26. In this CAT 2023 60 days preparation guide series of Careers360, we will discuss the strategies of day 25 that can help you prepare well and crack CAT entrance test 2023

This article includes alligations and mixtures CAT questions, CAT puzzle questions and CAT reading comprehension questions.

CAT Preparation 2023 in 60 days

Part-1: CAT 2023 QA Preparation Tips (Quantitative Aptitude)

CAT Exam Important Topic: Strategy to Prepare “Algebra (Math Mixture and Alligations)” for CAT-2023

  1. Quantity of dearer Quantity of Cheaper=Mean price m – C.P. of cheaper C.P of Dearer d – Mean price m

  2. If a Container contains ‘x’ units of pure liquid, and we replace the liquid with ‘y’ units of water:

Mastering Mixtures and  Intro to Selection: A Comprehensive CAT Exam Preparation Guide with RC & PYQs - Day 25
Mastering Mixtures and Intro to Selection: A Comprehensive CAT Exam Preparation Guide with RC & PYQs - Day 25

Then after ‘n’ successive replacements, the units of pure liquid left are

x(1- y/x)n

  1. The weighted average method can be useful as well.

  1. Getting an idea from CAT previous year questions helps in our preparation.

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Mixture and Alligation problems for CAT

Q1. If a certain weight of an alloy of silver and copper is mixed with 3 kg of pure silver, the resulting alloy will have 90% silver by weight. If the same weight of the initial alloy is mixed with 2 kg of another alloy which has 90% silver by weight, the resulting alloy will have 84% silver by weight. Then, the weight of the initial alloy, in kg, is [CAT exam 2021]

  1. 3

  2. 2.5

  3. 4

  4. 3.5

Solution: (A)

Case 1:

Let the weight of Silver = x; the weight of copper = y in the initial alloy.

According to first condition:

(x+3+y) x 90/100 = (3+ x)

On solving, 9y = 3 + x

According to second condition:

Quantity of silver = x + 90% of 2 Kg = 84 % of (x+ y+ 2)

On solving, 4x + 3 = 21y

Solve the two equations in two cases, we get x = 2.4 Kg and y = 0.6 Kg

Therefore, total weight of initial alloy = 3 Kg.

Q2. Two alcohol solutions, A and B, are mixed in the proportion 1:3 by volume. The volume of the mixture is then doubled by adding solution A such that the resulting mixture has 72% alcohol. If solution A has 60% alcohol, then the percentage of alcohol in solution B is [CAT exam 2020]

  1. 94%

  2. 92%

  3. 90%

  4. 89

Solution: (B)

Let Volume of A =100; Volume of B = 300; Volume of A +B = 400

On adding 400 litre volume of mixture becomes 800 litre (According to question)

Alcohol in new mixture = 72% of 800 = 576

Alcohol in A = 60% of 500 = 300

Alcohol in B = 576 – 300 = 276

Percent of alcohol in B = 276x 100/ 300 = 92%

CAT exam: Prerequisite:

  • Average

  • Weighted Average

  • Basics of Ratio

CAT Syllabus 2023: References to Study Theory

  1. How to Prepare for Quantitative Aptitude for CAT by Arun Sharma (7th Edition: Page No 177- 180)

  2. Mission CAT (YouTube Channel)

CAT Syllabus 2023: References to Study (Practice)

  1. How to Prepare for Quantitative Aptitude for CAT by Arun Sharma (7th Edition: Page No 181- 189)

  2. CAT Previous year Papers.

  3. CAT Sample Papers.

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

CAT 2023 Syllabus Topic: Strategy to prepare Problem Solving/Puzzle (Selection) for CAT

Such questions are solved by considering pre-conditions and few essential conditions for the selection of a group.

CAT Previous Year Questions on Selection based Puzzles:

Comprehension (CAT Puzzle Questions):

A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes. [CAT exam 2019]

Q1. What is the minimum possible number of different types of prizes?

Case Sensitivity: No

Answer Type: Equal

Possible Answer: 2

Explanation: If type a is 1 in number and Type b is 99 in number. Therefore, minimum 2 different types are possible.

Q2. What is the maximum possible number of different types of prizes?

Case Sensitivity: No

Answer Type: Equal

Possible Answer: 6

Explanation: If type a is 1 in number and type b is 2, type c is 4, type d is 8, type e is 16, type f is 32 in number. If we proceed further type g should be at-least 64 and the total count will be more than 100.

Therefore, a maximum of 6 different types are possible.

Q3. Which of the following is not possible?

  1. There are exactly 75 items of type e.

  2. There are exactly 45 items of type c.

  3. There are exactly 60 items of type d.

  4. There are exactly 30 items of type b.

Ans: (2)

Go through options:

Option 1:

If e is 75, we cannot have f (min 150 > 100)

So, the sum of a, b, c and d should be 25 where a is 1.

a = 1; b =2; c= 4; d = 18; e = 75, is a valid solution.

Option 2: If c is 45, we cannot have d (min 90 and sum will be > 100)

So, the sum of a and b should be 55 where a is 1. This is not possible at all.

In a similar way, we can check for option 3 and option 4 but it is not required now since we got our answer.

CAT Tips and Tricks on puzzles

  1. Find the criteria for selection

  2. Formation of groups on the basis of criteria

  3. A group is arranged in table

  4. Go through the options and eliminate the wrong option

  5. Go through CAT previous year papers to analyze the types of questions asked on selection

  6. Practice different types of problems

CAT exam: Prerequisite

  1. Ranking, Blood Relations, Directions

  2. Seating Arrangements

CAT Preparation: References to Study Theory

  1. LRDI for CAT by Nishit K. Sinha

  2. https://online.2iim.com › blogs › cat-preparation-strategy

  3. Cat preparation-iQuanta (YouTube Channel)

CAT Preparation: References to Study (Practice)

  1. Verbal and Non-Verbal Reasoning by R S Agrawal

  2. CAT Previous year Papers.

  3. CAT Sample Papers.

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

CAT Exam Important Topic: Reading Comprehension Part-2 (CAT reading comprehension questions) for CAT Exam

In this section, we will make strategies for Reading Comprehension with the help of CAT previous years questions based on CAT RC questions

CAT Previous Year Question on RC:

Comprehension:

Scientists recently discovered that Emperor Penguins—one of Antarctica’s most celebrated species—employ a particularly unusual technique for surviving the daily chill. As detailed in an article published today in the journal Biology Letters, the birds minimize heat loss by keeping the outer surface of their plumage below the temperature of the surrounding air. At the same time, the penguins’ thick plumage insulates their body and keeps it toasty. . . .

The researchers analyzed thermographic images . . . taken over roughly a month during June 2008. During that period, the average air temperature was 0.32 degrees Fahrenheit. At the same time, the majority of the plumage covering the penguins’ bodies was even colder: the surface of their warmest body part, their feet, was an average 1.76 degrees Fahrenheit, but the plumage on their heads, chests and backs were -1.84, -7.24- and -9.76-degrees Fahrenheit respectively. Overall, nearly the entire outer surface of the penguins’ bodies was below freezing at all times, except for their eyes and beaks. The scientists also used a computer simulation to determine how much heat was lost or gained from each part of the body—and discovered that by keeping their outer surface below air temperature, the birds might paradoxically be able to draw very slight amounts of heat from the air around them. The key to their trick is the difference between two different types of heat transfer: radiation and convection.

The penguins do lose internal body heat to the surrounding air through thermal radiation, just as our bodies do on a cold day. Because their bodies (but not surface plumage) are warmer than the surrounding air, heat gradually radiates outward over time, moving from a warmer material to a colder one. To maintain body temperature while losing heat, penguins, like all warm-blooded animals, rely on the metabolism of food. The penguins, though, have an additional strategy. Since their outer plumage is even colder than the air, the simulation showed that they might gain back a little of this heat through thermal convection—the transfer of heat via the movement of a fluid (in this case, the air). As the cold Antarctic air cycles around their bodies, slightly warmer air comes into contact with the plumage and donates minute amounts of heat back to the penguins, then cycles away at a slightly colder temperature.

Most of this heat, the researchers note, probably doesn’t make it all the way through the plumage and back to the penguins’ bodies, but it could make a slight difference. At the very least, the method by which a penguin’s plumage wicks heat from the bitterly cold air that surrounds it helps to cancel out some of the heat that’s radiating from its interior. And given the Emperors’ unusually demanding breeding cycle, every bit of warmth counts. . . . Since [penguins trek as far as 75 miles to the coast to breed and male penguins] don’t eat anything during [the incubation period of 64 days], conserving calories by giving up as little heat as possible is absolutely crucial.

Explanation:

Paragraph 1: About the discovery of Emperor penguins in Antarctica.

Paragraph 2: About the behavior of the body parts of penguins at very low temperatures.

Paragraph 3: About the heat transfer by penguins for their survival through radiation.

Since their outer plumage is even colder than the air, the simulation showed that they might gain back a little of this heat through thermal convection—the transfer of heat via the movement of a fluid (in this case, the air).

Paragraph 4: Given the Emperors’ unusually demanding breeding cycle, every bit of warmth counts, conserving calories by giving up as little heat as possible is absolutely critical.

On the basis of this analysis, we will solve the questions related to this passage. Strategies to solve an RC will be discussed in the next article.

CAT 2023: Prerequisite

  • Tenses and Parts of Speech

CAT Tricks/Strategies to understand the Comprehension

  1. Each paragraph indicates a different point.

  2. Summarize each paragraph in a word or phrase

  3. Skimming Text

  4. No facts or figure needs to be memorized (Just know where they are)

  5. Look for transition words to connect the ideas.

CAT preparation 2023: References to Study (Theory)

  1. How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)

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.
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CAT preparation 2023: References to Study (Practice)

  1. TCY Online

  2. CAT Previous year Papers.

  3. Bodhee Prep CAT Preparation (YouTube)

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We will be back with Day 26 of the CAT exam preparation guide 2023 for 60 days tomorrow. Do practice and be focused.

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Questions related to CAT

Have a question related to CAT ?

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.

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Thank you

Hope this information helps you.

Hello!

The educational qualification required for CAT exam is bachelor's degree or its equivalent from a recognized university with minimum of 50% for the open category and 45% for the SC/ST/PwD category. Since you have secured more than the required percentage in your bachelor's degree, you are eligible for CAT exam.

For more information, please visit the website by clicking on the link given below:

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I hope you will find this information helpful. Best wishes ahead!

Hello Aspirant,

Yes, you can sit for the CAT exam with a CGPA of 8.5. However when you do crack the CAT exam and have to sit for the interview round or the Group discussion round, you will be asked the question about 4 years of graduation, in which case, carry your hospital records and medical certificates to prove to them that you actually had some health issues during your graduation. This shouldn't be a problem because you had a genuine reason for the one-year gap.

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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