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

Part 1: Quantitative Aptitude For CAT 2024

Topic: Strategy to Prepare “Algebra (Math Mixture and Alligations)” for CAT-2024

When we combine two or more substances to form a single homogeneous entity, it is called a mixture. Whereas alligation is a rule that helps in finding the mean value of a mixture when the quantities and prices of the ingredients are known.

Mixture and Alligation involves combining two or more quantities with different prices, concentrations, or values to achieve a desired mixture.

1. The rule of alligation is used to find the ratio in which two or more ingredients at different prices (or concentrations) must be mixed to produce a mixture at a given price (or concentration).

2. If a Container contains ‘x’ units of pure liquid, and we replace the liquid with ‘y’ units of water, then after ‘n’ successive replacements, the units of pure liquid left are x(1- y/x)n

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

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

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 the first condition:

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

On solving, 9y = 3 + x

According to the 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, the total weight of the 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 the mixture becomes 800 litres (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 2024: 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 2024: 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 2024 Preparation Tips: CAT DILR (Logical Reasoning and Data Interpretation)

CAT 2024 Syllabus Topic: Strategy to prepare Problem-Solving/Puzzle (Selection) for CAT

Such questions are solved by considering pre-conditions and a 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, a minimum of 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, and 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

• Find the criteria for selection

• Formation of groups on the basis of criteria

• A group is arranged in a table

• Go through the options and eliminate the wrong option

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

• Practice different types of problems

Prerequisite

1. Ranking, Classification, Direction

2. Seating Arrangement

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)

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 2024: 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 of 1.76 degrees Fahrenheit, but the plumage on their heads, chests and backs was -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 the 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 behaviour 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.

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 figures need to be memorized (Just know where they are)

5. Look for transition words to connect the ideas.

References to Study (Theory)

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

References to Study (Practice)

1. TCY Online

2. CAT Previous year Papers.

3. Bodhee Prep CAT Preparation (YouTube)

We will be back with Day 26 of the CAT exam preparation guide 2024 for 60 days tomorrow. Do practice and be focused.

Free PDFs for CAT 2024 preparation

• Know all about CAT

• CAT Syllabus 2022 Verbal Ability and Reading Comprehension