Age problem questions, Distribution puzzle sets questions and introduction to what is RC and its PYQs- Day 23

Part-1: CAT 2024 QA Preparation Tips (Quantitative Aptitude)

Here we will discuss problems on ages, problems on ages questions for CAT, problems on ages solutions, problems on ages tricks, problems on ages with solutions free pdf, easy way to solve problems on ages etc.

Topic: Algebra (Problems on Ages)

Problems on ages consist of the following concepts in the CAT entrance exam.

• The present ages of two persons are to be calculated. A relation between future age and past age is given.

• A relation between present ages is given and future or past ages are asked

• Questions on the Sum of the Ages are being asked.

CAT Syllabus 2024: Importance of Ages

• Age is an important part of our lives. We may encounter situations when we need to calculate the ages. Learning this concept might help us. Students can also take online practice tests for quantitative aptitude.

• As we can see, in the CAT Exam the questions from ages are asked on a regular basis. CAT Previous Year Questions on Ages or can refer to problems on ages with solutions pdf

Q1. Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick’s age is 1 year less than the average age of all three, then Harry’s present age, in years, is (in numerical value) ___________. [CAT 2020, TITA]

Solution:

Let the age of Tom = x

Age of Dick = 3x

Age of Harry = 6x

According to the question:

3x = (x + 3x + 6x)/3 – 1

⇒ (3x + 1) 3 = 10x

⇒ 9x + 3 = 10x

⇒ x = 3

Therefore, Present age of Harry = 6 x 3 = 18 years

Q2. In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years? [CAT 2018]

1. 27

2. 28

3. 26

4. 25

Solution: (B)

Let the average age of people of age 51 years or above = x

and the average age of people less than 51 years = y and there are N people whose age is less than 51.

So, an average of 30 +N persons = (30x + Ny)/ (30 + N) = 38

y is the maximum when x is the minimum

The minimum value of x should be 51 since x is the average age of people age 51 years or above.

So, 1530 + Ny = (30 + N) 38

⇒ 1530 + Ny = 1140 + 38N

⇒ 390 = N (38 -y)

38 – y is minimum if N is maximum. Then y is also maximum.

Maximum value of N is 39. Therefore, maximum value of y is calculated by

390 = 39 (38 – y)

⇒ 10 = 38 -y

⇒ y = 28

Hence, the correct answer is 28 years.

Q.3. The ratio of A's age to B's age is 4: 3. A will be 26 years old after 6 years. The age of B now is:

1. 19 ½ years

2. 12 years

3. 21 years

4. 15 years

Answer: (D)

Let the present ages of A and B be 4x and 3x, respectively.

According to the question,

4x + 6 = 26

⇒ 4x = 20

⇒ x = 5

So, the present age of B = 3 × 5 = 15 years

Hence, the correct answer is 15 years.

Q.4. The ratio of the present ages of R and S is 11: 17. 11 years ago, the ratio of their ages was 11: 20. What is R's present age (in years)?

1. 51

2. 33

3. 22

4. 40

Answer: (B)

Let the present age of R be 11x, and S be 17x.

According to the given condition,

(11x-11)(17x-11) = 11/20

⇒ 220x - 220 = 187x-121

⇒ 33x = 99

⇒ x = 3

Thus, the present age of R = 11 × 3 = 33 years

Hence, the correct answer is 33 years.

Prerequisite:

• Average

• Linear Equations

• Ratio

Tips to solve CAT questions on Ages for CAT:

• If the age of a person is x years, then the age of that person after n years is (x+ n) years.

• If a person's age is x years, then that person's age before n years is (x- n) years.

• If the age of a person is x years, then n times the present age of that person is nx years.

Some tricks and approaches

• Assume the age of that person in terms of whose age, other relations are given.

• Assume the present ages of the person and draw the other relations in terms of the present ages.

• Transform the given statements into useful mathematical equations.

• Solve the equations to get the values of the variables.

References to Study (Theory):

• How to prepare quantitative aptitude by Arun Sharma (7th edition)

• MBAP CAT EBook

• Mission CAT (You-Tube)

References to Study (Practice):

• R S Agrawal for quantitative aptitude

• MBAP CAT EBook (Practice Questions)

• Previous Years Question Papers

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

Topic: Problem Solving/Puzzle (Distribution Part-2)

In this section, we will discuss different forms of puzzles based on distribution. We will make our strategies by solving some puzzles. Also, we will discuss the distribution puzzle, distribution puzzle tricks, distribution puzzle questions and solutions, distribution puzzle reasoning etc.

Distribution Puzzle Set-1

Directions for Questions 1 to 3: These questions are based on the following information.

Eight boys A, B, C, D, F, G and H are planning to go for a picnic. Each of them brought a different dish from P, Q, R, S, T, U, V, and W to the picnic. The following information is known about them.

1. Either B or E brought W.

2. Neither A nor H brought S and U.

3. D brought either T or U.

4. Either C or D brought P.

5. G and A brought either U or V.

6. F brought either U or Q.

1. Which of the following dishes is brought by A?

1. T

2. U

3. W

4. V

2. Which of the following can be the correct combination of the boy and the dish he bought?

1. C-T

2. B-S

3. C-Q

4. F-S

3. Who brought the dish W?

1. A

2. B

3. D

4. Cannot be determined

Solution:

Trick: Make a precision matrix as shown below:

1. Either B or E brought W: Mark the possibility of W being brought by B or E.

2. Neither A nor H brought S and U.

3. D brought either T or U.

4. 
   Either C or D brought P: Since D could not bring P (from the table). So, C must bring P.

5. G and A brought either U or V: Since A could not bring U (from the table). So, A must bring V. G must bring U. Therefore, D must bring T.

6. 
   F brought either U or Q: U is brought by G. So, F must bring Q and hence from the table H must bring R.

Answers:

1. 4

2. 2

3. 4

Distribution Puzzle Set-2 (Based on Ranking)

Five persons- Pramod, Qarim, Remo, Sam and Teena- are ranked according to their height and weight. In each case, one with the highest value is ranked first, the second highest is ranked second and so on. Further.

A. Pramod and Qarim got the first and second ranks in one parameter and the fourth and fifth ranks in the other.

B. Teena is ranked below Sam and Remo in one parameter while above in another parameter.

C. Only one person is heavier than Pramod.

Q1. Who is the tallest among the given person if Remo is at the 3rd in weight?

1. Pramod

2. Qarim

3. Sam

4. Teena

5. Remo

Q2. How many people are shorter than Sam if Sam is not the tallest?

1. 1

2. 2

3. 3

4. Either A or B

5. Either B or C

Q3. Who is the lightest?

1. Teena

2. Shyam

3. Qazi

4. Prem

5. Cannot be determined.

Q4. The exact ranks of how many persons can be determined in both the parameters with the available information.

1. 0

2. 1

3. 2

4. 3

5. 4

Solution:

Trick: Make a Separate rank table for height and weight. Consider all the possibilities.

Pramod and Qarim got the first and second ranks in one parameter and the fourth and fifth ranks in the other.

Case: 1

Case: 2

According to the third statement, only 1 person is heavier than Pramod. So, Case-1 cannot be true.

Teena is ranked below Sam and Remo in one parameter while above in another parameter. We cannot fix the positions of Teena, Sam or Remo here.

Ans 1: (D), Teena

Since Remo is third in the weight category i.e. Teena is below Sam and Remo. Therefore, Teena must be above Remo and Sam.

Teena will rank 1st in height.

Ans 2: (E), Either B or C.

If Sam is not at the top. He should be either at 2 or 3. Therefore, the Number of persons shorter than him is either 2 or 3.

Ans 3: (E), Data is insufficient

Ans 4: (E) Clearly from the table.

References to Study (Theory):

• LRDI for CAT and GMAT by Nishit K Sinha. (Advance)

• ELITES GRID for CAT entrance test preparation (YouTube Channel)

References to Study (Practice):

• Verbal and Non-Verbal Reasoning by R S Aggarwal. (Basic)

• Previous Years CAT Question Papers

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

Here we will discuss reading comprehension, reading comprehension passages with questions and answers, what is reading comprehension, reading comprehension worksheets etc.

Topic: Reading Comprehension Part-1

To prepare Reading Comprehension, we have divided this topic into 5 parts to understand the strategies in the proper sense.

In each part, we will discuss 1 RC from the actual CAT paper and will make a proper strategy.

What is Reading Comprehension and Why is it important?

Reading Comprehension is a long passage and its main purpose is to get meaning from written text.

Comprehension adds meaning to what is being read. As you read the passage, fetch the information and get a meaning from it.

It helps to improve the reading, writing and communication skills of a person. Students can also look up reading comprehension passages for CAT with answers in pdf.

CAT Exam Practice Questions on Reading Comprehension

CAT reading comprehension pdf

The passage below is accompanied by a set of questions. Choose the best answer to each question.

The word ‘anarchy’ comes from the Greek anarkhia, meaning contrary to authority or without a ruler, and was used in a derogatory sense until 1840, when it was adopted by Pierre-Joseph Proudhon to describe his political and social ideology. Proudhon argued that an organization without government was both possible and desirable. In the evolution of political ideas, anarchism can be seen as an ultimate projection of both liberalism and socialism, and the differing strands of anarchist thought can be related to their emphasis on one or the other.

Historically, anarchism arose not only as an explanation of the gulf between the rich and the poor in any community, and of the reason why the poor have been obliged to fight for their share of a common inheritance, but as a radical answer to the question ‘What went wrong?’ that followed the ultimate outcome of the French Revolution. It had ended not only with a reign of terror and the emergence of a newly rich ruling caste but with a new adored emperor, Napoleon Bonaparte, strutting through his conquered territories.

The anarchists and their precursors were unique on the political Left in affirming that workers and peasants, grasping the chance that arose to bring an end to centuries of exploitation and tyranny, were inevitably betrayed by the new class of politicians, whose first priority was to re-establish a centralized state power. After every revolutionary uprising, usually won at a heavy cost for ordinary populations, the new rulers had no hesitation in applying violence and terror, secret police, and a professional army to maintain their control.

For anarchists, the state itself is the enemy, and they have applied the same interpretation to the outcome of every revolution of the 19th and 20th centuries. This is not merely because every state keeps a watchful and sometimes punitive eye on its dissidents, but because every state protects the privileges of the powerful.

The mainstream of anarchist propaganda for more than a century has been anarchist communism, which argues that property in land, natural resources, and the means of production should be held in mutual control by local communities, federating for innumerable joint purposes with other communes. It differs from state socialism in opposing the concept of any central authority. Some anarchists prefer to distinguish between anarchist-communism and collectivist anarchism in order to stress the obviously desirable freedom of an individual or family to possess the resources needed for living, while not implying the right to own the resources needed by others.

There are, unsurprisingly, several traditions of individualist anarchism, one of them deriving from the ‘conscious egoism’ of the German writer Max Stirner (1806–56), and another from a remarkable series of 19th-century American figures who argued that in protecting our own autonomy and associating with others for common advantages, we are promoting the good of all. These thinkers differed from free-market liberals in their absolute mistrust of American capitalism, and in their emphasis on mutualism.

[CAT 2020 Question Paper Slot 1]

Q1. Which one of the following best expresses the similarity between American individualist anarchists and free-market liberals as well as the difference between the former and the latter?

1. Both reject the regulatory power of the state; but the former favour a people’s state, while the latter favours state intervention in markets.

2. Both prioritize individual autonomy; but the former also emphasise mutual dependence, while the latter do not do so.

3. Both are sophisticated arguments for capitalism; but the former argue for a morally upright capitalism, while the latter argue that the market is the only morality.

4. Both are founded on the moral principles of altruism; but the latter conceive of the market as a force too mystical for the former to comprehend.

Ans: B

We can find the answer from last paragraph where it was discussed. While in the other options the things given was not discussed in the passage.

Q2. The author makes all of the following arguments in the passage, EXCEPT:

1. Individualist anarchism is actually constituted of many streams, all of which focus on the autonomy of the individual.

2. The popular perception of anarchism as espousing lawlessness and violence comes from a mainstream mistrust of collectivism.

3. For anarchists, the state is the enemy because all states apply violence and terror to maintain their control.

4. The failure of the French Revolution was because of its betrayal by the new class of politicians who emerged from it.

Ans: B

Q3. According to the passage, what is the one idea that is common to all forms of anarchism?

1. There is no idea common to all forms of anarchism; that is why it is anarchic.

2. They all focus on the primacy of the power of the individual.

3. They all derive from the work of Pierre-Joseph Proudhon.

4. They are all opposed to the centralization of power in the state.

Ans: D

The passage clearly states that “for anarchists the state itself is the enemy and they have applied the same interpretation to the outcome of every revolution of the 19th and 20th centuries.”.

Q4. The author believes that the new ruling class of politicians betrayed the principles of the French Revolution, but does not specify in what way. In the context of the passage, which statement below is the likeliest explanation of that betrayal?

1. The new ruling class rode to power on the strength of the workers’ revolutionary anger, but then turned to oppress that very class.

2. The anarchists did not want a new ruling class, but were not politically strong enough to stop them.

3. The new ruling class was constituted mainly of anarchists who were against the destructive impact of the Revolution on the market.

4. The new ruling class struck a deal with the old ruling class to share power between them.

Ans: A

Discussed in the third paragraph.

Q5. Of the following sets of concepts, identify the set that is conceptually closest to the concerns of the passage.

1. Anarchism, Betrayal, Power, State.

2. Revolution, State, Strike, Egoism.

3. Revolution, State, Protection, Liberals.

4. Anarchism, State, Individual, Freedom.

Ans: D

We should look for anarchism first which is the main idea of the passage. So, option A and D can be the answers. Passage also talks about the ‘freedom’ and individual’.

So, D is the best choice.

Prerequisite:

• Parts of Speech

• Tenses

• Synonyms and Antonyms

Tips and Tricks to Solve Reading Comprehension:

1. Good reading habit will help you to understand RC well.

2. Read the passage in the CAT question paper thoroughly to get an idea about the flow of the passage. Understand the tempo of passage.

3. Understand the idea of the RC what the writer want to say.

4. Write down the important parts of RCs.

5. Learn New words every day.

6. Learn synonyms and antonyms.

7. Read Newspapers.

8. Practice RC every day.

9. Attempt CAT reading comprehension Mock tests.

References to Study (Theory)

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

• CAT Edurav (YouTube Channel)

References to Study (Practice)

• Mastering the verbal ability for CAT by Ajay Singh

• https://iim-cat-questions-answers.2iim.com/

• Practice CAT Sample Papers and CAT Previous Year Question Papers

Free PDFs for CAT 2024 preparation

• CAT Important Topics & Must read books

• How 99 Percentilers Prepared for CAT