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This article covers quantitative aptitude for CAT, DIRL and VARC sentence correction sessions. Students are recommended to go forward with this and practise a little more. Many aspirants also refer to books such as Quantitative books for CAT to learn and practise more regarding the subject. These Average mixture and allegation CAT questions are good for the aspirants to understand the usage of Averages. Aspirants can also refer to average questions for CAT pdf.
Free Study Material: VARC | DILR | Quant | Chapter-wise Practice MCQs
CAT 2024: 60-day study material | CAT'23 Official Question with Solutions (Slot 1, 2, 3)
Test: 20 Free Mock Test | 10 Year PYQs | Most Scoring Concepts
The Average or mean is calculated by the sum of observations divided by the number of observations.
Simple Average/ Simple Mean (X) = (x1 + x2 + x3 +… + xn)/n; x1, x2, x3, ………, xn are n number of observations.
Weighted Average/ Weighted Mean:
i.e, x1, x2, x3, ………, xn are n observations. w1, w2, ……., wn are their respective weights.
Average questions for CAT exam:
Difference between the persons added and who left = change in average × number of persons. When a person joins the group of n persons; if the average increases then the Age of the new person = Old average + (n + 1) × difference between averages
If the average decreases then:
Age of the new person = Old average - (n + 1) × difference between averages
The average of an AP of odd terms is always its middle term.
In the general case, the Average of an AP is the Average of its first and last term.
The average of an AP of even terms is the average of its two middle terms.
When a person replaces another person then the average age of the group will be increased or decreased.
Q1. Ramesh and Gautam are among 22 students who wrote an examination. Ramesh scores 82.5. The average score of the 21 students other than Gautam is 62. The average score of all 22 students is one more than the average score of the 21 students other than Ramesh. The score of Gautam is:
[CAT exam 2019, TITA]
Solution:
Let the score of Gautam be x.
According to the given condition,
Total marks of 22 students = 21 × 62 + x
∴ Average score of 22 students = (21 × 62 + x)/22
According to the second condition,
The average score of all 22 students is one more than the average score of the 21 students other than Ramesh,
So, (21 × 62 + x)/22 = (21 × 62 + x – 82.5)/21 + 1
⇒ (21 × 62 + x)/22 -1 = (21 × 62 + x – 82.5)/21
⇒ (21 × 62 + x - 22)/22 = (21 × 62 + x – 82.5)/21
⇒ (1280 + x) / 22 = (1219.5 + x) / 21
⇒ x = 51
Hence, the correct answer is 51.
Q2. Last year, the average age of the class of 25 students was 13 years. If the age of the class teacher was included, the new average of the class became 14 years. Exactly a year later (i.e. this year), the class teacher leaves the school and if the age of the new class teacher is included, then the new average of the class this year becomes 14.5 years. Find the age of the new class teacher. [CAT exam PYQ]
27
41
43
67
Solution:
Present average of 25 students = 14 years
Total age of 25 students = 25 × 14 = 350
Let the age of new teacher be x.
Average (including new class teacher) = (350 + x)/ 26
⇒ 14.5 = (350 + x)/ 26
⇒ 350 + x = 377
⇒ x = 27
Hence, the correct answer is 27 years.
Q3. In 2001, the average age of a family of 7 members was 36 years. In 2010 a family member expired and a child was born to the family. In 2018 another family member expired merely a week later after the marriage of the younger son of the family to his bride of age 27 years. It was found that the average age of the family in 2021 was 43 years. Out of the options provided, which could have been the individual age of the two family members when they expired in 2010 and 2018, respectively?
68 and 50
74 and 52
82 and 40
84 and 43
Solution:
If the average in 2001 is 36, then in 2021 the average must be 36 + 20 = 56 years
But actually, it is 43 years, that is a deficit of (56 – 43) = 13 years
Throughout the 20 years, at the end of every year, the total members of the family were 7.
∴ Deficit in years = 7 × 13 = 91 years
But the bride was added to the family at 27 years of age.
So the total deficit created by the expiry of the 2 members of the family was = 91 + 27 = 118 years
Out of the options, only the first one’s total comes to 118 years.
Hence, the correct answer is 68 and 50.
Q4. Out of 28 non-zero integers, exactly 12 exceed 10 and exactly 12 are less than 10. The average of these 28 integers is 10. What is the highest possible value of the average of the remaining 4 integers?
14
13
14.5
10
Solution:
Each of the remaining numbers is equal to 10. (the only possibility)
So, the average of the remaining 4 will be 10.
Hence, the correct answer is 10.
Arithmetic Progression, Geometric Progression
Arithmetic Mean and Geometric Mean
Knowledge of Linear Equations
To begin your CAT preparation, go through these steps in order.
At the initial stage of preparation for CAT 2024, try to solve at least 4 to 5 questions on averages to check your understanding of the concept.
Get familiar with fundamental questions like “What is Average in math formula”, “How to find the average in math”, “What is the meaning of average in math”, “Another name for average in math” and “What is weighted average”.
Try some basic questions on averages. (Probably level of difficulty 1)
Once you have figured out the basics, you can move on to more difficult problems by learning some shortcuts and special cases.
Start to solve difficult problems from the books which are suggested in this article.
CAT syllabus 2024: References for Study; CAT Aptitude books (Theory)
How to Prepare Quantitative Aptitude by Arun Sharma (7th edition)
Handa Ka Funda CAT Exam Prep
Mission CAT (YouTube)
CAT syllabus 2024: References to Study (Practice)
R S Agrawal for quantitative aptitude
https://iim-cat-questions-answers.2iim.com
Previous Year's Question Papers
The following concepts are used in distribution-based puzzles:
Distribution of objects among persons/places
Arrangement of persons based on some parameters like height, rank, weight, etc.
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CAT preparation: Importance of puzzles based on distribution:
Puzzles on distribution are used as an effective tool for learning.
It carries a good weightage in the CAT Exam as seen in CAT previous year papers.
Help a person in solving real-life situations.
Students need to practice the selection and distribution CAT questions to get a better idea about this topic.
Comprehension:
Adriana, Bandita, Chitra, and Daisy are four female students, and Amit, Barun, Chetan, and Deb are four male students. Each of them studies in one of three institutes - X, Y, and Z. Each student majors in one subject among Marketing, Operations, and Finance, and minors in a different one among these three subjects. The following facts are known about the eight students:
Three students are from X, three are from Y, and the remaining two students, both female, are from Z.
Both the male students from Y minor in Finance, while the female students from Y majors in Operations.
Only one male student majors in Operations, while three female students minor in Marketing.
One female and two male students major in Finance.
Adriana and Deb are from the same institute. Daisy and Amit are from the same institute.
Barun is from Y and majors in Operations. Chetan is from X and majors in Finance.
Daisy minors in Operations. [CAT exam 2018]
Q1. Who are the students from Institute Z?
Adriana and Bandita
Adriana and Daisy
Chitra and Daisy
Bandita and Chitra
Q2. Which subject does Deb minor in?
Marketing
Operations
Cannot be determined uniquely from the given information
Finance
Q3. Which subject does Amit major in?
Cannot be determined uniquely from the given information
Marketing
Finance
Operations
Q4. If Chitra majors in Finance, which subject does Bandita major in?
Cannot be determined uniquely from the given information
Marketing
Operations
Finance
Solution:
Form a table from the given information to better understand the problem as below:
Name of Student | Gender | Institute | Major | Minor |
Adriana | Female | Same as Deb | ||
Bandita | Female | |||
Chitra | Female | |||
Daisy | Female | Same as Amit | Operations | |
Amit | Male | Same as Daisy | ||
Barun | Male | Y | Operations | |
Chetan | Male | X | Finance | |
Deb | Male | Same as Adriana |
Bandita and Chitra must be from Z. Since two females are from Z. So, this is the only possibility.
Three females are Minor in Marketing. So, Adriana, Bandita and Chitra must minor in Marketing.
Daisy must not be from Y Since females from Y must have a major in Operation but Daisy is a minor in Operations. Therefore, Adriana must be from Y and So Deb does.
Bandita and Chitra must be from X.
Female from Y i.e. must have a major in Operation. And males from Y have a minor in Finance.
Two male students major in Finance. Deb cannot be that one since He is a minor in Finance. So, Amit should be Majoring in Finance.
Name of Student | Gender | Institute | Major | Minor |
Adriana | Female | Same as Deb (Y) | Operations | Marketing |
Bandita | Female | Z | Marketing | |
Chitra | Female | Z | Marketing | |
Daisy | Female | Same as Amit (X) | Operations | |
Amit | Male | Same as Daisy (X) | Finance | |
Barun | Male | Y | Operations | Finance |
Chetan | Male | X | Finance | |
Deb | Male | Same as Adriana (Y) | Finance |
From the given information, the table will look like as shown.
Answer 1: (D)
Answer 2: (D)
Answer 3: (C)
Answer 4: (C) If Chitra does major in Finance then Bandita must major in Operations since only one female can do a major in Finance.
Knowledge of the basics of
Ranking
Direction Sense
Blood Relation
Knowledge of Linear and Circular Arrangement.
Following are some tips and tricks to solve the puzzles based on distribution:
Read each and every piece of information carefully.
Note down important clues and information in short form.
Form tables to mark the possibilities.
Eliminate the wrong possibilities.
Make pairs of related information.
Use the least information at last.
Solving more and more puzzles will help you to build your concept.
CAT syllabus 2024: References to Study (Theory)
Verbal and Non-Verbal Reasoning by R S Aggarwal. (Basic)
ELITES GRID for CAT (YouTube Channel)
CAT syllabus 2024: References to Study (Practice)
Verbal and Non-Verbal Reasoning by R S Aggarwal. (Basic)
LRDI for CAT and GMAT by Nishit K Sinha. (Advance)
Previous Year's Question Papers
Problems of sentence correction involve errors based on
Wrong use of Tenses
Wrong uses of Articles, Propositions
Wrong use of Subject-Verb agreement
Error of Repetition
Error in the choice of phrases/ Words
Sentence correction Questions
Q1. There is no more room for you in this compartment. [IPMAT 2020-IPM Rohtak]
there is no more seat
there is no more space
there is no more accommodation
No improvement
Answer: (4) No correction required
Q2. The place where her father disappeared and the reason why he did are unknown to her. [IPMAT 2020]
her father disappeared and the reason why he did
where her father disappeared and the reason he did
her father disappeared and the reason he did
where her father disappeared and the reason why he did
Answer: (B) The words ‘reason’ and ‘why’ both should not be used there.
Q3. The Municipal Council can no longer wash its hands off its responsibilities. [IPMAT 2020]
wash its hands from its
wash their hands off their
wash their hand of their
wash its hands of its
Answer: (B) Council will have more than one person so ‘their’ should come in place of ‘its’.
Q4. Though disposing of nuclear waste remains a concern, nuclear plants are often subsidized because of the steady, carbon-free power provided. [Based on CAT PYQ]
off nuclear waste remains a concern, nuclear plants are often subsidized because of the steady, carbon-free power provided.
of nuclear waste remains a concern, nuclear plants are often subsidized because of the steady, carbon-free power they provide.
off nuclear waste remains a concern, nuclear plants are often subsidized because of the steady, carbon-free power they provide.
No correction required
Answer: (B) ‘disposing of’ is the correct use of phrasal verbs. So, 1 and 3 cannot be the answer.
The verb should be in accordance with the subject and the subject here is ‘nuclear plants. The verb ‘provided’ should be replaced with ‘they provide’.
Noun, Pronoun, Verb
Tenses
Articles, Prepositions
Subject- Verb Agreement
Look out for time indicators (before, after, ago, while etc) to check whether the correct form of the verb is used.
Find the best option by examining each one.
To find the error in the underlined part, pay attention to the non-underlined part.
If you find two choices correct then choose the shorter choice.
Substitute the selected choice in the place of the underlined part and check whether it makes sense or not.
Use the elimination technique.
Attempt CAT sample papers.
Check online English sentence correction.
CAT Syllabus 2024: 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)
CAT Syllabus 2024: References to Study (Practice):
Mastering the Verbal Ability for CAT by Ajay Singh
https://iim-cat-questions-answers.2iim.com/
Practice Sample Question Papers.
CAT Exam Pattern 2024 | CAT 2024 Mastery: Chapter-wise MCQs for Success for VARC, DILR, Quant |
Common types of average questions include:
Basic average questions
Weighted average questions
Combined average questions
Geometric and harmonic mean questions
Age problems
Increase and decrease in average problems
Seating arrangements
Assign items or peoples to groups or tasks
Arranging events or activities in a timetable.
Sorting items into different categories based on given attributes.
There are some basic ways to practice distribution-based puzzles for the CAT exam.
Those are:
Attempt puzzle questions from the previous year’s CAT exam
Give online and offline mock test exams. It will be time-based exams to improve your time allocation for exams.
Study from CAT preparation books which have puzzles.
Study from online materials, PDF’s to learn more.
Understand the sentence and observe the structure of the sentence
Try to look for the common types of errors we discussed above.
You can also eliminate options by eliminating the irrelevant options.
Choose the option which modifies and expresses the best meaning for the sentence without changing the real meaning.
Study basic grammar and its applications.
Improve these skills by practising more systematically.
Study online well written materials and observe sentence making style and usage of verbs, prepositions.
Analyse your mistakes after giving mock tests and review them to not happen further.
Hello aspirant,
Based on past years' statistics, the CAT cutoff, which is determined as a composite score for the FMS Delhi admission shortlist, is anticipated to be in the range of 52 to 55. On the other hand, the approximate CAT profile is said to be 99.
To know the cutoff you can visit the following link:
https://bschool.careers360.com/articles/fms-delhi-cat-cut-off
Thank you
Hope it helps you
Hello aspirant,
The only on-screen calculator that CAT permits use is a simple one. It is not permitted for you to bring the actual calculator into the center. This approach is predicated on the idea that the CAT assesses an individual's aptitude for solving challenging mathematical puzzles and making fast mental computations.
Thank you
A CAT percentile of 90 or above can strengthen your application to MICA, it is not the only factor that determines admission.MICA considers scores of CAT and MICAT which are weighted 50–50 percent for the interview call.
Strong performance in the Pshycometric test and descriptive writing increase your chances to get into mica even if you score 80 percentile.the admission is based upon whole performance including every marks.
ALL the best!!!!
Hello,
Here you can get study material for CAT :
https://bschool.careers360.com/download/ebooks/cat-quantitative-aptitude-questions-answers-pdf
Hope it helps !
Hello aspirant,
A timetable is essential if you are preparing for the CAT in addition to your college coursework. It will give you an idea of how long it will take you to finish your syllabus and then set aside the appropriate amount of time for revision and mock exams. Without a set timetable, you risk taking your time and not completing your preparation as thoroughly as is necessary.
Thank you
Hope it helps you.
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