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Beyond Basics: CAT Exam Hacks for Sentence Correction, Average, Intro to Distribution based puzzles - Day 22
Ongoing Event
CAT Application Date:01 Aug' 25 - 13 Sep' 25
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.
This Story also Contains
- CAT 2024 QA Preparation Tips (Quantitative Aptitude for CAT)
- CAT 2024 Preparation Tips: CAT DILR questions (CAT Logical Reasoning questions and Data Interpretation)
- CAT Exam Preparation 2024: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)
- Free PDFs for CAT 2024
CAT 2024 QA Preparation Tips (Quantitative Aptitude for CAT)
CAT Exam Important Topic: Average (Algebra)
What is average in math or algebra?
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.
Some tricks and approaches for CAT exam Preparation:
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.
CAT 2025: VARC, DILR, and Quant MCQs & Weightages
Comprehensive CAT prep guide with focused practice on Verbal Ability, Data Interpretation & Logical Reasoning, and Quantitative Aptitude.
Download NowThe 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.
CAT Questions from Averages (based on PYQs)
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.
Prerequisite:
Arithmetic Progression, Geometric Progression
Arithmetic Mean and Geometric Mean
Knowledge of Linear Equations
CAT Exam 2024 Preparation: Tips to solve CAT questions on Averages
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
CAT 2024 Preparation Tips: CAT DILR questions (CAT Logical Reasoning questions and Data Interpretation)
CAT 2024 Syllabus Topic: Problem Solving/Puzzle (Distribution)
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.
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.
CAT Previous Year Questions: Puzzles based on Distribution
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.
Prerequisite:
Knowledge of the basics of
Ranking
Direction Sense
Blood Relation
Knowledge of Linear and Circular Arrangement.
CAT Exam 2024 Preparation: Tips to solve CAT questions Puzzles based on distribution:
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
CAT Exam Preparation 2024: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)
CAT Exam Important Topic: To solve Problems on Sentence Correction
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
CAT Exam Practice Questions on Sentence Correction
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’.
Prerequisite:
Noun, Pronoun, Verb
Tenses
Articles, Prepositions
Subject- Verb Agreement
CAT Tips and Tricks to Solve Problems in Sentence Correction:
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.
Recommended eBooks
Related eBooks & Sample Papers
Free PDFs for CAT 2024
CAT Exam Pattern 2024 | CAT 2024 Mastery: Chapter-wise MCQs for Success for VARC, DILR, Quant |
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While filling the form:
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Popular CAT Questions
Directions for question :
M/s Deloitte Touche Tohmatsu Limited, one of the top four audit and accounting firms in the world with headquarters at London, UK, and with an operational presence in 153 countries, hires Management Trainees (MT) from all the premier management institutes of India thrice every year, in the months of January, May and September.
Each new group of Management Trainees (MT) have to go through a four month rigorous training schedule, after which they have to pass through a test consisting of a written assessment and a case-analysis. The top hundred ranked Management Trainees (MT) based on the performance in the test are confirmed as Management Executives (ME). The rest are given the opportunity of undergoing the training for four months one more time along with the next batch of Management Trainees (MT) and then passing through the subsequent test consisting of the written assessment and case-analysis. The Management Trainee (MT) who fails to get confirmed as a Management Executive (ME) the second time is fired.
The scatter-graph below depicts the number of Management Trainees (MT) at Deloitte taking the tests from January 2020 till May 2022, and the vis-à-vis hired Management Trainees (MT) at Deloitte who were fired :
It is also known that for the month of September 2019 at Deloitte, 96 hired Management Trainees (MT) failed to be confirmed as a Management Executive (ME) the first time, and that 36 hired Management Trainees (MT) were fired.
Question :
In which test did the minimum number of Management Trainees (MT) get confirmed as a Management Executive (ME) in the second attempt ?
Option: 1
September 2020
Option: 2
May 2021
Option: 3
January 2021
Option: 4
January 2022
Directions for question:
The bar-graph given below shows the foreign exchange reserves of Nepal (in million Rupees) from 2014 to 2021. Answer the following questions based on the graph :
Question:
What was the percentage increase (rounded to the nearest integer, if deemed necessary) in the foreign exchange reserves in 2020 over 2016 ?
Option: 1 None
Option: 2 None
Option: 3 None
Option: 4 None
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