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Beyond Basics: CAT Exam Hacks for Sentence Correction, Average, Intro to Distribution based puzzles - Day 22
Edited By Team Careers360 | Updated on Sep 20, 2024 04:12 PM IST | #CAT
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.
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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.
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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.
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.
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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Questions related to CAT
Have a question related to CAT ?
Hello,
achieving a 99.99 pecentile in the CAT exam significantly enhances your prospects for admission to JBIMS, which evaluates candidates using an application rating(AR) score, which includes
-entrance exam score (CAT/MH-CET/CMAT) : 60% weightage
-Past Academic Record (PAR) : 15% weightage (https://cracku.in/colleges/jbims/admission-process/?utm_source=chatgpt.com)
-Extra-curricular Activities/Work Experience : 20% weightage (https://jbims.edu/uploads/announcement/Revised_M_Sc__Finance_Admission_Procedure_Batch_2024-26.pdf?utm_source=chatgpt.com)
-Diversity (Academic/Gender): 5% weightage
while ahigh CAT percentile is crucial, a lower academic record may impact your overall AR score. Nonetheless, exceptional performance in other areas, such as entrance exams and extracurricular activities, can help offset weaker academic credentials. it's advisable to review JBIMS's detailed admission criteria and consider strengthening other aspects of your application to enhance your chances
Riya Dhoot 10 April,2025
Greetings! Here's a detailed response to your query
Okay, so you're a bit confused about what to put in those CAT, FMS, DSE, and IIFT forms regarding your 12th scores. Since you did CBSE, they usually only consider your final 12th standard marks.
Even though you did great in 11th, scoring 495 out of 500, for these entrance exam forms, they're specifically asking about your 12th board exam marks .You mentioned you got 400 out of 500 in 12th, which comes out to 80%.
Therefore, when filling out the forms for CAT, FMS, DSE, and IIFT, you should enter 80% as your 12th percentage. The aggregate of 11th and 12th isn't typically what they're looking for in these sections. They want to know how you performed in your final board exams. So, stick with the 80% from your 12th results. Good luck with your applications!
SUKRITI GUPTA 05 April,2025
Greetings! Here's a detailed response to your query:-
Determination of the best time to start the journey of CAT examination is based on individual factors like your current skill level, knowledge ,potential, learning pace and availability. To give yourself the best chance of success on the CAT exam , which usually takes place in November, it's advisable to begin studying between January and March of that same year. This 8 to 12-month preparation window is widely recommended by experts. But if you're managing your college along with the CAT preparations make sure you start from 2nd year onwards. It will hep you manage stress and you'll have ample amount of time to get along with the syllabus , pattern and various practice and mocks .
You'll be able to build a strong foundation in each sections and be able to know your strengths and weaknesses in different topics. The CAT syllabus is extensive, and early preparation allows for thorough coverage. Assess your learning speed and adjust your preparation timeline accordingly.
Essentially, while the ideal start time is subjective, beginning your CAT preparation well in advance is generally considered the most effective strategy for achieving optimal results.
SUKRITI GUPTA 01 April,2025
The CUSAT CAT previous year question papers are available on the Careers360 website. You can find question papers from 2012 to 2023, which can be downloaded in PDF format HERE
Additionally, the official website of Cochin University of Science and Technology (CUSAT) also provides previous year question papers. To access them, you can follow these steps:
- Visit the CUSAT official website - admissions.cusat.ac.in.
- Click on the resources tab from the homepage.
- Select the previous year's question papers from the drop-down menu.
- Select the Common Admission Test (CAT) question papers link.
- Now click on the B.Tech course.
By practicing with these previous year question papers, you can get familiar with the exam pattern, identify important topics, and improve your time management skills.
sadafreen356 28 March,2025
Hey Shathvika, that's a great question! So, you're wondering about MBA entrance exams besides the CAT , right? Absolutely, there are quite a few others you can consider in India. Here's a rundown: Xavier Aptitude Test (XAT) : XLRI Jamshedpur runs this one, and over 150 B-schools across India accept it. You'll usually find it in January. What's cool about the XAT is that it often includes sections on Decision Making and sometimes even an Essay Writing part. Management Aptitude Test (MAT) : This is conducted by the All India Management Association (AIMA). A lot of schools – over 600 in India – take MAT scores. The best part? You can take it four times a year: February, May, September, and December. Plus, you can choose between Paper-Based (PBT), Computer-Based (CBT), and even Internet-Based (IBT) options. Symbiosis National Aptitude Test (SNAP) : If you're eyeing a Symbiosis institute for your MBA, this is the one. Symbiosis International (Deemed University) conducts it, and it's usually in December. SNAP's also known for having a somewhat unique way of scoring. Common Management Admission Test (CMAT) : The National Testing Agency (NTA) conducts the CMAT. AICTE-approved institutions all over India will accept it. This one's also typically held in January. It checks you on things like quantitative skills, logical thinking, how well you understand language, and your general knowledge. NMAT by GMAC : The Graduate Management Admission Council (GMAC) is behind this exam. NMIMS and quite a few other management schools accept it. What’s interesting is that you have a 75-day window, usually from October to December, to take it. And, you can even retake it up to three times if you want to improve your score! Indian Institute of Foreign Trade (IIFT) Exam : NTA also conducts this one. If you are keen on IIFT Delhi and Kolkata, this is your ticket. Expect to take it in December. This exam puts a little more weight on questions about international business and trade. MICA Admission Test (MICAT) : MICA Ahmedabad uses this for its PGDM-C program. They hold it twice a year, generally in December and January. MICAT looks at how creative you are, how well you write, and your general abilities. Graduate Management Admission Test (GMAT) : GMAC runs the GMAT as well. Many B-schools in India, and even more worldwide, accept GMAT scores. You can take it pretty much any time of the year. People often go for the GMAT if they're thinking about executive MBA programs or schools with a focus on international business. Lovely Professional University National Entrance and Scholarship Test (LPUNEST) : LPU conducts it for admissions into its undergraduate and postgraduate programs. It's held multiple times throughout the year. It also works as a scholarship test, so doing well can get you some financial aid. So, there you have it! Each of these exams has its own quirks when it comes to structure, who can take it, and the scores you need. It’s worth digging into each one a bit to see which one fits best with what you've studied and where you want to take your career. Good luck!
Aditya .V. 27 March,2025
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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