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Unlocking CAT Exam Essentials: Exploring Unit Digits, Pie Charts, and Pronouns - Day 2
Edited By Team Careers360 | Updated on Sep 19, 2024 02:25 PM IST | #CAT
In our previous article, we covered the CAT Preparation Strategy for Quantitative Ability on Day 1, focusing on the number system and its components, such as classification, converting decimals to fractions, and base systems, along with relevant CAT quant questions.
In this article, we will study deep into the unit digit and the last two digits of a number as outlined in the CAT Quant syllabus for 2024. We'll also review previous year's CAT questions related to the number system. Typically, there are about 3-4 questions on this topic in the exam, based on past CAT quant papers.
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This Story also Contains
- Part 1: Quantitative Aptitude For CAT 2024
- Part 2: Data Interpretation And Logical Reasoning For CAT 2024
- Part-3: VARC for CAT 2024 Exam
- Free PDFs for CAT 2024 preparation
For instance, given the number 234432, how would you determine the unit digit and the last two digits of the number?
Part 1: Quantitative Aptitude For CAT 2024
Topic: What is “Cyclicity”?
Cyclicity is used to determine the unit digit. Cyclicity is the power of a number after a multiple in which a unit digit is repeated.
For example, 21 = 2; 22 = 4; 23 = 8; 24 = 16; 2 5= 32 and so on.
As it is shown in the above example, after every fourth power of 2, the unit digit is repeated. So, 4 is cyclicity of 2.
So, you have to learn the cyclicity of every digit.
Digit | Cyclicity (Power Cycle) | Digit | Cyclicity (Power Cycle) |
0 | 1 (Gives always 0 at unit place) | 5 | 1 (Gives always 5 at unit place) |
1 | 1 (Gives always 1 at unit place) | 6 | 1 (Gives always 6 at unit place) |
2 | 4 (2, 4, 6, 8) | 7 | 4 (7, 9, 3, 1) |
3 | 4 (3, 9, 7, 1) | 8 | 4 (8, 4, 2, 6) |
4 | 2 (4, 6) | 9 | 2 (9, 1) |
CAT quant questions based on the last two digits of a number are asked frequently in the CAT Exam.
Eg: Find the last two digits of 3737.
It is practically not so easy to solve this power. So, you need to learn the tricks to find the last two digits without actually solving this problem. Some of the tricks will be discussed later in this article, like dividing a number by 100 so that the remainder is the last two digits.
CAT Quant Questions From CAT Previous Year Papers
Question 1: The product of the last two digits of (1! + 2! + 3!….. 50!) is?
3
4
5
6
Ans: (A)
Divide the given number by 100 to find the last two digits.
Number 10! And greater than 10! are divisible by 100.
So, find (1! + 2! + 3!….. +9!) and divide the result by 100 to get the remainder and hence the last two digits of the number.
So, 1! + 2! + 3!….. +9! = 1 + 2 + 6 + 24 + 120 + 720 + 5040 + 40230 + 362880
So, the sum of the remainder is (1+ 2 + 6 + 24 + 20 + 20 + 40 + 30 + 80). On dividing this result by 100, we get 13 as the remainder.
Product of digits of 13 = 1 × 3 = 3.
Question 2: What are the last two digits of 72008? [CAT Question Paper 2008]
21
61
01
41
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Download NowAns: (C)
(1,3,7,9)20k = 01 (Last two digits) where k is a positive integer.
So, 72008 = 72000 x 74 x 74 = 01 x 01 x 01 (Taken last two digits only) = 01
So, the answer is 01.
Prerequisite:
While preparing for the number system, a student must learn:
Squares of the first 25 natural numbers
Cubes of natural numbers till 15
Knowledge of Prime and Composite
Knowledge of powers
Knowledge of factorial
Knowledge of Even and Odd Numbers
Basic Knowledge of Multiples and Factors
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Tips On CAT Preparation For the Number System (Unit Digit And Last Two Digits):
Learn Cyclicity to find the unit digits as discussed in this article.
Use the Concept of cyclicity in Practice Problems.
To find the last two digits, the following tips may help you
The last two digits of x2, (50+ x)2, (50- x)2, (100+ x)2, (100- x)2 are the same.
Eg: 022 = 04
522 = 04
482 = 04
1022 = 04
982 = 04Odd20k = 01(last two digits) except for 5. Where k is a positive integer.
Eg. 2342 = 01(a5)even = 25 (last two digits)
(a5)odd = 75 (last two digits); where can be any digit.
Eg: 13572 = 25, 13523 = 75Even20k= 76(last two digits) where k is a positive integer.
Eg: 48200 = 76 (last two digits)
Practice Mock Tests and CAT Question Paper
References for Study (Theory):
Learn the concept of class 9 Mathematics NCERT (for theory)
Arun Sharma: A Quantitative Approach for CAT (6th Edition)
YouTube Channel of 2iim
References for Practice(Number System Questions And Answers):
Master Number System for CAT and GMAT by Nishit K Sinha.
CAT previous year papers: practice previous year CAT questions on number system
Question bank from CAT-Holic
Part 2: Data Interpretation And Logical Reasoning For CAT 2024
Topic: Data Interpretation (Pie Graphs)
As discussed in the previous article, Data interpretation is the most important topic for the CAT exam and other management entrance Exams.
Skills of observation, doing calculations quickly, analyzing things, and comparison of values will help you in solving questions based on Data interpretation (Pie Charts).
In this topic, we are going to discuss strategies to prepare Data Interpretation based on Pie Charts. We will discuss some Pie chart questions on CAT below as well.
What is a Pie Chart (Pie chart basic concept for CAT Exam)?
Sample pie charts of distribution of 6 parameters.
In the pie chart, data is distributed in a circle, which forms 360 degrees at its centre and comprises 100% of its area. Students must know how to derive the relation between angle and Percentage to calculate the parameter’s value.
Pie chart questions and concepts for CAT preparation from CAT Previous Year Papers:
Direction: The break-up of the students in a university by subject major is given in the polar pie chart. The bar chart shows the number of students who major in physics by geographic location. [XAT 2019, based on CAT PYQ]
Question 1. How many students major in chemistry?
200
175
170
190
180
Solution: (B)
Students major in physics = 18 + 36 + 80 + 40 + 23 + 28 = 225 which is 18% of total students.
So, 18% = 225
Major in Chemistry
14% = (225/18) x 14 = 175
Question 2. If the proportion of physics majors who are from Delhi is the same as the proportion of engineering majors who are from Delhi, how many engineering majors are from Delhi?
22
26
18
20
24
Solution: (D)
Students major in physics = 18 + 36 + 80 + 40 + 23 + 28 = 225 which is 18% of total students.
So, 18% = 225
So, Total students in Engineering major = 225×20/18 = 250
According to question
18/225 = x/250 (where x are students from Delhi with Engineering major)
⇒ x = 20
Question 3. 12% of all students are from Chennai. What is the largest possible percentage of economics students that can be from Chennai, rounded off to the nearest integer?
73%
77%
75%
71%
69%
Solution: (A)
Total number of Physics majors = 225
Total number of students = 225 x 100/18 = 1250
Students from Chennai = 12% x1250 = 150
Number of Physics majors from Chennai (from graph) = 40
Maximum possible number of Economics majors from Chennai = 150 - 40 = 110
Maximum Percentage of Economics Major from Chennai = 110 x 100/150 = 73.33%.
Prerequisite:
To prepare Data Interpretation (Pie Chart), a student must learn
The Basics of Trigonometry
Percentage (Basic)
Squares and Cubes of 20-30 first natural numbers.
Knowledge of fractions and Ratio
Must know to find Average
Knowledge of mean, Mode , and median.
Tips On CAT Preparation For DI (Pie Chart):
Practice questions on simplification and approximation.
Practice questions on the basics of percentages.
Try to solve addition, subtraction, and multiplications mentally.
Understand the conversion of angles into percentages.
Practice the questions on the basics of average.
References To Study (Theory):
LRDI for CAT and GMAT by Nishit K Sinha.
To learn the basics of bar graphs read statistics of class 9 and Class 10 Mathematics from NCERT (For Theory)
2iim YouTube Channel
References To Study (Practice):
1. CAT previous year's papers
2. Question bank from CAT-Holic
3. How to Prepare for Data Interpretation for CAT by Arun Sharma
Part-3: VARC for CAT 2024 Exam
Topic: Pronoun and Its Type
Pronouns are used in place of nouns to avoid repetition of the nouns to which they refer. Pronouns have different forms and are used in different ways.
Eg: I, me, he, she, they, each, few, many, etc
To understand them in a better way, they are categorized into different categories as shown:
Type | Example | Uses |
Personal Pronoun (Used in place of the name of a person) | I, Me, He, She, You, They, Her, Us etc | He is going to meet her. |
Possessive Pronoun (Shows possession of something) | My, Mine, ours, your, its, hers, etc | This T-shirt is mine. |
Relative Pronoun (used before describing the features or properties of the subject) | That, who, whom, whose, which etc | The thief who stole the money has been successfully punished. |
Reflexive Pronoun (Used when the subject and the object of a sentence are the same) | herself, myself, yourself, yourselves, himself, oneself, etc | He used to believe in himself. |
Intensive Pronoun (Similar to Reflexive pronoun but emphasise more intensely on Subject) | herself, myself, yourself, yourselves, himself, oneself, etc | I myself cook my food. |
Indefinite Pronoun (Used when the subject is not certain) | nobody. anybody everybody, somebody Anyone, no one, everyone, someone etc. | No one is perfect in this world. |
Demonstrative Pronoun (Used to show the closeness of the subject or its position) | This, that, these, such, those, etc. | I had the privilege to visit the Prime Minister’s office, that was worth remembering. |
Interrogative Pronouns (used to ask questions) | What, which, whose, whom, who, etc. | Who is confident enough to clear the CAT this year? |
Reciprocal Pronoun (Used when the sentence has the two actions are performed by two parties) | Each other, one other | The kids threw stones at one another. |
Distributive Pronoun (refers to individuals in a group) | none, each, either, neither, any, everyone, no one etc. | None of our friends was involved in the fighting. |
Questions on Pronouns From CAT Previous Year Papers (CAT VARC pronoun)
Direction- Find the correct alternative for the underlined sentence:
Question 1. My mother bought ice creams for my brother and me, but she didn’t buy one herself.
for my brother and me, but she didn’t buy one for herself.
for my brother and myself, but she didn’t buy herself one.
for my brother and I, but she didn’t buy one for her.
for my brother and I, but she didn’t buy one for herself.
Ans. (A)
Option C and D are wrong because the use of ‘I’ does not make any sense, In place of I, ‘me’ should come (pronoun in place of a noun)
Option B is wrong since ‘myself’ (reflexive pronoun) refers to when I purchased the ice-cream but her mother purchased it.
Therefore, option A is correct because correct pronouns were used.
Question 2. He ____ saw the running Dog.
(a) himself (b) him (c) them (d) themselves
Ans: (a)
The correct pronoun for "he" is himself.
Question 3. Shreeti and ____ went to a movie.
(a) I (b) themselves (c) myself (d) ourself
Ans: (a)
Personal pronouns should be used here. So, the correct answer is option A.
Question 4. When a girl asked how I got _____ address, I told her that it was with the help of a relative of _____.
(a) my/ me (b) mine/ his (c) her/hers (d) she/ she
Ans: (c)
The address here is related to a girl, so "her" should come
Relative to mine or a relative of hers; both can be correct. However according to the options given, option (C) will be correct.
Tips On CAT Preparation for Verbal Ability (Pronoun):
Learn the pronouns by categorizing them and their uses in different situations.
Learn the basics of Grammar
Practice different pronouns in different situations.
Practice CAT Question Papers and Mock tests.
Develop the habit of reading (Newspapers, Novels, Articles etc)
References To Study (Theory):
Advanced English Grammar by Martin Hewings
2iim YouTube Channel
References To Study (Practice):
CAT's previous year's papers
Objective General English (Arihant)
Free PDFs for CAT 2024 preparation
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Questions related to CAT
Have a question related to CAT ?
Although, it's very unlikely that you will secure a seat in top ABM with CAT 67 percentile. Here's is a breakdown to your question:
· CAT Percentile vs. Score: A CAT score of 67 typically translates to a percentile in the range of 90-95 percentile based on the provided data from previous years. While this is a decent score overall, it falls short of the cutoffs for most top-tier ABM programs.
· Cutoffs for Top ABM Institutes:
- IIM Lucknow: For their PGP-ABM program, the qualifying CAT cutoff for the general category is around 85 percentile . However, the actual cutoff for shortlisting for the Written Ability Test (WAT) and Personal Interview (PI) stages is likely to be higher.
- IIM Ahmedabad: While they also offer an ABM program (PGP-FABM), their minimum qualifying CAT cutoff is around 80 percentile , but the final admission cutoffs are usually much higher, often in the 99+ percentile range for general candidates.
- MANAGE (National Institute of Agricultural Extension Management): Their cutoff in CAT percentile has been around 70 for the general category in recent years. With a 67 percentile, you might have a slim chance here, but it's still competitive.
- CCS NIAM (National Institute of Agricultural Marketing, Jaipur): They consider CAT scores with a significant weightage (30-51% in their selection criteria). While they don't explicitly state a cutoff, it's reasonable to assume it would be higher than 67 percentile for a good chance of admission.
· Overall Good CAT Score: Generally, a CAT percentile of 90 and above is considered a good score for securing admission to decent MBA programs in India. For top-tier institutes, a percentile of 95 and above is often preferred.
· MBA Colleges Accepting 60-70 Percentile: While there are MBA colleges that accept CAT scores in the 60-70 percentile range, these are generally not the top-ranked or most sought-after ABM programs. The focus of those lists is on general MBA programs, not specifically ABM.
While securing a seat in ABM can be tough, you can research about other colleges, consider other examinations, to improve your application profile.
You Got This !
Aman Kar 16 April,2025
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
To find the 2024 MHT CET answer key, you'll need to check the official Maharashtra State Common Entrance Test Cell website. This is the primary source for all official announcements and documents related to the MHT CET exam. After the exam concludes, the CET Cell typically releases a provisional answer key.
Once released, the provisional answer key will likely be available as a downloadable PDF file. You'll need to navigate to the official website, look for the MHT CET section, and find the link related to the answer key. This link might be labelled "MHT CET 2024 Answer Key" or something similar.
After downloading the answer key, you can compare your responses with the official answers. If you find any discrepancies or have objections, the CET Cell usually provides a window for raising objections. You'll likely need to pay a specified fee for each objection raised. The official website will provide instructions on how to submit your objections, which may involve logging into your candidate portal and following the provided steps.
Finally, after considering all objections, the CET Cell will publish a final answer key. This final version is considered definitive, and the MHT CET results will be based on it. Keep an eye on the official website for all updates and announcements regarding the 2024 answer key.
I hope this helps.
SUKRITI GUPTA 13 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
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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