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CAT with Confidence: Diving into Complex Numbers, Calendar Puzzles, and PYQs on Critical Reasoning- Day 54
Edited By Team Careers360 | Updated on Jun 19, 2025 02:23 PM IST | #CAT
Aspirants preparing for CAT 2024 should now concentrate on important topics like complex numbers and calendar-based aptitude questions, which often lead to confusion, particularly when differentiating between complex numbers and quadratic equations. Consistent practice and strong conceptual clarity are essential at this stage. Solving previous year questions and making use of helpful resources such as the calendar reasoning PDF can significantly enhance preparation and build confidence for the final exam.
This Story also Contains
- Part-1: Quantitative Aptitude for CAT exam
- Part-2: CAT 2023 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)
- Part-3: CAT Exam Preparation 2023: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)
- Short Tricks to Solve Complex Number Questions in CAT
- Short Tricks to Solve Calendar Puzzles Questions in CAT
Part-1: Quantitative Aptitude for CAT exam
Aspirants can also download questions on complex numbers with answers pdf for more practice questions and references for their studies.
Important Concept/Formula Used in CAT complex numbers questions
Concepts and Formulas Used in CAT complex numbers Exam questions are given below:
Contains real as well as imaginary parts.
Eg: 2+ 3i
Real part = 2
Imaginary part = 3
iota (i) = -1
The complex conjugate of (a+ ib) is (a- ib).
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 NowCAT Previous Years Questions On Complex Numbers
Q1. CAT 2023 complex numbers Questions and Answers are given below:
If z is a complex number, then the minimum value of |z- 1| + |z + 1| is ______.
[Based on MBA Entrance Exams]
CAT complex numbers problems with solutions are given below:
Solution:
If z = a+ ib
Then, |z- 1| = a-12+b2
and |z + 1| = a+12+b2
|z- 1| + |z + 1| = a-12+b2 + a+12+b2
This value is minimum if either a= 1 and b =0 or a =0 and b = 1
So, the minimum value of |z- 1| + |z + 1| = 2.
Q2. Complex numbers Questions with solutions are given below:
If the cube roots of unity are 1, ω, ω2, then find the roots of the equation (x − 1)3 + 64 = 0. where ω = 3-1 [Practice Question]
Complex numbers system problems with answer for CAT exam are given below:
Solution:
(x − 1)3 = −64 ⇒ x − 1 = (−64)1/3
x − 1 = −4, −4ω, −4ω2
x = −3, 1 − 4ω, 1 − 4ω2
CAT Exam Important Topic: Strategy to Prepare “Complex Numbers” for CAT exam 2023 ( important complex number questions).
Find the CAT tips and tricks for complex numbers Questions below:
i4k = 1 (where k is a positive integer)
Learn algebra of complex numbers
Addition: N1= a1+ ib1; N2 = a2+ ib2; N1+ N2 = (a1+a2) +i(b1+ b2)
Subtraction: N1= a1+ ib1; N2 = a2+ ib2; N1- N2 = (a1-a2) +i(b1- b2)
Multiplication: N1 x N2 = (a1a2 + b1b2) + i(a1b2 + b1a2)
Division: N1/ N2 = (a1+ ib1)/(a2+ ib2)
Less frequently asked in the CAT Exam. Do not waste much time. Keep this topic for last.
Practice Previous years questions to get familiar with the types of questions being asked.
CAT entrance exam: Prerequisite to complex numbers questions
Basics of the number system
Imaginary Numbers
References to Study (Theory) complex numbers
NCERT Class 11
TriOsEducate: YouTube (https://www.youtube.com/watch?v=CwxDoiXb1D0)
References to Practice complex numbers questions for CAT exam
Study sources of Complex Numbers Questions for CAT Exam are given below:
How to Prepare Quantitative Aptitude by Arun Sharma (7th Edition)
( https://www.youtube.com/watch?v=VlEwd_dq-9s&t=2920s)
Practice Sample Papers
Part-2: CAT 2023 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)
All the important tips of the calendar should be covered by the aspirants and for the aspirants Calendar reasoning questions with solutions are given below. Aspirants can also download calendar questions pdf and calendar reasoning questions pdf for more practice and references
CAT 2023 Syllabus Topic: Strategy to prepare “Concept of Calendar” and Calendar Aptitude Questions for CAT Exam
Important Concept/Formula Used in Calendar Questions for CAT Preparation
The concepts used in CAT calendar questions are given below:
Concept of odd days Number of days divided by 7 and the remainder is odd days.
Concept of leap year
Any year (Not multiple of 100) divisible by 4
Any year (multiple of 100) divisible by 400
Concept of finding a day on a given date.
Repetition of Calendar
Ordinary year after every 11 years (few exceptions)
Leap year after every 28 years (few exceptions)
CAT Calendar questions From CAT Previous Years Papers
Q1. CAT calendar questions are given below:
Given that 27th February 2003 is Thursday. What was the day on 27th February 1603? [CAT 2016]
Monday
Thursday
Sunday
Tuesday
Answer: [2]
After every 400 years, the calendar repeats itself. So, the answer is Thursday.
Q2. Calendar aptitude questions are given below:
Today is Monday. After 73 days, it will be [SNAP Sample Question]
Thursday
Friday
Saturday
Sunday
Calender reasoning questions with solutions are given below:
Ans: [1]
Divide 73 by 7, then odd days are 3.
So, 3 days after Monday will be Thursday.
Tips/Tricks for CAT on calendar based CAT questions
Tips and tricks: Calendar Questions for CAT Preparation are given below:
An ordinary year starts with and end on the same day.
A leap year-end with a day after it starts.
Odd days in a week is ‘0’.
A century can not end on Tuesday, Thursday or Saturday.
After every 400 years the calendar repeats.
Practice separately each kind of question.
Practice previous years questions from various MBA entrance Exams to get an idea of the pattern of questions being asked.
CAT entrance exam: Prerequisite to calendar reasoning questions
Knowledge of reading a calendar
Basics Calculations
CAT study material: References to Study (Theory) Concept of Calendar
R S Agrawal
Rodha
(https://www.youtube.com/watch?v=fnGRCej5qUw)
CAT study material: References to Practice ( calendar questions for CAT preparation)
Study sources of calendar aptitude questions for CAT exam are given below:
MBA Entrance Previous years Papers and Sample Papers.
Unacademy CAT
(https://www.youtube.com/results?search_query=calendars+for+CAT+Exam)
Part-3: CAT Exam Preparation 2023: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)
CAT Exam Important Topic: Strategy to Prepare “Statement and Conclusions” (Critical Reasoning) for CAT-2023
Important Concept of CAT Statement and Conclusions questions
The concepts used in Statement and Conclusions CAT questions are given below:
The question has three parts
Statement + Question+ Options (Conclusions)
Statement: A statement is a formal account of certain facts, views or situations in words.
Conclusions:
- No degree of assumptions
- It is derived
- It is not an opinion
- It should not be forced
CAT Practice Questions on Statements and Conclusions (critical reasoning questions for CAT)
Question 1: Statements and Conclusions (critical reasoning questions for CAT) are given below:
Read the passage and answer the questions based on it. (CAT 2017)
Typewriters are the epitome of a technology that has been comprehensively rendered obsolete by the digital age. The ink comes off the ribbon, they weigh a ton, and second thoughts are a disaster. But they are also personal, portable and, above all, private. Type a document and lock it away and more or less the only way anyone else can get it is if you give it to them. That is why the Russians have decided to go back to typewriters in some government offices, and why in the US, some departments have never abandoned them. Yet it is not just their resistance to algorithms and secret surveillance that keeps typewriter production lines - well one, at least - in business (the last British one closed a year ago). Nor is it only the nostalgic appeal of the metal body and the stout well-defined keys that make them popular on eBay. A typewriter demands something particular: attentiveness. By the time the paper is loaded, the ribbon tightened, the carriage returned, the spacing and the margins set, there's a big premium on hitting the right key. That means sorting out ideas, pulling together a kind of order and organising details before actually striking off. There can be no thinking on screen with a typewriter. Nor are there any easy distractions. No online shopping. No urgent emails. No Twitter. No need even for electricity - perfect for writing in a remote hideaway. The thinking process is accompanied by the encouraging clack of keys, and the ratchet of the carriage return. Ping!
Question. Which one of the following best describes what the passage is trying to do?
It describes why people continue to use typewriters even in the digital age.
It argues that typewriters will continue to be used even though they are an obsolete technology.
It highlights the personal benefits of using typewriters.
It shows that computers offer fewer options than typewriters.
Ans: [1]
Explanation:
The author is trying to explain:
why the typewriter continues to be used even in today's digital age. For this, he has given reasons that typewriters are personal and private and cannot be hacked. These can be used anywhere without the requirement of electricity.
Q2. CAT exam 2023 statements and Conclusions questions with solutions are given below:
Comprehension: [CAT 2018]
[The] Indian government [has] announced an international competition to design a National War Memorial in New Delhi, to honour all of the Indian soldiers who served in the various wars and counter-insurgency campaigns from 1947 onwards. The terms of the competition also specified that the new structure would be built adjacent to the India Gate – a memorial to the Indian soldiers who died in the First World War. Between the old imperialist memorial and the proposed nationalist one, India’s contribution to the Second World War is airbrushed out of existence.
The Indian government’s conception of the war memorial was not merely absent-minded. Rather, it accurately reflected the fact that both academic history and popular memory have yet to come to terms with India’s Second World War, which continues to be seen as little more than mood music in the drama of India’s advance towards independence and partition in 1947. Further, the political trajectory of the postwar subcontinent has militated against popular remembrance of the war. With partition and the onset of the India-Pakistan rivalry, both of the new nations needed fresh stories for self-legitimisation rather than focusing on shared wartime experiences.
However, the Second World War played a crucial role in both the independence and partition of India. . . . The Indian army recruited, trained and deployed some 2.5 million men, almost 90,000 of which were killed and many more injured. Even at the time, it was recognised as the largest volunteer force in the war. . . .
India’s material and financial contribution to the war was equally significant. India emerged as a major military-industrial and logistical base for Allied operations in Southeast Asia and the Middle East. This led the United States to take considerable interest in the country’s future and ensured that this was no longer the preserve of the British government.
Other wartime developments pointed in the direction of India’s independence. In a stunning reversal of its long-standing financial relationship with Britain, India finished the war as one of the largest creditors to the imperial power.
Such extraordinary mobilization for war was achieved at a great human cost, with the Bengal famine the most extreme manifestation of widespread wartime deprivation. The costs on India’s home front must be counted in millions of lives.
Indians signed up to serve on the war and home fronts for a variety of reasons. . . . [M]any were convinced that their contribution would open the doors to India’s freedom. . . . The political and social churn triggered by the war was evident in the massive waves of popular protest and unrest that washed over rural and urban India in the aftermath of the conflict. This turmoil was crucial in persuading the Attlee government to rid itself of the incubus of ruling India. . . .
Seventy years on, it is time that India engaged with the complex legacies of the Second World War. Bringing the war into the ambit of the new national memorial would be a fitting – if not overdue – recognition that this was India’s War.
Question: In the first paragraph, the author laments the fact that
- the new war memorial will be built right next to India Gate.
- there is no recognition of the Indian soldiers who served in the Second World War.
- funds will be wasted on another war memorial when we already have the India Gate memorial.
- India lost thousands of human lives during the Second World War
Ans: [2]
In the first paragraph, the author says that ‘India’s contribution to the second world war is airbrushed out of existence.’ This means, there is no recognition of the Indian soldiers’ contribution to the second world war.
Tips and Tricks for Statement and Conclusions questions for CAT exam 2023
Conclusions are not generalised.
Conclusions have to be “No exception at all”.
Understand the difference between Inference and Conclusion
Rephrase the question in your words.
Generally, indirect questions are asked in CAT Exam (generally in the RCs). So, Practice different RCs appeared in CAT Exam.
Practice questions daily (Fewer questions but daily)
CAT 2023: Prerequisite to Statement and Conclusions
Knowledge of basic components of statements and arguments.
Reading Skills.
References to Study (Theory) Statement and Conclusions for CAT
How to Prepare for Verbal Ability and Reading Comprehension for CAT | 9th Edition Book by Arun Sharma and Meenakshi Upadhyay
Rodha (YouTube: https://www.youtube.com/watch?v=EL9hYXQteUU)
References to Practise CAT Questions on Statement and Conclusions
Verbal Reasoning by Disha Experts (kindle)
Unacademy CAT4MBA
(https://www.youtube.com/watch?v=p1KwwOjk-zI)
Short Tricks to Solve Complex Number Questions in CAT
Complex number questions in the CAT exam often appear in the Quantitative Aptitude section and can be solved quickly with the right approach. Here are six effective tricks to simplify your preparation:
1. Use i2=−1i^2 = -1i2=−1 Efficiently
Always reduce powers of iii using:
i1=ii^1 = ii1=i,
i2=−1i^2 = -1i2=−1,
i3=−ii^3 = -ii3=−i,
i4=1i^4 = 1i4=1.
Repeat this cycle to simplify powers of iii instantly.
2. Convert to Polar Form When Multiplying
For multiplication or division of complex numbers, convert them to polar form:
z=r(cosθ+isinθ)z = r(\cos \theta + i \sin \theta)z=r(cosθ+isinθ).
Use De Moivre’s Theorem to handle powers and roots easily.
3. Use Conjugates to Simplify Divisions
To divide complex numbers, multiply numerator and denominator by the conjugate of the denominator to eliminate the imaginary part from the denominator.
4. Apply Modulus for Distance-Based Questions
Use modulus ∣z∣=x2+y2|z| = \sqrt{x^2 + y^2}∣z∣=x2+y2 for any complex number z=x+iyz = x + iyz=x+iy. This is helpful in geometry-based or coordinate format questions.
5. Visualise on the Argand Plane
Plotting complex numbers on the Argand plane (real vs. imaginary axes) can simplify addition, subtraction, and understanding geometrical relationships like collinearity or symmetry.
6. Use Properties of Roots of Quadratic Equations
If a quadratic equation has complex roots, use the identity:
If zzz is a root, the conjugate zˉ\bar{z}zˉ is also a root. This helps in quickly identifying missing roots or verifying options.
Short Tricks to Solve Calendar Puzzles Questions in CAT
Calendar-based puzzles in CAT test logical reasoning and date-based calculations. With smart shortcuts, you can solve them quickly and accurately. Here are six effective tricks to tackle calendar questions with ease:
1. Memorise Odd Days of Each Month
Know how many odd days each month contributes:
Jan: 3, Feb: 0/1 (non-leap/leap), Mar: 3, Apr: 2, etc.
Use this to calculate the day of the week efficiently.
2. Use the “Odd Days” Concept for Day Calculations
Total days ÷ 7 = Quotient + Remainder
The remainder gives the odd days, which determine the day of the week. For example, 3 odd days after Sunday means Wednesday.
3. Learn Century Code Tricks
Each century has a fixed code:
1600s: 6, 1700s: 4, 1800s: 2, 1900s: 0, 2000s: 6.
This helps in quickly determining the base weekday for any date.
4. Zeller’s Rule Shortcut
Use Zeller’s Congruence Formula for exact day calculation, or its simplified version if you're comfortable with modular arithmetic.
5. Check Leap Year Pattern
A year is a leap year if divisible by 4 (but not 100 unless also divisible by 400). This affects February and must be considered in day calculations.
6. Use Date Reversal Logic
Some puzzles ask about days like “what day is it 100 days from now?” Quickly find the remainder when divided by 7 and count forward using odd days logic.
Practice, stay focused, and we'll be back tomorrow with Day 55 CAT Preparation Tips.
Thank You. All the Best!
Frequently Asked Questions (FAQs)
1. What are Complex Numbers?
In mathematics, a complex number is an element of a number system that extends the real numbers with a particular element labeled i, known as the imaginary unit, and satisfies the equation; every complex number may be represented in the form a+bi, where a, and b are real numbers.
2. Why is this topic important for the CAT exam?
Complex numbers are those that have both real and imaginary parts. Complex number problems on the CAT examine your knowledge of equations and mathematics. Knowing this subject may help you answer difficult problems quickly, which is critical for scoring well.
3. How can I distinguish between Complex Numbers and Quadratic Equations?
Many candidates mix up complex numbers with quadratic equations. To prevent misunderstanding, review each subject independently and understand their distinct features. Practice answering a lot of questions for more clarity.
4. How can I answer the complex number and Calendar Questions quickly?
Here are some useful tips. For complex numbers, concentrate on learning crucial formulae and learning shortcuts to save time. For calendar questions, master particular strategies such as determining the day of the week for a given date. Regular practice will help you become more efficient and accurate.
5. How can previous year's questions (PYQs) help me with the reasoning section of CAT?
PYQs help you understand the sorts of questions that have previously been asked, as well as their degree of complexity. Solving these will give you an idea of what to anticipate and help you prepare for similar critical thinking questions on the CAT Exam.
6. Why are complex numbers important for CAT preparation?
Complex numbers are frequently tested in the Quantitative Aptitude section. Questions may involve basic properties, powers of i, conjugates, and modulus
7. How can I quickly solve calendar puzzle questions in CAT?
Use tricks like the odd days method, century codes, and leap year rules. These shortcuts help you determine the day of the week or solve date-based puzzles quickly and accurately.
8. What is the best way to avoid confusion between complex numbers and quadratic equations?
Focus on understanding their distinct properties: quadratic equations may have complex roots, but complex numbers involve operations on real and imaginary parts. Practice problems involving both to clarify differences.
9. How helpful are previous year questions (PYQs) for Critical Reasoning?
PYQs offer insight into the type and pattern of logical reasoning questions CAT typically asks. Regular practice with them helps build familiarity and speed in tackling critical reasoning problems.
10. What resources can I use to practice these topics more effectively?
Utilise curated PDFs, topic-wise question banks, and online mock tests. Careers360’s calendar reasoning PDF and targeted exercises on complex numbers and reasoning are great tools to reinforce concepts.
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Questions related to CAT
Have a question related to CAT ?
Hey Paridhi ,
I hope you are absolutely fine. As per your mentioned query , you have to understand the exam pattern first. Its syllabus, the type of questions and so on. Here i am mentioning some tips i hope this will be helpful for you.
- Analyse the exam pattern first and read the syllabus thoroughly. So you will get to know what subjects and topics asked in the exam.
- Collect the resources which will be beneficial for you. Like some standard books , mock papers .
- Make your foundation strong so that you can solve the standard questions easily. As foundation is important to solve difficult questions.
- Current affairs also plays important role in this exam so make yourself update by knowing the current things in environment.
- Practice mocks so that your speed will also enhance.
- Give PYQs so you will have idea of questions coming in exam.
- Do revision weekly if you not revise whatever you study then you will forget the things. So revise weekly.
To know more you can refer this :
https://bschool.careers360.com/articles/cat-preparation-strategy
Revert for further query!
Good luck !
Sakshi Sharma 18 June,2025
Hello Abhishek,
No, you cannot take admission into B. Tech Marine Engineering at CUSAT if you do not take the CAT 2025 exam. CUSAT CAT is a mandatory exam for admission into all undergraduate programs including B Tech Marine Engineering. Admission to the program will only be possible for candidates with valid CAT scores.
gopi 18 June,2025
Hi aspirant,
The Common Admission Test (CAT) is a highly competitive exam, and practicing sample questions is essential for efficient preparation.
Kindly refer to the link attached above for the sample papers.
All the best!
Rajeswari Dey 16 June,2025
Hello,
States you can apply in (B-category/management quota):
Telangana, Andhra Pradesh, Karnataka, Tamil Nadu, Kerala, and Puducherry. All allow non-domicile students for private colleges.
Approx MBBS fees (per year):
-
Telangana: Rs. 12–15 lakh
-
Andhra Pradesh: Rs. 12–18 lakh
-
Karnataka: Rs. 15–20 lakh
-
Tamil Nadu: Rs. 15–22 lakh
-
Kerala: Rs. 7–8.5 lakh
Karnataka registration:
Closed in Feb 2025. Likely to reopen for mop-up/stray rounds in June–July 2025.
Kerala registration:
Closed in March 2025. Stray round expected in June–July 2025. Dates not announced yet.
Hope it helps !
Prachi Kumari 19 June,2025
Dear Aspirant
Your rank at eleven thousand eight hundred eighty seven under the OBC reservation has a strong chance for admission to the Computer Science Engineering (CSE) program at one of the three CUSAT campuses The exact seat depends on opening and closing ranks for CSE in each campus and the round of counselling
CUSAT campuses offering BTech CSE
• School of Engineering Thrikkakkara – flagship campus in Kochi
• CUCEK Kuttanad – second campus in Alappuzha district
• Lakeside campus does not offer CSE so only two campuses are relevant
Previous closing ranks under OBC quota for CSE
• Thrikkakkara campus closed near rank one thousand
• CUCEK Kuttanad closed around six thousand two hundred in 2024
Your likelihood with rank 11887
• Thrikkakkara campus is unlikely as CSE closes much lower than your rank
• CUCEK has potential since closing ranks in recent years have extended into the high six thousands
• Seats may remain open in later rounds so you may gain admission at CUCEK
Other CSE seat possibilities under OBC
• School of Engineering might open seats in spot or mop up rounds if higher ranked students do not confirm
• CUCEK will likely accept OBC candidates up to rank one two thousand to thirteen thousand
• Keep an eye on real time counselling as closing ranks may shift downward with seat cancellations
Alternative branches and campuses
If CSE is not available at CUCEK you may consider similar branches like Electronics and Communication Engineering Information Technology Mechanical Engineering and Civil Engineering closing beyond twelve thousand under OBC
You may also add interdisciplinary programs or lateral entry courses available in Lakeside or Thrikkakkara depending on available seats
Counselling strategy recommendations
• Register and fill choices on the CUSAT admissions portal in all counselling rounds
• Place CUCEK CSE as a high preference followed by ECE or IT at Thrikkakkara or CUCEK
• Monitor round wise closing ranks through the portal or official communications
• Participate in mop up and spot rounds where seats are more likely available near your rank
Key considerations
• Cutoffs decrease between rounds allowing more opportunities in later phases
• OBC candidates compete within their category reducing competition compared to open rankings
• CUCEK is your best target campus for CSE at your rank under OBC
• You must have all documents ready like previous marksheet category certificate and CUSAT admit card for verification
Let me know if you would like a suggested list of choices tailored to your academic interest or want help tracking counselling round data
Swati 12 June,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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In a business analyst job role a lot of analysis is done, things are learned from past mistakes and the successful strategies are enhanced further. A business analyst goes through real-world data in order to provide the most feasible solutions to an organisation. Students can pursue Business Analytics to become Business Analysts.
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