Hello CAT 2024 aspirants! We are now in the final week of the 60-day CAT 2024 preparation guide. For MBA admissions for the 2025-2027 session, the Common Admission Test is scheduled for November 24, 2024. On day 55 of Careers360's 60-day CAT 2024 preparation guide, we’ll explore strategies and approaches for Data Sufficiency questions in Quantitative Aptitude, Number and Letter Series in Logical Reasoning , and “Flaws and Paradox” (Critical Reasoning) in Verbal Ability. These insights will help you study effectively and excel in the CAT entrance test this year.
This Story also Contains
Part-1: Quantitative Aptitude for CAT exam
Part-2: CAT 2024 Preparation Tips: CAT DILR tips Logical Reasoning and Data Interpretation)
On Day 55 of your CAT 2024 preparation guide, we dive into the 'Number and Letter Series' questions and answers for CAT preparation. Alongside detailed explanations, we provide you with the tools needed to succeed. As you continue your CAT 2024 preparation, don't overlook the significance of mastering 'Number and Letter Series' questions. We've included comprehensive solutions to help you excel in this area of the exam. You can also download the data sufficiency questions PDF to further your preparation.
As the CAT 2024 entrance test approaches, make sure you've thoroughly covered 'Number and letter series questions with answers for CAT preparation.' Our article not only offers solutions but also presents effective strategies for conquering these challenging problems.
Part-2: CAT 2024 Preparation Tips: CAT DILR tips Logical Reasoning and Data Interpretation)
CAT Exam Important Topic: Strategy to Prepare ”Data sufficiency questions for CAT-2024”s
Important Concept/Formula Used in CAT data sufficiency reasoning
Concepts and Formulas Used in CAT data sufficiency reasoning are given below:
Data Sufficiency question, have the answer options which generally feature in this question type:
Give answer (A) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
Give answer (B) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
Give answer (C) if the data either in Statement I or in Statement II alone are sufficient to answer the question.
Give answer (D) if the data even in both Statements I and II together are not sufficient to answer the question.
Give answer (E) if the data in both Statements I and II together are necessary to answer the question.
CAT exam 2024:
Data Sufficiency In Quantitative Aptitude: CAT Previous Years Questions On Data Sufficiency
General Instructions for Data Sufficiency Questions for CAT exam:
Choose option A: If Statement 1 ALONE is sufficient; statement 2 is not sufficient
Choose option B: If Statement 2 ALONE is sufficient; statement 1 is not sufficient.
Choose option C: If Statements 1 & 2 TOGETHER are sufficient but are not sufficient independently.
Choose option D: If Each statement is INDEPENDENTLY sufficient.
Choose option E: If Statements together are NOT sufficient. Additional data is required.
Q1. Is the positive integer P prime?
Statement 1: 2P+1 is prime
Statement 2: P - 8 is a perfect square less than 25 [CAT Level]
A
B
C
D
E
Solution: C
Statement 1: 2P+1 is prime
Prime numbers are 2, 3, 5,7, 11, 13, 17, …….
If 2P+1 = 3, then P = 1 which is not a prime number.
If 2P+1 = 5, then P= 2 which is a prime number.
If 2P+1 = 7, then P= 3 which is a prime number.
If 2P+1 = 11, then P= 5 which is a prime number.
We can never get a prime number further.
So, we cannot say that the P is a prime or not.
Therefore, statement 1 is not sufficient.
Statement 2:
P - 8 is a perfect square
i.e. P- 8 = x2, where x is a positive integer.
So, P = x2 + 8
If x2 =1, then P= 9 is not a prime
x2 = 4, then P = 12 is not a prime number
x2 = 9, then P =17 which is a prime number.
x2 = 16, then P =24 which is a prime number.
So, we cannot say that the P is a prime or not.
Therefore, statement 2 is not sufficient.
Combined 1 and 2:
We are not getting any common solution. So, we will say there is no such Prime number.
Therefore, we can say our answer is “No”. Hence, both statements together are sufficient to answer the question.
The answer is option ‘C’.
Q2. What is n (n is an integer)?
Statement 1: n > 10
Statement 2: n2 < 144 [Practice Question: Easy]
A
B
C
D
E
Solution: C
Statement 1: n> 10, n can be anything greater than 10.
No unique answer.
Therefore, statement 1 is not sufficient.
Statement 2:
n2 < 144
n= 11, 10, 9, …
n= -11, -10, -9, …
Therefore, statement 2 is not sufficient.
Combined 1 and 2:
We have a unique value in common i.e.. n =11.
The answer is option ‘C’.
Tricks and Tips for CAT questions on data sufficiency problems
Find the CAT tips and tricks for Data Sufficiency Questions below:
Never assume anything on your own.
Be careful while answering questions like
Is the value of x can be calculated?”
When we get the answer to the question as 'No', we tend to mark the answer as Data Insufficient. But, even 'no' is an answer in some cases and this might mean that the data is sufficient
Carefully read the directions.
We need not solve the question completely. We must find out whether the answer can be calculated or not.
Practise Previous years questions to get familiar with the types of questions being asked.
CAT entrance exam: Prerequisite to solve data sufficiency questions
Prerequisites to data sufficiency reasoning are given below:
Knowledge of basics of each topic in quants.
Observational Skills
Analytical and problem-solving abilities
References to Study (Theory) CAT data sufficiency
Best sources to study data sufficiency for CAT are given below:
How to Prepare Quantitative Aptitude by Arun Sharma (7th Edition)
CAT Exam Important Topic: Strategy to Prepare “Flaws and Paradox” (Critical Reasoning) for CAT-2024
Important Concept of CAT Flaws and Paradox (Critical Reasoning questions)
The concepts used in Flaws and Paradox CAT questions are given below:
Paradox question contains two seemingly contradictory statements and you were asked to resolve the discrepancy.
Format of question is generally as follows:
Which of the following, if true, would best explain the discrepancy above?
Or
Which of the following, if true, would best resolve the paradox?
CAT Practice Questions on Flaws and Paradox (critical reasoning questions for CAT)
Flaws and Paradox CAT Sample Question:
A recent archaeological expedition in the American sub-continent revealed many skeletons of animals that were supposed to die about thousands of years ago. Further research suggested that all the skeletons had been exposed to temperatures in excess of 600 degrees Kelvin. This fact provided grounds for speculation that they were killed and cooked by local tribes at that time. However, some of the skeletons belonged to animals that were considered sacred by those tribes and were never hunted or eaten.
Which of the following best explains the apparent discrepancy above?
Some of the skeletons found during the expedition belonged to animals that no longer inhabit the area.
Skeletons of most animals did not have damages typical of the skeletons of animals that had been killed, cut, and cooked.
Tribes that inhabited the American sub-continent 1000 years ago used fire to cook food.
Another study indicated that there was a great famine in the American sub-continent at that time, which forced local tribes to look for alternative sources of food.
A further study indicated evidence of a large fire that had occurred in the American sub-continent approximately 1000 years ago.
Solution and Strategy for Flaws and Paradox(critical reasoning questions for CAT) are given below:
CAT Strategy 1: Identify the paradox.
Studies revealed that animals were killed and cooked.
Studies also revealed that some skeletons belonged to those animals which were considered sacred.
These are the two contradicting statements. (Paradox)
CAT Strategy 2: Changing a paradox into a simple problem.
One can ask a simple question:
“Why were the scared animals exposed to a temperature in excess of 600-degree kelvin?”
CAT Strategy 3: Elimination of choices that have no relevance:
Go through each option:
Option (1): does not make any sense.
Option (2): Increasing the paradox.
Option (3): It does not answer the question.
Option (4): It does not explain the burning of sacred animals.
Option (5): In a fire, all animals will be burnt irrespective of their sacredness. Hence resolving the paradox.
Tips and Tricks for Flaws and Paradox questions for CAT exam 2024
Tips to approach questions on paradoxes
Understand “the line of reasoning”.
Find the possible contradictions in the argument.
Find the assumption which might reconcile and reconnect the contradictions
Tips to approach questions on paradoxes
Understand “the line of reasoning”.
Find the possible errors in the argument.
Practice questions daily (Fewer questions but daily)
CAT 2024: Prerequisite to Flaws and Paradox
Knowledge of basic components of statements and arguments.
Reading Skills.
References to Study (Theory) Flaws and Paradox for CAT exam
How to Prepare for Verbal Ability and Reading Comprehension for CAT | 9th Edition Book by Arun Sharma and Meenakshi Upadhyay
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The CAT 2025 exam is a national-level MBA entrance test for IIMs and top B-schools in India. It will be held on 30th November 2025 in computer-based mode across ~170 cities.
The registration is open from 1st August to 13th September 2025 on
iimcat.ac.in
.
Admit cards will be available from 5th November 2025 onward.
Graduates with at least 50 marks (45 for SC/ST/PwD) are eligible to apply.
The exam tests English, Reasoning, and Quantitative Aptitude in three timed sections.
With 305 marks in ICAR PG and being from ST category, your chances of getting an AIEEA (CAT) seat is good, especially in plant sciences and less competitive subjects
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 ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
Assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the first customer's order be considered closed ?
Six sticks of equal lengths were kept in the vertical position in an empty flower-vase, to be arranged at the six corners of a regular hexagon. The two ends of each of the sticks were of different colours.
The top ends of the sticks were one of each of the following colours – Red, Cyan, Pink, Brown, Black and Green. The bottom ends were one of each of the following colours – Blue, Yellow, White, Orange, Purple and Grey. Both the sets of colours mentioned were in no particular order.
It was also known that :
a) The stick with the red colour was opposite to the stick with the blue colour
b) There were exactly two sticks whose both ends had colours whose names started with the same letter
c) The stick with the grey colour was adjacent to the stick with the white colour
d) The stick with the cyan colour was adjacent to both the sticks with the brown colour and the one with the blue colour
e) The stick with the purple colour was adjacent to both the sticks with the grey colour and the one with the green colour
f) The stick with the white colour was opposite to the stick with the green colour
Question :
What was the colour of the bottom end of the stick having brown colour at the top end ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
Assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the third customer's order be considered closed ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis, when would the second customer's order be considered closed ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis, when would the third customer's order be considered closed ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
A fourth customer comes in and orders two plates of French Toast at 6.24 pm. Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis. For exactly how many minutes would one of the friends be idle from 6.00 pm till serving the last customer, assuming that the four customers were the only ones to have come in within the period being discussed ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
Had Niloy been absent on that day, and assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the fourth customer's order (refer to the previous question) be considered closed ?
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 ?
The Jadavpur University’s Prince Anwar Shah Road hostel consists of two large separate buildings, one for the ladies and the other for the gents, while having a common kitchen and dining hall. It is the hostel of the CS and the EEC department of engineering students of the university.
In recognition of the growing dissatisfaction and hence complaints among the inmates of the hostel regarding the menu served for dinner, the Dean of the engineering department, Dr Aparesh Sanyal, personally decided to investigate the matter. He set about collecting information about the preference of dinner among the inmates, separately from the gents and the ladies wing of the hostel.
Dr Sanyal was able to gather the following partial information :
Hostel inmates
Menu preference for dinner
Total
Egg Meal
Fish Meal
Chicken Meal
Gents
20
Ladies
64
Total
60
The Warden of the hostel was consulted, who after investigation declared that the following facts were clear :
1. Forty percent of the hostel inmates were ladies
2. One-third of the gentlemen inmates preferred an egg meal for dinner
3. Half the hostel inmates preferred either fish meal or chicken meal
Question:
What proportion of the lady hostel inmates preferred a fish meal for dinner ?
A career as Marketing Director is also known as a marketing expert who is responsible for the overall marketing aspect of the company. He or she oversees plans and develops the company's budget. The marketing Director collaborates with the business team to plan and develop the marketing and branding strategies for the company's products or services.
A Business Development Executive identifies and pursues new business opportunities to drive company growth. They generate leads, build client relationships, develop sales strategies, and analyse market trends. Collaborating with internal teams, they aim to meet sales targets. With experience, they can advance to managerial roles, playing a key role in expanding the company’s market presence and revenue.
Content Marketing Specialists are also known as Content Specialists. They are responsible for crafting content, editing and developing it to meet the requirements of digital marketing campaigns. To ensure that the material created is consistent with the overall aims of a digital marketing campaign, content marketing specialists work closely with SEO and digital marketing professionals.
A Sales Manager leads a sales team to meet targets, formulates strategies, analyses performance, and monitors market trends. They typically hold a degree in management or related fields, with an MBA offering added value. The role often demands over 40 hours a week. Strong leadership, planning, and analytical skills are essential for success in this career.
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A Marketing manager plans and executes marketing initiatives to create demand for goods and services and increase consumer awareness of them. A marketing manager prevents unauthorised statements and informs the public that the business is doing everything to investigate and fix the line of products. Students can pursue an MBA in Marketing Management courses to become marketing managers.
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Digital marketing is growing, diverse, and is covering a wide variety of career paths. Each job function aids in the development of effective digital marketing strategies and techniques. The aims and objectives of the individuals who opt for a career as a digital marketing executive are similar to those of a marketing professional: to build brand awareness, promote company services or products, and increase conversions. Individuals who opt for a career as Digital Marketing Executives, unlike traditional marketing companies, communicate effectively through suitable technology platforms.
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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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