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CAT Number System, HCF & LCM Questions, LR & DI| Day 6

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CAT Number System, HCF & LCM Questions, LR & DI| Day 6

Edited By Irshad Anwar | Updated on Sep 19, 2023 06:42 PM IST | #CAT

In previous article 5, we discussed the strategy on how to prepare the Factors and Trailing zeroes, table (DI), conjunction and interjection - Day 5 of CAT preparation on the basis of the CAT syllabus. We have covered a major part of the number system questions for CAT under the CAT syllabus which includes HCF and LCM questions for CAT. The remaining number system topics for CAT will be covered in the upcoming articles. HCF and LCM CAT questions are also considered a good major chunk of CAT quants section which the students should revise. We are back with the strategic plan for Day 6 to propel our preparation to crack CAT-2023. In this article, we will be discussing strategy for the following topics along with CAT number system questions based on HCF and LCM questions for CAT. The topics in number system for CAT are very vast and need constant practice.

Part-1: Quantitative Aptitude for CAT 2023

Topic: Number System questions for CAT (HCF LCM CAT questions) Highest Common Factor (HCF/ GCD):

HCF is the highest common divisor which divides two (or more) numbers completely.

For Example,

12 is HCF of 36 and 48.

17 is HCF of 340 and 357

3 x 22 is LCM of (3x 24 and 33 x 22)

The most common ways of finding HCF are

Prime Factorization Method:

Eg: To find HCF of 27 and 36

27 = 33

36 = 22 x 32

HCF = 32

Division Method:

Eg: To find HCF of 27 and 36

Divide 36 by 27; the remainder is 9

Divide 27 by 9; the remainder is 0.

(This process is repeated till the remainder is 0)

Least Common Multiple (LCM):

The least value which is divisible by two or more values completely, is LCM.

For Example:

72 is LCM of 8 and 9.

2184 is LCM of 8, 13 and 21.

33 x 24 is LCM of (3x 24 and 33 x 22)

The most common way of finding LCM is

Prime Factorization Method:

Eg: To find LCM of 27 and 36

27 = 33

36 = 22 x 32

LCM = 22 x 33

LCM HCF questions, CAT Number System Questions From CAT Previous Year Papers/ HCF and LCM questions for CAT exam

The two previous year CAT questions on number system (HCF and LCM)are given below:

Q1. How many pairs of positive integers x, y exist such that HCF of x, y = 18 and product of x and y = 1620? [ CAT Question Paper]

  1. 2

  2. 8

  3. 1

  4. 3

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Solution: C

Let the two numbers be 18a and 18b where a and b are co-prime numbers.

Also, 18a x 18b = 1620

So, a x b = 1620/ (18 x 18) = 5

Therefore, (a, b) = (1, 5); the only possible pair in a and b.

Q2. A red light flashes three times per minute and a green light flashes five times in 2 min at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour? [CAT Question Paper ]

  1. 30

  2. 24

  3. 20

  4. 60

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Solution: A

Red light flashes after every 60/3=20 sec

Green light flashes after every 120/5=24 sec

Both lights will flash together if the multiples of flushing times are common

i.e. LCM (20,24) =120 sec = 2min

Thus, both lights will flash together at intervals of 120 sec= 2 minute

In 1 hour, both lights flash together 60/2 = 30 times.

Prerequisite:

To prepare for the number system for CAT exam, students must have knowledge of:

  • Prime, composite, and Co-primes

  • Factors

  • Multiples

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Tips On CAT Preparation For Number System (HCF and LCM):

  • The smallest number which when divided by a, b and c leaves a remainder R in each case then the number will be (L.C.M of a, b, c) + R.

  • The greatest number which divides a, b and c to leave the remainder R is H.C.F of (a – R), (b – R) and (c – R)

  • The greatest number which divide x, y, z to leave remainders a, b, c respectively is

  • H.C.F of (x – a), (y – b) and (z – c)

  • LCM of (a/b, c/d, e/f) = LCM (a, c, e)/ HCF (b, d, f)

  • HCF of (a/b, c/d, e/f) = HCF (a, c, e)/ LCM (b, d, f)

  • Practise different kinds of problems.

  • HCF of a and b × LCM of a and b = a × b

  • Apply the concepts to practise HCF and LCM questions.

  • Practise previous year CAT questions on number systems and LCM and HCF problems.

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References to Study (Theory):

  • Learn the concept of HCF and LCM from class 10 Mathematics NCERT (For Theory)

  • Arun Sharma: A Quantitative Approach for CAT (6th Edition)

  • 2iim Online Learning Classroom

References to Study (Practice):

  • MASTER Number System for CAT and GMAT by Nishit K Sinha.

  • Sample Papers

  • CAT previous year papers

Part-2: Logical Reasoning and Data Interpretation

Topic: Data Interpretation (Spider/ Radar Graph)

In previous articles-Day 5, strategies for DI based on Bar graph, Pie chart, Table graph and Line graph have been discussed. A different kind of DI on spiders will be discussed in this article for the CAT exam. Data interpretation is a must-come topic in the CAT Exam and other management entrance exams.

DI on Spider (Radar) Graph

It consists of equiangular spokes and each spoke represents one variable. These charts contain 0 at its centre.

1695127996344

This is a spider chart for 5 variables.

A=70

B=58

C=5

D=15

E=25

Blue line shows the value of a commodity on 5 different parameters.

Questions Based On Spider Graph From CAT Previous Year Papers

Five vendors are being considered for a service. The evaluation committee evaluated each vendor on six aspects – Cost, Customer Service, Features, Quality, Reach, and Reliability.

Each of these evaluations are on a scale of 0 (worst) to 100 (perfect). The evaluation scores on these aspects are shown in the radar chart. For example, Vendor 1 obtains a score of 52 on Reliability, Vendor 2 obtains a score of 45 on Features and Vendor 3 obtains a score of 90 on Cost. [CAT Question Paper 2019- slot 1]

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Q1. On which aspect is the median score of the five vendors the least?

  1. Customer Service

  2. Cost

  3. Reliability

  4. Quality

Ans: (1)

The median is the mid-value. For all six parameters median is as follows:

Reliability=52-53

Reach=65

Quality=62

Features=55

Customer Service = 50 (least)

Cost =75

Q2. A vendor's final score is the average of their scores on all six aspects. Which vendor has the highest final score?

  1. Vendor 1

  2. Vendor 2

  3. Vendor 3

  4. Vendor 4

Ans: (2)

Total Score of Vendors:

Vendor 1 = (52+ 80+ 73+ 40 + 55 + 75) = 375

Vendor 2 = (40+ 58+ 70+ 45 + 42 + 80) = 335

Vendor 3 = (75+ 66+ 60+ 50+ 55+ 90) = 396

Vendor 4 = (25+ 45+ 40+ 90+ 70+ 70) = 340

Vendor 3 has the highest total and hence the highest average.

Q3. A list of all the vendors who are among the top three vendors on all six aspects is?

  1. None of the Vendors

  2. Vendor 1

  3. Vendor 3

  4. Vendor 1 and Vendor 3

Ans: (3)

Vendors in top 3 in each aspect:

Reliability = Vendor 3, Vendor 5 and Vendor 1

Reach = Vendor 1, Vendor 5, Vendor 3

Quality = Vendor 1, Vendor 2, Vendor 3

Features= Vendor 4, Vendor 5, Vendor 3

Customer Service = Vendor 4, Vendor 1, Vendor 3

Cost = Vendor 3, Vendor 2, Vendor 1

Clearly only vendor 3 appears in all the three.

Prerequisite:

To Prepare Data Interpretation (Spider graph) for the CAT 2023, a student must learn:

  • Percentage (Basic)

  • Simplification and approximation

  • Mean, Mode and Median

  • Observational Skills

References to Study (Theory):

  • LRDI for CAT and GMAT by Nishit K Sinha.

  • Crack XAT YouTube Channel

References to Study (Practice):

  • https://online.2iim.com

  • How to Prepare for Data Interpretation for CAT by Arun Sharma

  • CAT previous year papers

Part-3: VARCTopic: Articles And Its Uses

Article is one of the parts of speech in English grammar which is used to modify the Noun entities.

Indefinite Articles (A and An): Used with singular nouns only.

Examples:

  • An honest man.

  • A tall man.

  • Tomorrow a man will come to see you.

  • Definite Article (The): Refers to specific nouns and can be used with both singular and plural nouns.

  • Examples:

  • The man on dice is my ideal.

  • The Bible.

Practice Questions On Articles

Direction: Choose the correct article

Q.1 Who is _________ of England now.

  1. the prime minister

  2. a prime minister

Ans: A

Q2. There is _________ restaurant near my house.

  1. a nice

  2. nice

  3. Ans: A

Q3. My grandparents live in _____________ of the city

  1. south

  2. the south

Ans: B

Q4. Is this _____________ Australian breed?

  1. a

  2. an

Ans: B

Prerequisite:

  • Knowledge of Verbal sound.

  • Knowledge of Noun (singular and Plural)

CAT Preparation Tips To Prepare Articles And Its Uses

  • Articles do not use uncountable nouns.

  • Learn the specific cases where articles should not be used

Ex: Let’s go out for dinner tonight. (Incorrect)

Let’s go out for dinner tonight. (Correct)

  • Articles should not be used with pronouns.

  • Use no Article before names of sports, subjects, nationalities, and languages.

  • Develop reading habits.

  • Practice more and more exercises.

References to Study (Theory):

  • Advanced English grammar by Wren and Martin (Oxford)

  • engvid.com (YouTube channel as well as Web)

References to Study (Practice):

  • Questions bank from iquanta.com

  • Oxford Practice Grammar (sixth edition)

  • How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)

We will be back with Day-7 strategy tomorrow at the same time. keep practising and be focused. Students can practice number system mock test for CAT and can also practice DILR and VARC alongside as well.

Thank You

All the best.

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GMAT quant section is often considered to be easier, however, its verbal section is tougher for non-native English speakers. Whereas, CAT quant section is considered to be trickier in comparison to the verbal section. Therefore, students are advised to analyse both CAT and GMAT exam pattern carefully before opting for one.

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Colleges like NIBM specialize in Finance, and IRMA has a lot of sales marketing Roles. So ultimately the choice is yours which specialization you want to pursue.

View All

1-radian measures 600. (True/False)

Option: 1

True


Option: 2

False


$111111^2$ = 

Option: 1

123456654321


Option: 2

123454321


Option: 3

123454321


Option: 4

12345654321


1111112 =___________ 

Option: 1

 123456654321


Option: 2

1234554321


Option: 3

123454321


Option: 4

12345654321


159702 is divisible by

Option: 1

7


Option: 2

9


Option: 3

11


Option: 4

6


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What best can be said about the number of satellites serving C? 

Option: 1

Must be between 450 and 725 

 


Option: 2

Cannot be more than 800 
 


Option: 3

Must be between 400 and 800 

 


Option: 4

Must be at least 100 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What is the minimum possible number of satellites serving B exclusively? 

Option: 1

100


Option: 2

200


Option: 3

500


Option: 4

250


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S? 

Option: 1

At most 475 

 


Option: 2

Exactly 475 
 


Option: 3

At least 475 

 


Option: 4

No conclusion is possible based on the given information 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

 If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE? 

Option: 1

The number of satellites serving C cannot be uniquely determined 

 


Option: 2

The number of satellites serving B is more than 1000 
 


Option: 3

All 1600 satellites serve B or C or S 

 


Option: 4

The number of satellites serving B exclusively is exactly 250 


2839155 is divisible by

Option: 1

2


Option: 2

7


Option: 3

55


Option: 4

None of the above


'a' for which x^{2}-ax+9= 0 can be written as square of a linear factor is

Option: 1

6


Option: 2

-6,6


Option: 3

\left ( 6,\infty \right )


Option: 4

\left ( -\infty,-6 \right )


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Actor

For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs. 

4 Jobs Available
Acrobat

Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.

3 Jobs Available
Video Game Designer

Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.

Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

3 Jobs Available
Radio Jockey

Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

3 Jobs Available
Choreographer

The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.

2 Jobs Available
Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

2 Jobs Available
Photographer

Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.

2 Jobs Available
Producer

An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story. 

They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.

2 Jobs Available
Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook. 

5 Jobs Available
Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. 

Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article. 

3 Jobs Available
Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available
Reporter

Individuals who opt for a career as a reporter may often be at work on national holidays and festivities. He or she pitches various story ideas and covers news stories in risky situations. Students can pursue a BMC (Bachelor of Mass Communication), B.M.M. (Bachelor of Mass Media), or MAJMC (MA in Journalism and Mass Communication) to become a reporter. While we sit at home reporters travel to locations to collect information that carries a news value.  

2 Jobs Available
Corporate Executive

Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.

2 Jobs Available
Multimedia Specialist

A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications. 

2 Jobs Available
Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues. 

5 Jobs Available
QA Manager
4 Jobs Available
Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product. 

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
Production Manager
3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
QA Lead

A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans. 

2 Jobs Available
Structural Engineer

A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software. 

2 Jobs Available
Process Development Engineer

The Process Development Engineers design, implement, manufacture, mine, and other production systems using technical knowledge and expertise in the industry. They use computer modeling software to test technologies and machinery. An individual who is opting career as Process Development Engineer is responsible for developing cost-effective and efficient processes. They also monitor the production process and ensure it functions smoothly and efficiently.

2 Jobs Available
QA Manager
4 Jobs Available
AWS Solution Architect

An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party. 

4 Jobs Available
Azure Administrator

An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems. 

4 Jobs Available
Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack 

3 Jobs Available
ITSM Manager
3 Jobs Available
Automation Test Engineer

An Automation Test Engineer job involves executing automated test scripts. He or she identifies the project’s problems and troubleshoots them. The role involves documenting the defect using management tools. He or she works with the application team in order to resolve any issues arising during the testing process. 

2 Jobs Available
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