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

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

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]

1695127996804

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.

Articles

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Questions related to CAT

Have a question related to CAT ?

Hello aspirant,

A bachelor's degree from an accredited university with a CGPA of at least 50% (or an aggregate of 45% for the SC, ST, and PwD/DA categories) is required in order to appear in the CAT exam in 2024. Duration and manner of degree: The course needs to last three years. The mode might be online, distant, or regular.

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Thank you

Hope this information helps you.

Hello student

As a self-employed individual with your own cafe, you'll need to provide documents that establish your business and work experience. Here are some documents you can prepare for your CAT application:


1. *Business Registration Documents*:

- Partnership Deed (already have)

- Business PAN Card (already have)

- FSSAI License (already have, though it's in your partner's name)

2. *Proof of Business Ownership*:

- Affidavit or declaration stating your ownership and role in the cafe

- Business registration certificate (if you have one)

3. *Proof of Work Experience*:

- A letter or certificate from your partner or co-owner confirming your work experience and role in the cafe

- A detailed resume highlighting your entrepreneurial journey and responsibilities

4. *Financial Documents*:

- Income Tax Returns (ITRs) for the last 2-3 years (if applicable)

- Balance Sheets and Profit & Loss statements for your cafe (if audited)

5. *Rental Agreement*:

- Already have, but ensure it's updated and signed


Additional tips:


- Ensure all documents are scanned and uploaded in the required format (usually PDF or JPEG)

- Keep your documents organized and easily accessible for the application process

- Be prepared to provide additional information or clarification if requested by the admission authorities


Remember to check the specific requirements for each B-school you're applying to, as they may vary. Good luck with your CAT application!

Hello aspirant,
The CAT exam syllabus is not officially prescribed, but it generally includes topics from the following sections:

1. Verbal Ability and Reading Comprehension (VARC)
2. Data interpretation and logical reasoning
3. Quantitative ability

  • Arithmetic

  • Algebra

  • Geometry and Mensuration

  • Number System

  • Modern Math

It seems unlikely that you would be able to get admission in the BTech CS branch at BIT Sindri or Mesra with a CML rank of 2058 and category rank of 433.

Key points:

1. The search results indicate that a CML (Common Merit List) rank of 2058 is quite low for admission to premier engineering colleges like BIT Sindri or NIT Mesra.

2. The cutoff ranks for BTech CS branch at these institutes are usually much higher, often in the range of 1000-2000 for the general category.

3. With a category rank of 433, you may have a better chance of getting admission in the reserved category quota, but the competition is still quite high.

4. The search results do not provide specific cutoff details for BIT Sindri or NIT Mesra, but the general trend suggests your current ranks may not be sufficient for the CS branch in these institutes.

My advice would be to:

1. Check the latest cutoff ranks and admission criteria on the official websites of BIT Sindri and NIT Mesra.

2. Explore other options like state-level engineering colleges or NITs where your current ranks may have a better chance of securing admission.

3. Consider improving your performance in the next attempt of the entrance exam to increase your chances of getting into your desired BTech program.



For VARC, read daily from diverse sources (newspapers, novels, journals) to improve comprehension and vocabulary. Practice RC passages and verbal ability questions regularly. For DILR (Data Interpretation and Logical Reasoning) and QA (Quantitative Aptitude), solve previous years' papers and take mock tests to identify weak areas. Join a coaching institute or online courses for guidance and stay consistent with your study schedule. Review and analyze your performance in mocks to understand mistakes and improve. Maintain a positive mindset and stay disciplined in your preparation.

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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