CAT Number System, HCF & LCM Questions, LR & DI | Day 6 Preparation for CAT 2025

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

HCF and LCM 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

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

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.

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.

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]

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 2024, 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)

HCF LCM Question Weightage for CAT Exam

The HCF and LCM topic consistently appears in the CAT exam, with around 2 questions each year from 2020 to 2024. Mastering these concepts is crucial for scoring well in the Quantitative Aptitude section and improving overall performance and CAT marks.

Short Tricks to Crack LCM HCF Questions for CAT 2025

LCM and HCF questions are quick to solve once you master a few smart tricks. These concepts are based on number properties and often appear in the CAT Quantitative Aptitude section. Use the shortcuts below to solve such questions faster and with greater accuracy.

1. Prime Factorisation Method

Trick:

Break numbers into their prime factors.

LCM = Product of the highest powers of all primes

HCF = Product of lowest powers of common primes

Example:

Find LCM and HCF of 12 and 18.

• 12 = 2² × 3

• 18 = 2 × 3²

• LCM = 2² × 3² = 36

• HCF = 2 × 3 = 6

2. Product Rule

Trick:

For two numbers:

LCM × HCF = Product of the numbers

Example:

Find LCM if HCF of 8 and 32 is 8.

Product = 8 × 32 = 256

LCM = 256 ÷ 8 = 32

3. Co-Prime Shortcut

Trick:

If two numbers are co-prime (HCF = 1),

LCM = Product of the numbers

Example:

Find LCM of 5 and 12

Since HCF(5,12) = 1 → LCM = 5 × 12 = 60

4. Euclidean Algorithm for HCF

Trick:

Use repeated division

HCF(a, b) = HCF(b, a % b)

Example:

Find the HCF of 48 and 18

48 % 18 = 12

18 % 12 = 6

12 % 6 = 0 → HCF = 6

5. HCF and LCM of Fractions

Trick:

HCF of fractions = HCF of numerators / LCM of denominators

LCM of fractions = LCM of numerators / HCF of denominators

Example:

Find HCF of 2/5 and 4/15

HCF(2, 4) = 2

LCM(5, 15) = 15

HCF = 2 / 15

6. Work Backwards Using Product Rule

Trick:

If LCM or HCF is given, use options and check if:

LCM × HCF = Product of numbers

Example:

If HCF = 4 and LCM = 60, find the pair.

Check options like (12, 20): 12 × 20 = 240;

LCM × HCF = 60 × 4 = 240

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.