# 50+ Important Formulas for CAT 2023 Preparation: Topic-Wise Formulas

Every MBA aspirant must be well-versed in all the formulas that may be required when solving the CAT question paper. Here is a topic-wise list of 50+ formulas for CAT 2023.

Ask any MBA aspirant and they will easily be able to tell you the importance of learning important formulas for CAT preparation. It is essential that every candidate be aware of several key CAT formulas aside from any of the tips and tricks for the CAT exam preparation. CAT formulas are mostly relevant to the Quantitative Aptitude section, which includes Maths topics. Many of these questions require the use of basic or advanced preparation formulas.

Strategies mentioned in the CAT reparation tips can also help a candidate understand the concepts and theorems better. There are many formula-based questions in CAT where all you need to do is use a formula to reach the answer. Such questions become very easy to answer if you are aware of all of the important formulas for the QA section in CAT preparation. Here is a comprehensive list of important formulas for CAT preparation that every candidate must practice. Also, check the important tips to remember these CAT formulas.

## Important Formulas in CAT 2023 Preparation

There are a number of important formulas in CAT preparation that a candidate must become fluent in. All of the formulas used in CAT 2023 are from up to the Class 12th level. Candidates must already be familiar with these formulas from their school days. However, since there is at least a 3 to 4-year gap between Class 12th and CAT preparation, it becomes easy to forget these formulas. Hence, it makes sense to regularly revise and practice using formulas when solving CAT questions. Before moving on further, here is a quick glance at the revised exam pattern of CAT 2023.

Section

No. of Questions

Time

24

40 minutes

Data Interpretation & Logical Reasoning

20

40 minutes

Quantitative Ability

22

40 minutes

TOTAL

66

120 minutes

The QA section of CAT includes many topics such as Percentages, Ratio & Proportion, Profit & Loss, HCF & LCM, Mensuration, Geometry, etc. Here are some important formulas to remember for each topic.

## Important CAT Formulas for Algebra

Square of a + b

• (a + b)(a – b) = (a2 – b2)

• (a + b)2 = (a2 + b2 + 2ab)

• (a – b)2 = (a² + b² – 2ab)

Square of a + b + c

• (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)

Cube of a + b

• (a + b)3 = a3 + 3a2b + 3ab2 + b3

• (a – b)3 = a3 – 3a2b + 3ab2 – b3

• (a3 + b3) = (a + b)(a2 - ab + b2)

• (a3 – b3) = (a – b)(a2 + ab + b2)

• (a3 + b3 + c3 – 3abc) = (a + b + c)(a2 + b2 + c2 – ab – bc – ac)

• When a + b + c = 0, then a3 + b3 + c3 = 3abc

Root Formula

(a+b)= anC1 an – 1 b + nC2 an – 2 b2 + ..... nCx an – x bx + ....... bn

## Important CAT Formulas for Number System

• (12 + 22 + 32 + ….. + n2) = n ( n + 1 ) (2n + 1) / 6

• 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2

• (13 + 23 + 33 + ….. + n3) = (n(n + 1)/ 2)2

• Sum of first n odd numbers = n2

• Sum of first n even numbers = n (n + 1)

## Important CAT Formulas for Permutation and Combination

• Combination: nCr = n! / (n-r)!r! = nPr / r!

• Permutation: nPr = n! / (n-r)!

## Important CAT Formulas for Percentages

• Percentage Change = {(Final Value – Initital Value) / Initial Value} x 100

• Total Percentage Change for two successive changes of a% and b% = (a + b + ab/100)%
eg. for two successive changes of 10% and 20%, the total percentage change will be = (10 + 20 + 10*20/100)% = 32%

### Important Fractions and Their Percentage Values

Fraction

Equivalent Percent

Decimal Value

1/2

50%

0.5

1/3

331/3%

0.333...

2/3

662/3%

0.666...

1/4

25%

0.25

3/4

75%

0.75

1/5

20%

0.2

1/6

162/3%

0.1666....

5/6

831/3%

.8333...

1/8

121/2%

0.125

3/8

371/2%

0.375

5/8

621/2%

0.625

7/8

871/2%

0.875

1/9

111/9%

0.111...

1/10

10%

0.1

1/11

91/11%

0.999...

5/11

455/11%

0.4545...

1/12

81/3%

0.08333...

1/16

61/4%

0.0625

1/25

4%

0.04

1/32

31/8%

0.03125

1/50

2%

0.02

## Important CAT Formulas for Averages

• Average = Total Sum / Total Number

• Weighted Average = (w1x1 + w2x2 + w3x3 .... + wnxn) / (w1 + w2 + ..... + wn)

## Important CAT Formulas for Simple Interest and Compound Interest

• Amount = Principle + Interest

• Simple Interest = P x r x n

• Compound Interest = P(1 + r)n – P

## Important CAT Formulas for Profit, Loss and Discount

• Profit = SP – CP

• Profit Percentage = (SP – CP)/CP x 100

• Loss = CP – SP

• Loss Percentage = (CP – SP)/CP x 100

• Discount = MP – SP

• Discount Percentage = (MP – SP)/MP x 100

• Total Discount on successive discounts of a% followed by b% = (a + b – ab/100)%

• If articles worth Rs. b are free along with articles worth Rs. a, Discount = y/(x+y) x 100

## Important CAT Formulas for HCF and LCM

• HFC of Fractions = (HCF of numerators) / (LCM of denominators)

• LCM of Fractions = (LCM of numerators) / (HCF of denominators)

• LCM x HCF = Product of Numbers

## Important CAT Formulas for Set Theory & Function

Demorgan’s Law is the basic and most important formula for sets, which is defined as

• (A ∩ B) ‘ = A’ U B’ and (A U B)’ = A’ ∩ B’

The relation R⊂A×AR⊂A×A is said to be called:

• Reflexive Relation: If a R a ∀∀ a ∈∈ A.

• Symmetric Relation: If aRb, then bRa ∀∀ a, b ∈∈ A.

• Transitive Relation: If aRb, bRc, then aRc ∀∀ a, b, c ∈∈ A.

If any relation R is reflexive, symmetric, and transitive in a given set A, then that relation is known as an equivalence relation.

## Important CAT Formulas for Logarithms

• log1 = 0

• logx = 1

• logx (mn) = logx m + logx n

• log(m/n) = logx m – logx n

• logx ab = b logx a

• logx ax = a

• logx m = (logy n) x (loga n)

## Important CAT Formulas for Time, Speed, and Distance

• Speed = Distance / Time

• 1 km/h = 5/18 m/s

• 1 m/s = 18/5 km/h

## Important CAT Formulas for Boats and Streams

• Sdownstream = Sboat + Sstream

• Supstream = Sboat - Sstream

## Important CAT Formulas for Mixtures and Alligations

Alligation: It is the rule that enables us to find the ratio in which two or more ingredients at the given price must be mixed to produce a mixture of the desired price.

Mean Price: The cost of a unit quantity of the mixture is called the mean price.

Rule of Alligation:

If two ingredients are mixed, then

• (Quantity of cheaper / Quantity of dearer) = (C.P. of dearer – Mean Price / Mean price – C.P. of cheaper)

## Important CAT Formulas for Trigonometry

• sin A = Perpendicular / Hypoteneuse = a / c

• cos A = Base / Hypoteneuse = b / c

• tan A = Perpendicular / Base = a / b

• cot A  = 1 / tan A

• sec A = 1 / cos A

• cosec A = 1 / sin A

Trigonometric Identities:

• Sine=Opposite/Hypotenuse

• Co−Secant=Hypotenuse/Opposite

The reciprocal identities:

• sinΘ=1/CosecΘ

• cosΘ=1/secΘ

• tanΘ=1/cotΘ

• CosecΘ=1/sinΘ

• secΘ=1/cosΘ

• cotΘ=1/tanΘ

## Important CAT Formulas for Mensuration

Rectangle

• Area of a Rectangle = length (l) x breadth (b)

• Perimeter of a Rectangle  = 2(l + b)

Square

• Area of a Square = Side x Side = s2

• The perimeter of a Square = 4s

Triangle

• Area =b×h/2 or √s(s-a)(s-b)(s-c)…………….where s=a+b+c/2

Circle

• Area =  πr2 or πd2/4

• Circumference = 2πr  or πd

• Area of sector of a circle = (θπr2)/360

Cuboid (length = l, breadth = b, height = h)

• Volume of Cuboid = l x b x h

• Surface Area of Cuboid = 2(lb + bh + lh)

• Length of Diagonal = √(l2 + b2 + h2)

Cube

• Volume of Cube = l3

• Surface Area of Cube = 6l2

• Length of Diagonal = l√3

Cylinder

• Volume of a Cylinder = (3.14) r2h

• Curved Surface Area of a Cylinder = 2 (3.14) rh

• Total Surface Area = 2 (3.14) rh + 2 (3.14) r2

Sphere

• Volume of a Sphere = 4/3 (3.14) r3

• Surface Area of a Sphere = 4 (3.14) r2

Cone (height = h, slant height = l)

• Volume of a Cone = 1/3 (3.14) r2h

• Curved Surface Area of a Cone = (3.14) rl

• Total Surface Area of a Cone = (3.14) rl + (3.14) r2

NOTE: (3.14) is an approximation of pi.

Sample Space: When performing an experiment, the set S of all possible outcomes is called the sample space.
Event: Any subset of a sample space is called an event.
The probability of Occurrence of an Event: Let S be the sample and let E be an event.
Therefore, P(E) =n(E) / n(S)

## Important CAT Formulas for Coordinate Geometry

The Distance Between Two Points A and B:

• AB2 = (Bx – Ax)2 + (By – Ay)2

The Equation of a Line Using One Point and the Gradient

The equation of a line that has gradient m and which passes through the point (x1, y1) is:

• y – y1 = m(x – x1)

The Midpoint of a Line Joining Two Points

The midpoint of the line joining the points (x1, y1) and (x2, y2) is:

• [½(x1 + x2), ½(y1 + y2)]

## How to Remember Important Formulas for CAT 2023

Candidates are often seen worried about how to remember the important CAT 2023 formulas. There are various methods, mnemonics, and learning tricks you can use to remember the important formulas. If your basic mathematical concepts are clear, you may even be able to figure out some of the formulas used in CAT 2023 without the need for learning them.

• As an example, if we imagine a Cylinder as infinite disks stacked on top of each other, the Curved Surface Area of a Cylinder becomes equal to the Perimeter of the Base Circle times Height. Hence, 2 (3.14) r multiplied by h.

However, the best way to remember important formulas for CAT is to use them in solving questions. Practicing will help you become familiar with important formulas. It will also train you to use these formulas with more speed and accuracy.

## CAT 2023 Best Coaching Institutes in India

Candidates can prepare for CAT 2023 at the following coaching institutes:

Related Articles:

If you have any queries, please write to us on the CollegeDekho QnA Zone. For help with admission to MBA colleges accepting CAT, apply through the Common Application Form (CAF) or call our helpline number 1800-572-9877. Stay tuned with us for all the tips and tricks to crack CAT 2023!

## FAQs

Is it possible to excel in CAT without a thorough knowledge of formulas?

While formulas are an integral part of CAT preparation, it is also crucial to develop logical reasoning, critical thinking, and analytical skills. Understanding the concepts and their applications will allow you to solve problems even if you momentarily forget a specific formula.

What are some important formulas for CAT preparation?

Some important formulas for CAT preparation include those related to arithmetic, algebra, geometry, number systems, percentages, profit and loss, time and work, probability, and permutations and combinations.

How can I memorize and retain the CAT formulas?

To memorise and retain CAT formulas, practice regularly and apply the formulas in solving various types of problems. Create flashcards or cheat sheets to revise the formulas frequently. Understand the derivation and logic behind each formula to enhance comprehension and retention.

Are there any shortcuts or tricks for remembering CAT formulas?

Yes, there are certain mnemonic techniques and patterns that can help in remembering CAT formulas. For example, creating acronyms or using visual imagery can make it easier to recall the formulas during exams.

Should I focus on memorizing CAT formulas or understanding their applications?

It is crucial to strike a balance between memorizing CAT formulas and understanding their applications. While memorizing helps in quick recall during exams, understanding the underlying concepts and applications will enable you to apply the formulas effectively in problem-solving.

How can I practice using these CAT formulas effectively?

Solve a variety of CAT-level problems that require the application of these formulas. Practice from previous years' question papers and CAT preparation books. Additionally, take mock tests to simulate exam-like conditions and enhance your speed and accuracy in utilizing the formulas.

Can I create my own formula sheet for CAT preparation?

Yes, creating a personalized formula sheet can be helpful for CAT preparation. Include formulas that you find particularly important or difficult to remember. Writing them down and reviewing them regularly will aid in reinforcement and familiarity.

Are there any online resources or books specifically dedicated to CAT formulas?

Yes, there are several online resources and CAT preparation books that provide comprehensive formula compilations. Some popular books include Arun Sharma's "How to Prepare for Quantitative Aptitude for CAT" and Nishit Sinha's "The Pearson Guide to Quantitative Aptitude for CAT."

Should I focus only on CAT formulas or also practice problem-solving techniques?

It is essential to not solely rely on memorizing CAT formulas but also develop problem-solving techniques. Understanding the logic and approach behind different types of questions will allow you to apply the appropriate formulas effectively.

How can I revise and reinforce the CAT formulas regularly?

Set aside dedicated time for CAT formula revision regularly. Use flashcards, practice problems, and solve mock tests to reinforce your understanding and memorization of the formulas.

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