Most Important Formulas for CAT exam 2024

Important formulas or CAT exam (Quantitative Aptitude) are listed here. In the last few days before the exam, CAT 2024 aspirants must make sure that they are thorough with these CAT formulas in order to solve the Quantitative Aptitude accurately and score above 99 percentile. Check here CAT Important formulas. 

CAT Quant formulas to score 99 percentile

Being thorough with CAT important formulas is extremely necessary for aspirants if they want to score 99+ percentile in the exam. In CAT and other MBA entrance exams, Quantitative Aptitude is an important section, there are about 20 Quants questions in every exam and are usually of higher difficulty level than VARC or DILR.

CAT Quantitative Aptitude is a calculation intensive section and one needs to be thorough with the basic concepts, theorems and formulae of the topics. The CAT quant topics include Number Systems, Profit, Loss and Discount, LCM and HCF, Time and Work, Averages, Logarithm, Surds and Indices, Probability, Set Theory & Function, Trigonometry, Permutation & Combination, Co-ordinate Geometry, Mensuration, etc. All these topics have certain formulae on the basis of which the questions can be solved.

All these CAT exam topics can be mastered only by understanding their application which is possible only with practicing questions regularly. But for that, you need to understand and memorise important Quant formulas. The CAT Quantitative Aptitude questions cannot be solved without applying formulas correctly. With only a few days to go for the CAT 2024 exam, as part of your revision process, you need a CAT formulas cheat sheet. To help you with this, we have listed below the most important formulas for CAT. Also find a CAT formula sheet PDF for download (free), for CAT 2024 preparation. 

Also Read:

• CAT 2024: Last week Quantitative Aptitude Tips
• CAT 2024: Last week DILR Tips
• CAT 2024: Last week VARC Tips

CAT Important Formulas: Mensuration

There are a number of questions in CAT which belong to Mensuration. Thus, you need to know and memorise the following important CAT formulas for Mensuration

Triangle

Area = (1/2) × b × h

or

√[s(s – a)(s – b)(s – c)], where s = (a + b + c)/2

Square

Area = a × a

Perimeter = 4a

Rectangle

Area = lb

Perimeter = 2(l+b)

Cube

Volume: V = a³

Lateral surface area = 4a²

Surface Area: S = 6a²

Diagonal (d) = √3 a

Cuboid

Volume of cuboid: lbh

Total surface area = 2 (lb + bh + hl) or 6l²

Length of diagonal =√(l² + b² + h²)

Circle

Area =  πr² or πd²/4

Circumference = 2πr  or πd

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

Also Read:

• Square Root and Cube Root
• Permutation and Combination
• Mean, Mode, Median
• Binomial Theorem

CAT Important Formulas: Trigonometry

Here are important formulas for CAT Trigonometry section. Understand and memorise these formulas for solving Trigonometry questions of CAT Quantitative Aptitude.

Trigonometric Identities:

• Sine = Opposite/Hypotenuse
• Secant = Hypotenuse/Adjacent
• Cosine = Adjacent/Hypotenuse
• Tangent = Opposite/Adjacent
• Co−Secant = Hypotenuse/Opposite
• Co−Tangent = Adjacent/Opposite

The reciprocal identities are given as:

• cosec θ = 1/sin θ
• sec θ = 1/ cos θ
• cot θ = 1/tan θ
• sin θ = 1/cosec θ
• cos θ = 1/sec θ
• tan θ = 1/cot θ

CAT Important Formulas: Coordinate Geometry

Given below are the important CAT formulas for Coordinate Geometry. You need to be thorough with these formulas to be able to solve the problems accurately.

The Distance Between two Points A(x₁, y₁) and B(x₂, y₂):

AB² = (x₂ – x₁)² + (y₂ – y₁)²

The Midpoint of a Line Joining Two Points

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

[(x₁ + x₂)/1, (y₁ + y₂)/2]

The Equation of a Line Using One Point and the Gradient

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

y – y₁ = m(x – x₁)

CAT Important Formulas: Number Systems

Check below important CAT formulas for Number Systems. The questions on Number Systems asked in the Quantitative Aptitude section of CAT are based on these formulas.

• 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2
• (1² + 2² + 3² + ….. + n²) = n ( n + 1 ) (2n + 1) / 6
• (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)

Mathematical Formulas:

• (a – b)² = (a² + b² – 2ab)
• (a + b)² = (a² + b² + 2ab)
• (a + b)(a – b) = (a² – b²)
• (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
• (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
• (a + b)ⁿ = aⁿ + (ⁿC₁)a^n-1 b + (ⁿC₂)a^n-2 b² + … + (nC_n-1)ab^n-1 + bⁿ

CAT Important Formulas: Profit, Loss and Discount

Check below important CAT formulas for Profit, Loss and Discount. Memorizing these formulas will be helpful to you for solving CAT questions based on the topic.

• Profit (or) Gain = SP – CP
• Profit % = (Profit/CP) × 100
• SP = (100 + gain % )/100  × CP
• CP = 100/(100 + gain %) × SP
• Loss = CP – SP
• Loss % = Loss/(CP) × 100
• SP = (100 – loss %)/100 × CP
• CP = 100/(100 – loss %) × SP

CAT Important Formulas: LCM and HCF

Given below are the important CAT formulas you need to know to solve LCM and HCF questions of Quantitative Aptitude section of the exam.

LCM × HCF = Product of the numbers

LCM of co-prime numbers = Product of the numbers

CAT Important Formulas: Speed, Time and Distance

Given below are the important CAT formulas that you should memorise to solve Speed, Time and Distance questions of the Quantitative Aptitude section.

Distance = Speed × Time

Time = Distance/Speed

Speed= Distance/Time

CAT Important Formulas: Percentages

To solve Percentages questions of CAT exam, you need to know the following formulas:

To find what percentage of x is y: (y/x) × 100

Increase N by S % = N(1+ S/100 )

Decrease N by S % = N (1 – S/100)

CAT Important Formulas: Time and Work

To solve Time and Work questions of CAT exam, understand and memorise the following formula:

If X can do a piece of work in n days, then X’s 1 day’s work = 1/n

If X’s 1 day’s work =1/n, then X can finish the work in n days.

CAT Important Formulas: Averages

Given below is the formula for Averages. To solve CAT questions based on Averages, you must know these formulas.

Average = (Sum of observations/Number of observations)

CAT Important Formulas: Simple and Compound Interest

Simple and Compound Interest questions are always there in CAT. To solve the Simple and Compound Interest questions accurately, you should memorise these formulas.

Interest compounded Annually:

Amount= P (1+ R/100)ⁿ

Interest compounded half-yearly:

Amount=  P (1+R/2) ²ⁿ
                      100

Interest compounded quarterly:

Amount= P (1+R/2) ⁴ⁿ
                      100

When interest is compounded annually but time is in fraction:

Amount= P (1+ R)³ X P (1+R/2) ⁴ⁿ
                      100           100

When rates are different for different years, say R₁%, R₂%, R₃% for 1st, 2nd and 3rd year, respectively.

Amount= P (1+R₁) + P (1+R₂)  + P (1+R₃)
                      100            100           100

Present worth of Rs. x due n years hence is given by:

Present worth= _______x_________
                                P (1+R₃)
                                       100

CAT Important Formulas: Probability

Given below is the formula that you must memorise for solving CAT questions on Probability.

Sample Space: When we perform an experiment, then 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 E be an event.

Therefore, P(E) =n(E) / n(S)

CAT Important Formulas: Logarithm

To crack the questions based on Logarithm, here are the important CAT formulas you need to know:

• log_a (xy) = log_a x + log_a y
• log_a (x/y) = log_a x – log_a y
• log_x x = 1
• log_a 1 = 0
• log_a (xn) = n(log_a x)
• log_a x = 1/(log_x a)
• log_a x = (log_b x)/(log_b a) = (log x)/(log a)

CAT Important Formulas: Set Theory and Function

Given below are the important CAT formulas for Set Theory and Function. If you are thorough with these formulas, you can solve all the questions.

De Morgan’s Law:

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

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

• Reflexive Relation: If aRa ∀ 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.

Permutation Formula: A permutation is the choice of r things from a set of n things without replacement. Order matters in permutation.

Combination Formula: A combination is the choice of r things from a set of n things without replacement. The order does not matter in combination.

CAT Important Formulas: Mixtures and Alligations

To solve questions on Mixtures and Alligations, you must be thorough with the formula given below:

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)

Check below PDF for CAT formulas cheat sheet:

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