# Important Formulas for CAT 2024 Quantitative Aptitude Preparation

**Important Formulas for CAT Preparation:** Formulas are crucial aspects of CAT exam preparation. So let's get familiar with the importance of CAT formulae and some important CAT formula sheet crucial for CAT exam preparation. When it comes to CAT preparation for the Quantitative Aptitude (QA) section, the most important thing is remembering the formulas and how to apply them in an actual CAT exam. It will help to solve the questions with accuracy and speed.

Here, we have mentioned all the important formula for CAT 2024 along with the important CAT Quantitative Aptitude formulas. Also, over the internet and in recommended CAT preparation books, CAT formula cheat sheet are available which a candidate can use during their preparation. Also, candidates are required to keep revising the following CAT quant formulas from this CAT formula sheet right before the examination.

## Important Formulae for CAT 2024 - Quantitative Ability Section

Check out below the CAT formulas for quantitative aptitude. In this article, we have also attached a CAT Formulas pdf file to help candidates revise CAT formula sheet easily.

### CAT 2024 Basic Mathematical Formulas

- (a + b)² = (a² + b² + 2ab)
- (a – b)² = (a² + b² – 2ab)
- (a + b)(a – b) = (a² – b²)
- (a + b)² = (a² + b² + 2ab)
- (a³ – b³) = (a – b)(a² + ab + b²)
- (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
- (a³ + b³) = (a + b)(a² – ab + b²)
- When a + b + c = 0, then a³ + b³ + c³ = 3abc
- (a³ + b³ + c³ – 3abc) = (a + b + c)(a² + b² + c² – ab – bc – ac)
- (a + b)n = an + (nC1)an-1b + (nC2)an-2b² + … + (nCn-1)abn-1 + bn

**Important formula for CAT**** 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)

**Formulas for LCM and HCF**

- LCM × HCF = Product of the Numbers
- LCM of Co-prime Numbers = Product Of The Numbers

**Mathematical Formulas for Profit, Loss, and Discount**

- Profit % = Profit/(C P)×100
- Profit/Gain = (S.P.) – (C.P.)
- C P = 100/(100+gain %)×S P
- S P = (100+gain % )/100 ×C P
- Loss % = Loss/(C.P.)×100
- Loss = (C.P.) – (S.P.)
- C P = 100/(100-loss %)×S P
- S P = (100-loss %)/100×C P

**Important formula for CAT ****Percentages Topic**

Find what percentage of X is Y: Y/X x 100

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

**Important Formulas for Speed, Time, and Distance**

- Speed= Distance/ Time
- Distance= Speed x Time
Time= Distance/ Time

**Time and Work Formulas (Basic Formulas)**

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= is 1/n, then X can finish the work in n days.

**Averages Formula**

Average= Sum of observations/ Number of observations

**Simple and Compound Interest Formula**

- Simple Interest: P x i x n (P= Principle, i= interest rate and n= term of the loan)
- Compound Interest:
Compound Interest = [P(1+i)

^{n}] - PCompound Interest = P[(1+i)

^{n-1}]

**Mathematical Logarithm Formulas**

- If n and a are positive real numbers, and a is not equal to 1, then If ax = n, then log a n = x
- log of 1 to any base is 0 (log b 1 = 0)
- log of any number to base as itself is 1, log a a = 1
- The logarithm of a Product (log a pq = log a p + loga q)
- The logarithm of a Fraction (log a (p/q) = log a p – log a q)
- log a pn = n log a p
- a(log a p) = p
- Base Change Rule of Logarithms: (log a n = log b n × log a b)

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### CAT 2024 Trigonometry Formulae

Apart from basic Mathematics fundamental formulas check out some CAT Quant formula cheat sheet for the trigonometry part given below.

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

CosecΘ=1/sinΘ

secΘ=1/cosΘ

cotΘ=1/tanΘ

sinΘ=1/CosecΘ

cosΘ=1/secΘ

tanΘ=1/cotΘ

**Mathematical Mensuration Formulas**

Rectangle

Area = lb

Perimeter = 2(l+b)

Square

Perimeter = 4a

Area = a×a

Triangle

Area =b×h/2 or √s(s-a)(s-b)(s-c)___where s=a+b+c/2

Cube

Volume: V = l3

Surface Area: S = 6s2

Diagonal (d) = √3l

Lateral surface area = 4a2

Circle

Circumference = 2πr or πd

Area = πr² or πd²/4

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

Cuboid

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

Volume of cuboid: lbh

Length of diagonal =√(l²+b²+h²)

**Mixtures and Allegations**

If two ingredients are mixed, then

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

**Coordinate Geometry**

The Distance Between two Points A and B:

- AB² = (Bx – Ax)² + (By – Ay)²

The Midpoint of a Line Joining Two Points

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

- [½(x
_{1}+ x_{2}), ½(y_{1}+ y_{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 – y
_{1 }= m(x – x_{1})

**Read more;**

- CAT Question Papers with Solutions PDF
- CAT Quantitative Aptitude Syllabus

### Important Formulae for CAT 2024: Surds and Indices

**Law of Indices**

i. a^{m} × a^{n} = a^{(m+n)}

ii. (a^{m}) / (a^{n}) = a^{(m-n)}

iii. (a^{m})^{n} = a^{(m n)}

iv. (a b)^{n} = a^{n} b^{n}

v. (a / b)^{n} = a^{n} / b^{n}

vi. a^{0} = 1

**Surds**

Surds:

Let a be a rational number and n be a positive integer such that a^(1/n) = √[n]{a}. Then, √[n]{a} is called a surd of order n.

Laws of Surds:

i. ^{n}√[a = a^{(1/n)}

ii. ^{n}√ab = ^{n}√a× ^{n}√b

iii. ^{n}√a/b = ^{n}√a / ^{n}√b

iv. (^{n}√a)^{n} = a

v. ^{m}√^{n}√a = ^{mn}√a

vi. (^{n}√a)^{m} = ^{n}√a^{m}

**Mixtures and Allegation Formula**

If 2 ingredients are mixed, then

(Quantity of cheaper/ Quantity of dearer) = (C.P of dearer - Mean price/ Mean price - C.P of cheaper)

**Know more on;**

- CAT Preparation Strategy
- CAT Preparation Tips for Beginners

**Permutation and Combination Formulae for CAT **Permutation Formula

Permutations: ^{n}P_{r} = n! / (n - r)!

Combinations: ^{n}C_{r} = n! / [(n - r)! r!] = ^{n}P_{r} / r!

**Formulas for Set Theory and Function**(A ∩ B) ‘ = A’ U B’ and (A U B)’ = A’ ∩ B’f

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## Important Formula for CAT Preparation in 2024

The questions in the QA section are from various topics such as Profit, Loss and Discount, Number System, Time and Work, LCM and HCF, Logarithm, Averages, Set theory and function, Probability, Permutation and combination, Trigonometry, Mensuration, Coordinate Geometry, etc. All formulas for Quantitative Aptitude are the basic and indispensable part of CAT revision tips that will help candidates ace the quantitative section in the CAT 2024 exam.

CAT important formulas act as an elixir to doing excellent in the QA section. So as aspirants start their CAT preparation 2024, here is the list of important formulas that a candidate must master in order to crack the Common Admission Test with a high score.

**Know how the CAT score vs percentile is calculated.**

**Exam:**CAT