Important Quant Formulas for CAT Preparation 2025, Check Key Formulas

Important Quant Formulas for CAT Preparation 2025: The Quantitative Aptitude section in CAT 2025 can be tough for many students. To do well in this section, candidates must understand the concepts and know how to use the right formulas quickly and correctly. With the CAT 2025 examcoming up, this is the right time to revise and strengthen the basics. The following cheat sheet will help learn and remember all the important formulas for the CAT Quant Section. Practice these formulas regularly through questions to improve speed and accuracy. Continue reading blog to know all the Important Quant Formulas for CAT Preparation 2025 in detail. 

CAT 2025 Quant Formula of Mensuration

Mensuration is a core topic in CAT 2025 Quantitative Aptitude, focusing on the measurement of geometric figures. Questions from this section often involve calculating areas, perimeters, volumes, and surface areas of various 2D and 3D shapes. A solid grasp of these formulas is essential for solving geometry-based problems.

Formulas for 2D Shapes

The 2D shape formulas are as given below- 

• Triangle:
  • Area = (1/2)×b×h
  • or square root of [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)
• Circle:
  • Area = πr^2 or πd^2/4
  • Circumference = 2πr or πd
  • Area of sector of a circle = (θπr2)/360

Formulas for 3D Shapes

The 3D shape formulas are as given below- 

• Cube:
  • Volume: V=a^3
  • Lateral surface area = 4a^2
  • Surface Area: S=6a^2
  • Diagonal (d)=Square root of 3​a
• Cuboid:
  • Volume of cuboid: l x b x h
  • Total surface area = 2(lb+bh+hl) or 6l^2
  • Length of diagonal = square root of (l^2+b^2+h^2)​

CAT 2025 Quant Formula of Trigonometry

While not as heavily weighted as other topics, a fundamental understanding of trigonometry formulas can prove beneficial for certain CAT 2025 questions. These identities and relationships are crucial for solving problems involving angles and triangles.

Trigonometric Identities

The trigonometry formulas are as given below- 

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

Reciprocal Identities

The reciprocal formulas are as given below- 

• 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 2025 Quant Formula of Coordinate Geometry

Coordinate Geometry is a significant topic in CAT Quant, dealing with geometric shapes on a coordinate plane. Knowing these formulas allows you to calculate distances, find midpoints, and determine equations of lines, which are frequently tested concepts.

Key Coordinate Geometry Formulas

The important formulas for Coordinate Geometry are as given below- 

• The Distance Between two Points A(x1, y1) and B(x2, y2):
  • AB^2=(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​)/2,(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 2025 Quant Formula of Number Systems

Number Systems form the backbone of CAT Quantitative Aptitude, encompassing various types of numbers and their properties. Questions often involve series, sums, and basic algebraic identities. A firm grasp of these formulas is fundamental for a strong performance.

Important Number System Formulas

The formula for Important Number System Formulas are s given below- 

• 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 / Algebraic Identities

The formula for Mathematical Formulas/ Algebraic Identities are s given below-

• (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)an−1b+(nC2)an−2b2+⋯+(nCn−1)abn−1+bn

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CAT 2025 Quant Formula of Profit, Loss and Discount

Profit, Loss and Discount problems are consistently featured in the CAT 2025 exam. These questions test the ability to calculate profits, losses, and discounts, and apply these concepts to real-world scenarios. Mastering these formulas is crucial for solving these common business arithmetic problems.

Important Formulas for Profit, Loss and Discount

The important formulas of profit, loss, and discount are as given below- 

• 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 2025 Quant Formula of LCM and HCF

Least Common Multiple (LCM) and Highest Common Factor (HCF) are fundamental concepts in number theory. Questions involving LCM and HCF often appear in the CAT 2025, and a simple relationship between them is key to solving many problems.

Key Formulas for LCM and HCF

The important LCM and HCF formulas are as given below- 

• LCM × HCF = Product of the numbers
• LCM of co-prime numbers = Product of the numbers

CAT 2025 Quant Formula of Speed, Time and Distance

Speed, Time, and Distance is a common CAT 2025 Topic with numerous variations, including relative speed and average speed. These three quantities are interlinked, and understanding their relationships through formulas is essential for solving movement-based problems.

Key Formulas for Speed, Time and Distance

The important formulas of Speed, Time, and Distance are as given below- 

• Distance = Speed × Time
• Time = Distance/Speed
• Speed= Distance/Time

CAT 2025 Quant Formula of Percentages

Percentages are a foundational concept in Quantitative Aptitude, appearing in various forms across different topics like profit and loss, interest, and data interpretation. Being adept at percentage calculations is important for quick and accurate problem-solving at the CAT 2025 exam in the QA section. 

Important Formulas for Percentages

The important formulas of percentages are as given below- 

• 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 2025 Quant Formula of Time and Work

Time and Work problems are common in the CAT 2025 exam and often involve calculating the time taken by individuals or groups to complete a task. The core idea is to determine the rate of work.

Key Formula for Time and Work

The key formulas of Time & Work are as given below- 

• 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 2025 Quant Formula of Averages

Averages is a fundamental concept in statistics and a frequently tested topic in CAT 2025. Questions typically involve finding the average of a set of numbers or working backward from a given average.

Formula for Averages

• Average = (Sum of observations/Number of observations)

CAT 2025 Quant Formula of Simple and Compound Interest

Simple and Compound Interest problems are a staple of the CAT exam, testing candidates’ understanding of how money grows over time. Distinguishing between the two and applying the correct formulas is important.

Interest Formulas

The key interest formulas are ass given below- 

• Interest compounded Annually:
  • Amount$= P (1+ R/100)^n$
• Interest compounded half-yearly:
  • Amount$= P (1+R/200)^{2n}$
• Interest compounded quarterly:
  • Amount$= P (1+R/400)^{4n}$
• When interest is compounded annually but time is in fraction:
  • Amount$= P (1+ R/100)^x \times P (1+ (\text{fraction part of time})R/100)$ (Note: The provided formula for this section was unclear and potentially incorrect. The corrected format assumes 'x' is the integer part of time and the remaining is a fraction.)
• When rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year, respectively:
  • Amount$= P (1+R1/100) (1+R2/100) (1+R3/100)$
• Present worth of Rs. x due n years hence is given by:
  • Present worth$= x / (1+R/100)^n$

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CAT 2025 Quant Formula of Probability

Probability is a branch of mathematics concerned with the likelihood of events occurring. In CAT 2025, probability questions can range from simple coin tosses to more complex scenarios involving permutations and combinations.

Key Probability Formulas

The key probability formulas are as given below- 

• 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 2025 Quant Formula of Logarithm

Logarithms are the inverse operation to exponentiation. Questions on logarithms in CAT often involve applying their properties to simplify expressions or solve equations.

Important Logarithm Formulas

The important formulas of Logarithm are as given below- 

• loga​(xy)=log a x +log a y
• loga​(x/y)=log a x - log a y
• logx​x=1
• loga​1=0
• loga​(xn)=n(loga​x)
• loga​x=1/(logx​a)
• loga​x=(logb​x)/(logb​a)=(logx)/(loga)

CAT 2025 Quant Formula of Set Theory and Function

Set Theory and Functions are important for understanding relationships between elements and defining mappings. While sometimes intertwined with other topics, questions on these concepts require knowledge of specific laws and definitions.

Formulas for Set Theory and Function

The important formulas of Set Theory and Functions are as given below- 

• De Morgan’s Law:
  • (A∩B)’=A’∪B’ and (A∪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.
  • P(n,r)=n!/(n−r)!
• 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.
  • C(n,r)=n!/(r!(n−r)!)

CAT 2025 Quant Formula of Mixtures and Alligations

Mixtures and Alligations is a handy tool for solving problems involving the mixing of two or more ingredients with different properties or prices. The rule of alligation simplifies these calculations.

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)

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Importance of Knowing the Important Quant Formulas for CAT Preparation 2025

Knowing Important Quant formulas for CAT 2025 Preparation is very helpful. These formulas are the basic tools required to solve Quant questions. It can help candidates save time and get the right answers quickly without wasting any time. If aspirants understand them well, they can solve even tough problems with ease. So, practice these formulas often to improve your speed and accuracy in the CAT exam.

Final Thoughts

Candidates should follow the CAT 2025 Quant Formulas cheat sheet and build a solid foundation for the Quantitative Aptitude preparation. Remember, merely memorizing these formulas isn't enough. Candidates must understand the derivation of the CATQuant Formulas and their application to various problem types. Consistent practice, analyzing mistakes, and regular revision of these formulas will undoubtedly increase speed and accuracy in the CAT 2025 exam. Start early, stay disciplined, and good luck with your CAT 2025 Preparation!