50+ Important Formulas for CAT 2025 Preparation: Topic-Wise Formulas
50+ important formulas for CAT 2025 preparation mostly include formulas from common CAT QA topics like profit and loss, algebra, number system, percentages, etc. Learning these formulas can help you speed up your problem-solving skills for CAT 2025!
50+ formulas for CAT 2025 preparation cover topics like profit and loss, algebra, number system, permutation & combination, percentages, etc. It is essential that every candidate be aware of several key CAT formulas aside from these topics for CAT 2025 exam preparation. CAT formulas are mostly relevant to the Quantitative Aptitude section, which includes Maths topics. Strategies mentioned in the CAT 2025 preparation tips in addition to these important formulas can help you perform better in the exam. There are many formula-based questions in CAT 2025 where all you need to do is use a formula to reach the answer. You must learn all the formulas mentioned here to the best of your abilities to ensure a stellar performance in CAT 2025!
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Important Formulas in CAT 2025 Preparation
There are a number of important formulas in CAT preparation 2025 that you must become fluent in. All of the formulas used in CAT are from up to the Class 12th level. You 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 2025.
Section | No. of Questions | Time |
Verbal Ability & Reading Comprehension | 24 | 40 minutes |
Data Interpretation & Logical Reasoning | 20 | 40 minutes |
Quantitative Ability | 22 | 40 minutes |
TOTAL | 66 | 120 minutes |
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The QA section of CAT 2025 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 2025 Formulas for Algebra
Square of a + b
(a + b)(a – b) = (a 2 – b 2 )
(a + b) 2 = (a 2 + b 2 + 2ab)
(a – b) 2 = (a² + b² – 2ab)
Square of a + b + c
(a + b + c) 2 = a 2 + b 2 + c 2 + 2(ab + bc + ca)
Cube of a + b
(a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3
(a – b) 3 = a 3 – 3a 2 b + 3ab 2 – b 3
(a 3 + b 3 ) = (a + b)(a 2 - ab + b 2 )
(a 3 – b 3 ) = (a – b)(a 2 + ab + b 2 )
(a 3 + b 3 + c 3 – 3abc) = (a + b + c)(a 2 + b 2 + c 2 – ab – bc – ac)
When a + b + c = 0, then a 3 + b 3 + c 3 = 3abc
Root Formula
(a+b) n = a n + n C 1 a n – 1 b + n C 2 a n – 2 b 2 + ..... n C x a n – x b x + ....... b n |
Important CAT 2025 Formulas for Number System
(1 2 + 2 2 + 3 2 + ….. + n 2 ) = n ( n + 1 ) (2n + 1) / 6
1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2
(1 3 + 2 3 + 3 3 + ….. + n 3 ) = (n(n + 1)/ 2) 2
Sum of first n odd numbers = n 2
Sum of first n even numbers = n (n + 1)
Important CAT 2025 Formulas for Permutation and Combination
Combination: n C r = n! / (n-r)!r! = n P r / r!
Permutation: n P r = n! / (n-r)!
Important CAT 2025 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 | 33 1 / 3 % | 0.333... |
2/3 | 66 2 / 3 % | 0.666... |
1/4 | 25% | 0.25 |
3/4 | 75% | 0.75 |
1/5 | 20% | 0.2 |
1/6 | 16 2 / 3 % | 0.1666.... |
5/6 | 83 1 / 3 % | .8333... |
1/8 | 12 1 / 2 % | 0.125 |
3/8 | 37 1 / 2 % | 0.375 |
5/8 | 62 1 / 2 % | 0.625 |
7/8 | 87 1 / 2 % | 0.875 |
1/9 | 11 1 / 9 % | 0.111... |
1/10 | 10% | 0.1 |
1/11 | 9 1 / 11 % | 0.999... |
5/11 | 45 5 / 11 % | 0.4545... |
1/12 | 8 1 / 3 % | 0.08333... |
1/16 | 6 1 / 4 % | 0.0625 |
1/25 | 4% | 0.04 |
1/32 | 3 1 / 8 % | 0.03125 |
1/50 | 2% | 0.02 |
Also Read : 15+ CAT 2025 Percentage Questions
Important CAT 2025 Formulas for Averages
Average = Total Sum / Total Number
Weighted Average = (w 1 x 1 + w 2 x 2 + w 3 x 3 .... + w n x n ) / (w 1 + w 2 + ..... + w n)
Important CAT 2025 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 2025 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 2025 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
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Important CAT 2025 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 2025 Formulas for Logarithms
log x 1 = 0
log x x = 1
log x (mn) = log x m + log x n
log x (m/n) = log x m – log x n
log x a b = b log x a
log x a x = a
log x m = (log y n) x (log a n)
Important CAT 2025 Formulas for Surds and Indices
Important CAT 2025 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 2025 Formulas for Boats and Streams
S downstream = S boat + S stream
S upstream = S boat - S stream
Important CAT 2025 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 2025 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
Cosine=Adjacent/Hypotenuse
Tangent=Opposite/Adjacent
Secant=Hypotenuse/Adjacent
Co−Secant=Hypotenuse/Opposite
Co−Tangent=Adjacent/Opposite
The reciprocal identities:
sinΘ=1/CosecΘ
cosΘ=1/secΘ
tanΘ=1/cotΘ
CosecΘ=1/sinΘ
secΘ=1/cosΘ
cotΘ=1/tanΘ
Important CAT 2025 Formulas for Mensuration
Check out the important formulae for mensuration mentioned below:Plane Figures
Solids
NOTE: (3.14) is an approximation of pi.
Important CAT 2025 Formulas for Probability
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 2025 Formulas for Coordinate Geometry
The Distance Between Two Points A and B:
AB 2 = (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)]
Best Formula Books for CAT Preparation 2025
The best formula books for CAT 2025 preparation have been tabulated below.
Section | Book Title | Author/Publisher |
Data Interpretation & LR | Logical Reasoning and Data Interpretation for CAT | Nishit K. Sinha (Pearson) |
Quantitative Aptitude | Quantitative Aptitude for CAT | Arun Sharma (TMH) |
VARC / Vocabulary | Word Power Made Easy | Norman Lewis |
Quantitative Aptitude | Quantum CAT | Sarvesh K. Verma |
How to Remember Important Formulas for CAT 2025?
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 2025 without the need to learn 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.
Why are CAT Formulas Important?
While studying for the CAT 2025 exam, efficiency in preparation is necessary. In order to solve difficult questions quickly, one requires the suitable formulas by their side. The CAT formulas are important because:
- Quick Revision: Instead of going through various books, the formulas can be referred to in one place for fast revision
- Better Time Management: When you are aware of the formulas, you can solve the problems faster, which is crucial in a time-limited exam such as CAT.
- Enhanced Retention: Repeatedly practicing with the formulas helps improve long-term memory.
- Increased Accuracy: Knowing the basics of formulas helps you to make fewer mistakes during the exam, especially while dealing with CAT quant formulas.
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