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50+ Important Formulas for CAT Preparation: Topic-Wise Formulas Used in CAT 2021

Abhinav Chamoli
Abhinav ChamoliPublished On: February 26, 2021 | CAT

There are many important formulas that every CAT aspirant must know and well-versed with. Here is a topic-wise list of more than 50 formulas that you must learn if you are preparing to take CAT this year.

50+ Important Formulas for CAT Preparation: Topic-Wise Formulas Used in CAT 2021

Ask any CAT aspirant and they will easily be able to tell you the importance of learning formulas in CAT preparation. It is essential that every candidate be aware of several key CAT formulas aside from any of the tips and tricks for CAT 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 CAT preparation formulas. Formulas in CAT 2021 preparation 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. All of the information about CAT 2021 can be found in the following article.

All About the CAT Exam - Check Exam Details & Procedure

Here is a comprehensive list of important formulas for CAT preparation that every candidate must practice. Also, check the important tips to remember formulas.

Important Formulas in CAT 2021 Preparation

There are a number of important formulas in CAT preparation that a candidate must get fluent with. All of the formulas used in CAT 2021 are from up to 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 2021.

 Section

No. of Questions

Time

Verbal Ability & Reading Comprehension

34

60 minutes

Data Interpretation & Logical Reasoning 

32

60 minutes

Quantitative Ability

34

60 minutes

TOTAL

100180 minutes

Also Check:CAT 2021 Important Dates

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.

1. 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)

Sqaure 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)

Root Formula

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

2. Important CAT Formulas for Permutation and Combination

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

3. 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

4. Important CAT Formulas for Averages

  • Average = Total Sum / Total Number

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

5. Important CAT Formulas for Simple Interest and Compount Interest

  • Amount = Principle + Interest

  • Simple Interest = P x r x n

  • Compound Interest = P(1 + r)n – P

6. 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

7. Important CAT Formulas for HCF and LCM

  • HFC of Fractions = (HCF of numof erators) / (LCM of denominators)

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

  • LCM x HCF = Product of Numbers

8. 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)

9. 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

10. Important CAT Formulas for Boats and Streams

  • Sdownstream = Sboat + Sstream
  • Supstream = Sboat - Sstream

11. Important CAT Formulas for Trigonometry

Right Angle Triangle with Sides AB, BC and CA
Right Angle Triangle with Angles A, B and C
  • 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

12. 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
  • Perimeter of a Square = 4s

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.

Also Read:How to Prepare for CAT Quantitative Ability (QA) - Check Expert Advice, Tips and Tricks

How to Remember Important Formulas for CAT 2021

Candidates are often seen worried about how to remember the important CAT 2021 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 2021 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. Practising will help you become familiar with important formulas. It will also train you in using these formulas with more speed and accuracy.

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