CAT Formula Sheet - Important Formulas for CAT 2024 Quantitative Aptitude Preparation

The Common Admission Test (CAT) is the gateway to the world of management for a student in India. The question paper is prepared by the top IIMs (Indian Institute of Managements) of the country every year, CAT easily creates a niche for itself among the top admission tests of the country’s academia.

When preparing for the CAT exam, mastering the important formulas for CAT quantitative aptitude is essential. These key formulas for CAT preparation cover a wide range of topics, including algebra, geometry, arithmetic, and number systems. Familiarity with essential CAT formulas will help candidates solve problems quickly and accurately, especially in the time-constrained environment of the exam. Regular practice of quant formulas for CAT exam will not only boost confidence but also improve problem-solving speed, making it easier to tackle the quantitative aptitude section effectively.

There are basically 3 sections in CAT Examination, which are:

Each correct answer fetches 3 marks. Hence the total marks of the examination are 66 x 3 = 198.

Overview of CAT Quantitative Aptitude section

Syllabus

The syllabus of CAT is only what we have studied in our schools till the tenth standard. However, no specific syllabus exists. But for better understanding of Quantitative Aptitude syllabus we can refer to following table:

Important Quant Formulas

Quantitative Aptitude formulas form the foundation of the Quantitative Aptitude section in the CAT exam. Here are some important CAT quant formulas section-wise for CAT 2024 preparation:

Arithmetic

Arithmetic section is the most important section in the Quantitative Aptitude Section which is also useful to solve the D.I. problems. Following are some 50+ Important Formulas for CAT Preparation of this section which are given in this CAT Formula Sheet:

1. Percentage:

Following are some Important CAT Formulas of this topic:

a. X is what percentage of Y = XY . 100%

b. X is what percentage more/less than Y = Diff. between X & YY . 100%

c. If X is a% more than Y then, X = Y. (100 + a) %

d. If X is a% less than Y then, X = Y. (100 - a) %

Shortcut Formulas

Following are some formulas which can be used as Cat Quant Formula

Cheat Sheet for the preparation and exam point of view:

1. If price of an item is changed by x% initially and then again changed by y%, then- {Successive percentage change}

overall % change in price = (x + y + x.y/100) %

1. A = B X C

If B is changed by x% and C is changed by y%, then-

overall % change in A = (x + y + x.y/100) %

1. If price of an item is increased by x% and then decreased by y%, then-

overall % change in price = -(x²/100) %

2. Profit & Loss:

Following are some Important CAT Formulas of this topic:

a. S.P. (selling price) = C.P. (cost price) + Profit

b. S.P. = C.P. – Loss

c. Profit or Loss % = Profit or LossC.P. . 100%

d. Discount % = Discount M.P.(Marked Price) . 100%

e. S.P. = C.P. (100 + Profit) % or C.P. (100 – loss) %

Shortcut Formulas

Following are some formulas which can be used as Cat Quant Formula

Cheat Sheet for the preparation and exam point of view:

1. If an article is marked m% more than cost price and then discount of d% is given over marked price, then-

Overall profit or loss % = (m – d – m.d/100) %

3. Simple Interest (S.I.) & Compound Interest (C.I.):

Following are some basic and Important Formulas for CAT 2024 related to this topic:

1. S.I. = Principal(P) x Rate of Interest(R) x Time(T) / 100

= P.R.T/100

1. If interest is compounded annually, then-

Amount = P [1 + R100 ]T

1. If interest is compounded half-yearly, then-

Amount = P [1 + R2 x 100 ]2T

1. Amount = P + Interest

Shortcut Formulas

Following are some formulas which can be used as Cat Quant Formula Cheat Sheet for the preparation and exam point of view:

1. If an amount is invested in a scheme in which interest is compounded annually at the rate of R%, then the amount will be double in 72/R years.

ex: P = 2000, R = 8%, then it will be double in 72/8 = 9 years.

1. Scheme A: (S.I.) P = x, R = r%

Scheme B: (C.I.) P = x, R = r%

• For 2 years, C.I. – S.I. = P. [ R/100 ]²

• For 3 years, C.I. – S.I. = P. [ R/100 ]² [3 + R/100 ]

4. Time, Speed & Distance:

Following are some basic and Important Formulas for CAT 2024 related to this topic:

1. Distance(D) = Speed (S) X Time (T)

2. Average Speed = Total Distance covered/ Total time taken

Trains:

1. Time taken by train to cross a pole/person –

Time= Length of Train (l) / Speed of Train (s)

1. Time taken by train to cross a platform/tunnel –

Time= Length of Train (l) + Length of platform or tunnel (d) / Speed of Train (s)

1. Time taken by trains to cross each other after their meeting (if there are running in the same direction)

Time= Length of Train-1(l₁) + Length of Train-2(l₂) / Diff. of Speeds of Train

= (l₁ + l₂)/ (s₁ - s₂)

1. Time taken by trains to cross each other after their meeting (if there are running in the opposite direction)

Time= Length of Train-1(l₁) + Length of Train-2(l₂) / Sum of Speeds of Train

= (l₁ + l₂)/ (s₁ + s₂)

Boat & Streams:

Speed of Boat in still water = x kmph

Speed of Stream/water/current = y kmph

Travelling time = t hr.

1. If a boat is travelling downstream (Boat and water are in same direction)

Then Distance travelled by boat –

D = (x + y). t km.

1. If a boat is travelling Upstream (Boat and water are in different direction)

Then Distance travelled by boat –

D = (x - y). t km.

Clocks:

1. Speed of Hour hand = 0.5° per minute

{Hour hand covers 1 round = 360° in 12 hours or 720 minutes}

1. Speed of Minute hand = 6° per minute

{Hour hand covers 1 round = 360° in 1 hours or 60 minutes}

1. At time H:M, The angle (in degrees) between hour hand and minute hand

angle θ = |112M-30H|

Shortcut Formulas

Following are some Quantitative Aptitude Formulas which can be used as Cat Quant Formula Cheat Sheet for the preparation and exam point of view:

1. If the distance covered in each stage of journey is same, but speeds are different then, the average speed is the harmonic mean of the different speeds.

Ex: If distance between point A to B and B to C are same and are covered with the speed of S₁ and S₂ respectively. Then-

Average speed = 2/1/S1+1/S2 = 2S1. S2/S1+S2

1. If the time taken in each stage of journey is same, but speeds are different then, the average speed is the average of the different speeds.

Ex: If time taken between points A to B and B to C is same and these distances are covered with the speed of S₁ and S₂ respectively. Then-

Average Speed = S1+S2/2

1. If two people start running on a circular track of length D km in the same direction from the same point with speeds a & b kmph, then-

(i) Time taken in first meeting = D/|a-b| hr.

(ii) Time taken to meet again at the starting point = LCM (D/a ,D/b)

(iii) No. of Distinct meeting Points = |x - y|

{x & y are the simplified ratio of speeds, Ex: If speeds a & b are 12 kmph & 9 kmph

respectively, then- x: y = 12: 8 = 3: 2; So, x = 3 & y =2}

1. If two people start running on a circular track of length D km in the opposite direction from the same point with speeds a & b kmph, then-

(i) Time taken in first meeting = D|a+b| hr.

(ii) Time taken to meet again at the starting point = LCM (Da ,Db) hr.

(iii) No. of Distinct meeting Points = |x + y|

{x & y are the simplified ratio of speeds}

1. If a person P starts from A and heads towards B and another person Q starts from B and heads towards A and they meet after a time 't' then, t = √ (?. y)

[where x = time taken (after meeting) by P to reach B and y = time taken (after meeting) by Q to reach A]

1. If the speed of the boat downstream is u kmph and the speed of the boat upstream is v kmph, then-

Speed of the boat in still water = u + v2 kmph

Rate of stream = u- v2 kmph

Geometry

Geometry section is the lengthiest section in the Quantitative Aptitude Section which has lots of properties and formulas. Following are some 50+ Important Formulas for CAT Preparation of this section which are given in this CAT Formula Sheet:

1. Triangles:

Properties of Triangles:

1. Sum of all interior angles in a triangle is 180° and Exterior angles is 360°.

2. Sum of any two sides is always greater than third one and difference of any two sides is less than third one.

Let a,b,c are the sides of triangles, then

|b-c| < a < b + c

1. In a Scalene Triangle greatest side is always greater than the one-third of perimeter and less than half of the perimeter.

• Let a,b,c are the sides of triangles and a is the greatest side of the triangle. Perimeter of the triangle is P.

P/3 < a < P/2

Ex: In a scalene triangle ABC, perimeter of the triangle is 24 cm and all sides are integers.

Sol: Let a,b,c are sides of triangle, and a is the greatest side.

24/3 < a < 24/2

8 < a < 12

So, all possible value of a are 9,10,11 cm.

1. Let a,b,c are sides of triangle, and a is the greatest side.

If a² < b² + c² {Then triangle is an acute angled triangle}

If a² = b² + c² {Then triangle is a Right-angled triangle= Pythagoras theorem}

If a² > b² + c² {Then triangle is an Obtuse angled triangle}

1. (Here D is the midpoint of the AC side or AD = DC).

1. Length of the Median-

BD = ½ X √2(AB² + BC²) – AC²

1. 3 (Sum of squares of sides) = 4 (Sum of squares of medians)

3(a² + b² + c² )= 4(M_a² +M_b² + M_c² )

{Where a,b,c are sides of triangle and M_a, M_b, M_c are medians of the triangle}

1. In a right-angle triangle, Median of Hypotenuse= Hypotenuse/2

CD = AB/2

1. If all the medians are drawn in the triangle, then the 6 small triangles are generated in the triangle, which are equal in the Area.

Area of Triangle:

1. Heron’s Formula

If all sides of a triangle are given. Let a,b,c are sides of triangle-

Area = √s(s-a)(s-b)(s-c) {s is the semi-perimeter. s = (a+b+c)/2}

1. If two sides and one included angle is given-

Area = ½ x Product of given sides x Sin(given included angle)

= ½ x a.b. SinC

{ex: sides a, b are given and included angle C is given}

1. If a side and its respective Altitude (perpendicular drawn on a side from the opposite vertex) is given, then-

Area of the triangle = ½ x Base x Height (Altitude)

Shortcut Formulas

1. Area of Equilateral Triangle = 34 a²

2. Height/Altitude of Equilateral Triangle = 32 a

3. Area of Triangle = Inradius (r) x semi-perimeter (s)

4. Area of Triangle = Product of sides of triangle/4 X Circumradius (R)

2. Quadrilaterals:

3. Circle:

1. Circumference of Circle = 2πr

2. Area of Circle = πr²

Semi-circle

1. Circumference of semi-circle = πr

2. Perimeter of semi-circle = πr + 2r {Circumference + Diameter}

3. Area of semi-circle = πr² /2

Sector & Segment of circle

{OAXC is called the sector of the circle & AXC is called the segment}

1. Length of Arc AXC = 360. 2πr {r is the radius of circle}

2. Area of sector OAXC = 360. πr²

3. 2 x Area of sector = length of arc x radius

4. Area of segment AXC = Area of sector OAXC – Area of triangle OAC

= 360. πr² - 1/2r²sinθ

Common Tangent

1. PQ & RS are the direct common tangents of the circle, which are equal in length. Length of direct common tangent (L)-

L² = d² – (r₁-r₂)²

{d = distance between centers of circle, r₁,r₂ are radius of circle}

1. PQ & RS are the transverse common tangents of the circle, which are equal in length. Length of transverse common tangent (L)-

L² = d² – (r₁+r₂)²

{d = distance between centers of circle, r₁,r₂ are radius of circle}

4. Mensuration:

Algebra

The Algebra section is a critical part of the Quantitative Aptitude section in the CAT exam. Below are over 50 important formulas for CAT preparation in this section, which are provided in this comprehensive CAT Formula Sheet:

1. Quadratic Equations

1. General Quadratic equation will be in the form of ??2 + ?? + ? = 0; Values of ‘x’ which satisfies the equation are called roots of the equation. To find the roots the Shreedhara Acharya's Formula is used.

Roots of the equation, x = 12a(-b±b2-4ac )

1. Sum of the roots = -ba

2. Product of the roots = ca

3. Difference of the roots = Da {where D = b2-4ac }

4. If D > 0, Then roots of the equation will be real and distinct

{i. If D is perfect square, then roots will be rational; ex: x = 1,6

ii. If D is non-perfect square, then roots will be irrational or conjugate surds

ex: x = 3-√5, 3+√5}

1. If D = 0, Then roots of the equation will be real and equal.

1. If D < 0, Then roots of the equation will be imaginary and distinct.

1. y = ??2 + ?? + ?; If a > 0

Minimum value of y =-D4a , when x = -b2a

1. y = ??2 + ?? + ?; If a < 0

Maximum value of y =-D4a , when x = -b2a

1. If roots of the quadratic equation are a & b, then-

Quadratic Equation = x2 – S.x + P; {where S = sum of roots; P= product of roots}

= x2 – (a+b).x + a.b

2. Progression & Series

In this chapter there are three types of progression, which are-

1. Arithmetic Progression

2. Geometric Progression

3. Harmonic Progression

Arithmetic Progression (A.P.)

If a is the first term and d is the common difference then the A.P. can be written as-

a, a+d, a+2d, a+3d, ………………..

1. Nth term of the A.P. –

Tn = a + (n-1).d {n is the no. of terms}

1. Sum of the n terms of the A.P. (Sn) = Average of all the terms x no. of terms(n)

Average of the terms can be found out easily

• If no. of terms is odd then the middle term will be the average

Ex: 2,5,8,11,14 are the terms of the A.P. then middle term 8 is the average

So, the sum = avg. x n = 8 x 5 = 40

• If no. of terms is even then the average of middle terms will be the average of the A.P.

1. Sn = n2 [2a+n-1d]

Shortcut Formulas

1. Sn = n₂ (a+l) {where a = first term, l = last term, n= no. of terms}

2. No. of terms in A.P.

n = l-ad+1

Geometric Progression (G.P.)

If a is the first term and r is the common ratio then the G.P. can be written as-

a, a.r, a.r², a.r³, ……………….

1. N^th term of the G.P. –

Tn = a.rn-1 {n is the no. of terms}

1. Sum of n terms of the G.P.-

Sn = a.1-rn1-r If r < 1 or Sn = a.rn-1r-1 If r > 1

1. Sum of infinite terms of the G.P.-

S∞ = a1-r; If |r| < 1

Shortcut Formulas

1. 
   

   If there are odd no. of terms in a G.P., then the product of all terms are equal to the nth power of middle term.

Ex: 2,6,18,54,162 are the terms of a G.P.

Then the products of all the terms = 18⁵

Harmonic Progression (H.P.)

If a,b,c are in A.P. then 1/a, 1/b, 1/c will be in the H.P.

1. Nth term of the H.P.= 1/Nth term of the A.P.

Series

1. Sum of first n natural numbers-

1 +2 + 3 + 4 + 5 +………..+ n = nn+12

1. Sum of squares of first n natural numbers-

12 + 22 + 32 + …………….+ n2 = nn+1(2n+1)6

1. Sum of cubes of first n natural numbers-

13 + 23 + 33 + …………….+ n3 = nn+122

1. Sum of first n natural odd numbers-

1 + 3 + 5 + 7 + ………. = (no. of terms)2

1. Sum of squares of first n natural even numbers-

2² + 4² + …………….+ (2n)² = 2nn+1(2n+1)/3

1. Sum of squares of first n natural even numbers-

1² + 3² + …………….+ (2n+1)² = n2n+1(2n-1)/3

3. Indices & Surds

1. A¹ = A

2. A⁰ = 1

3. A^m x Aⁿ = A^m + n

4. A^m / Aⁿ = A^m - n

5. (A^m)ⁿ = A^m. n

6. A^m x B^m = (A.B) ^m

7. A^m / B^m = (A/B) ^m

8. A^-m = 1/A^m

9. xA = (A)^1/x

Shortcut Formulas

1. aaaa…..x times = a1-12x

2. aaaa…..∞ times = a

4. Logarithm

1. If A^N = B ⬄ N =B

2. N =B ; {A > 0 but not equal to 1, B > 0, N € Real no.}

3. 1 = 0

4. A = 1

5. B^p = pq B

6. x.y = x + y

7. x/ y = x - y

8. B = 1/A

9. B = B /A

10. X^B = B^X

11. X^B = 1

CAT Quantitative Aptitude Preparation

If you're preparing for the CAT exam, having a well-organized CAT formula sheet can be a game-changer for your Quantitative Aptitude section. This CAT quant formula cheat sheet will serve as your go-to resource, covering all the important formulas needed for the exam. Whether you're revising or solving practice questions, this CAT formulas cheat sheet ensures that you have quick access to essential quant formulas. It's crucial to keep this CAT formula sheet handy, as it consolidates all the CAT quant formulas in one place, making your preparation more efficient and effective. Careers360 has designed an ebook on the top 100 facts that each of the candidates must be aware of to enhance their CAT 2024 quantitative aptitude preparation along with the necessary formulas. The candidates are requested to download and study the ebook for an enhanced CAT quantitative aptitude 2024 preparation.

CAT Preparation 2024 Important Books

When preparing for CAT 2024, using the right set of books is essential for thorough and targeted preparation. These books are designed to cover all the sections of the exam—Verbal Ability and Reading Comprehension (VARC), Data Interpretation and Logical Reasoning (DILR), and Quantitative Aptitude (QA)—providing in-depth knowledge of the core concepts.