**Introduction**

With a few days left for CAT 2021, every MBA aspirant should focus on the last minute revision of every section- Quantitative Aptitude, Verbal Ability, Data Interpretation and Logical Reasoning. Even though all the units should be given equal importance, the Quantitative Aptitude or Quant generally needs an intense revision and wholehearted preparation. As Quant is a subject relying on the path of practice, these last-minute formula sheets would help you quickly revise the concepts. Thus, keep your thinking hats handy, and slide this formula sheet in the corner of your mind to ace CAT 2021!

**Weightage of each topic **

Even though the weightage segregation is not defined in CAT and it keeps changing each year. Supporting the analysis of the last three years in mind, we can get a rough idea of the number of questions asked from each section.

**TOPICS**

**NUMBER OF QUESTIONS**

Geometry and Mensuration -20%

Number System and Basic Arithmetic – 25%

Algebra – 18%

Trigonometry, Logarithms and Sets – 7%

Permutation and Combination – 5%

Probability – 5%

Profit Loss Discount – 5%

Time Speed Distance – 5%

Time and Work – 5%

Interest – 5%

**Mathematical formulas for Quant Section of CAT**

Now, let’s look at the topic Wise Formulas for Quant Prep as below-

**Mensuration and Geometry **

- Rectangle- Area = lb

Perimeter = 2(l+b)

- Square- Perimeter = 4a

Area = a×a

- Cube
- Volume: V = l3
- Surface Area: S = 6s2
- Diagonal (d) = √3l
- Lateral surface area = 4a2

- Triangle

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

- Circle
- Circumference = 2πr or πd
- Area = πr² or πd²/4
- Area of 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)

- Coordinate Geometry
- AB² = (Bx – Ax)² + (By – Ay)²
- The midpoint of the line joining the points (x1, y1) and (x2, y2) is:
- [½(x1 + x2), ½(y1 + y2)]

**Number System and Arithmetic**

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

**Trigonometry, Logarithms and Sets**

**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
- 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)

**Trigonometry**

- Sine=Opposite/Hypotenuse
- Secant=Hypotenuse/Adjacent
- Cosine=Adjacent/Hypotenuse
- Tangent=Opposite/Adjacent
- Co−Secant=Hypotenuse/Opposite
- Co−Tangent=Adjacent/Opposite
- CosecΘ=1/sinΘ
- secΘ=1/cosΘ
- cotΘ=1/tanΘ
- sinΘ=1/CosecΘ
- cosΘ=1/secΘ
- tanΘ=1/cotΘ

**Law of Indices**

- a^m x a^n= a^(m+n)
- a^m/a^n= a^(m-n)
- (a^m)^n= a^mn
- (ab)^n= a^nb^n
- (a/b)^n=a^n/b^n

**Permutation and Combination**

Permutation Formula- nPr= n!/(n-r)!

Combination Formula- nCr= n!/(n-r)!r!= nPr/r!

**Probability**

Conditional- P(A | B) = P(A∩B) / P(B)

Bayes- P(A | B) = P(B | A) ⋅ P(A) / P(B)

**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

**Speed, Time and Distance**

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

**Time and Work **

- 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.

**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] – P
- Compound Interest = P[(1+i)n-1]

**Formulae for Percentages**

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)

**Averages Formula**

Average= Sum of observations/ Number of observations

**Mixtures and Alligation 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)

**Conclusion **

These formulas eloquently cover the syllabus of Quantitative Aptitude for CAT 2021. So, keep these with you for the next few weeks while practising the questions and solving them with finesse and ease.

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