# Quantitative Aptitude Formulas – CAT 2018

# Key To The Most Important Quantitative Aptitude Formulas

Quantitative Aptitude is a full mathematical based section. The problem in this section under CAT is to memorize all the formulas. Many a times, student lack in this section even after 100% preparation, it is because each time when they solve any question they have formulas in front of their eyes. Once a topic finishes and other starts, focus goes to that particular topic and forgets the previous one. This article will act as a key to the most important Quantitative Aptitude Formulas which student can easily grasp the formula just after reading it thrice a time.

Some basic topics under this article like Ratios and percentages, Speed Time and Distance, Averages, Simple and Compound Interest, Linear Equation, Permutation and Combination, Probability will be covered.

## Guide to Quantitative Aptitude Formulas:

### 1. Simple and Compound Interest:

**Simple Interest:** Principal x Interest Rate x Time specified

= P x I x N

**Compound Interest:** [P(1+I)^n] – P

or, P[(1+I^n] – 1

**Rule of 72:** This rule calculates the approximate time over which an investment will get double at a given rate of ROI. And is given by (72/I). But it will always used for Annual compounding only.

### 2. Ratio and Proportion:

**Ratio:** The ration of two quantities let say a and b in the same units, will be written as a:b

**Proportion:** The equality of two ratios is known as proportion.

For example: there are 2 ratios , first say, a:b and second c:d

Say a:b=c:d, the proportion will be a:b::c:d and it means a, b, c, and d all are in proportion.

**Third Proportional:** If a:b=c:d, then c is called as third proportion to a and b

**Fourth Proportional**: If a:b=c:d, then d is called as fourth proportion to a and b.

**Mean Proportional:** The mean proportional between a and b is root of product of a and b.

**Variation: **If x is directly proportional to y, then x = k y for any constant k.

Also, we can say that x is inversely proportional to y, if x y=k

**3. Speed, Time and Distance:**

Speed = Distance/Time , Time= Distance/Speed, Distance= Speed x Time

**Km/hr to m/sec conversion:** X km/hr= (X x 5/18)m/sec

**m/sec to km/hr conversion:** (X x 5/18)km/hr

### 4. Time and Work Formula:

**Work from Days:** If X can do a piece of work in n days, then X’s 1 day work will be 1/n

**Days from Work:** If X’s 1 day work = 1/n, Then X can finish the work in n days.

**Ratio:** If X is twice as good a workman as Y, then:

The Ratio of work done by X and Y = 2:1

So, Ratio of time taken by X and Y to finish the work= 2:1

### 5. Permutation and Combination:

**Permutation:** All permutations (or arrangements) made with the letters a, b, c by taking two at a time are (ab, ba, ac, ca, bc, cb).

All permutations made with the letters a, b, c taking all at a time are: ( abc, acb, bac, bca, cab, cba)

**Number of Permutation:** Number of permutation of n things, with r at a time,

n Pr = [n(n – 1)(n – 2) … (n – r + 1)] = {n! /(n – r)!}

**Combination: **Each of different groups or selections which can be formed by taking some or all of a number of objects is called as Combination.

1. Suppose we want to select two out of three boys A, B, C. Then, possible selections are AB, BC and CA.

2. All the combinations formed by a, b, c taking ab, bc, ca.

3. The only combination that can be formed of three letters a, b, c taken all at a time is abc.

4. Various groups of 2 out of four persons A, B, C, D are: AB, AC, AD, BC, BD, CD.

5. Note that ab ba are two different permutations but they represent the same combination.

### 6. Geometry:

**Perimeter of Square**= P= 4 a

where a = Length of the sides of square

**Perimeter of Rectangle** = P = 2(l+b)

where, l = length and b= breadth

**The Area of square** = A = a^2

**Area of Rectangle** = A= l x b

where, l = length and b= breadth

** Area of Triangle** = A = h x b/2

where b is the base of triangle and h is the height

**Area of Trapezium** = A = (b 1+b 2)h/2

**Area of circle** = A= pie r square

**Circumference of Circle** = A= 2 π r

where r is the radius of circle

**Surface Area of Cube** = S = 6 a^2

a is the length of sides of the cube

**Surface area of Cylinder** = S = 2 π r h

**Volume of Cylinder** = V = π r^2 h

**Surface Area of Sphere**= S = 4πr^2

**Volume of Cone** = V = πr^2 h

### 7. Probability:

**Probability of Event:** No. of Favorable Outcomes/Total no. of Possible Outcomes.

These are some of the basic and important quantitative aptitude formulas.

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