# Maths Formula and Tips- Quantitative Aptitude

In this section we will list down all the Maths Formula and Tips useful in Quantitative Aptitude.Tips and notes will be listed down Topic wise. Keep them handy and memorize them during Competitive and Entrance Exams, GRE Test.

## 1. Number System (Tips and Formula)-

**Natural Numbers**– Counting numbers are called Natural numbers. eg 1,2,3,4 … are all Natural numbers.

**Whole Numbers**– All counting numbers together with Zero (0) forms the set of whole numbers.

**Integers**– All counting numbers , Zero and negative of counting numbers form the Integers. Eg ……,-3,-2,-1,0,1,2,3,…..are all integers. So positive integers will be [1,2,3,4,5….] Negative integers will be [……,-4,-3,-2,-1]

**Even Numbers**– All natural numbers divided by 2 are called Even Numbers eg 2,4,6, etc

**Odd Numbers**– All natural numbers not divided by 2 are called odd numbers eg 1,3,5,7 etc

**Prime Number**– All natural numbers which can not be divided further are called prime numbers etc 2,3,5,7,11,13,17,19,23,29,31 etc … Smallest prime number is 2 , The only even prime number is 2

**Composite Numbers**– All natural numbers which are not prime is called Composite numbers.

**Perfect Numbers**– All natural numbers , the sum of whose factors is equal to the number itself, is called a Perfect Numbers. Eg 6 is a composite number -The factor of 6 1,2 and 3 … 1 + 2 + 3 = 6. Another eg. 28 is Composite number – factors 1 + 2 + 4 + 7 + 14 = 28

**Twin-Prime**s – Two prime numbers whose is 2 are called twin-primes, eg (3,5), (5,7),(11,13) are pair of twin-primes.

**Rational Numbers**– Numbers which can be expressed in the form of x/y, where x any y are integers and y is not equal to Zero

## 2. Divisibility Test Maths Formula & Tips

**Divisibility by 2**– A number is divisible by 2 if its unit digit is any of 0, 2 , 4 , 6 and 8.**Divisibility by 3**– A number is divisible by 3 if sum of its digits is divisible by 3. Ex. Number 273, sum of its digit is 2 + 7 + 3 = 12 which is divisible by 3 , hence 273 is divisible by 3.**Divisibility by 9**– A number is divisible by 9 if sum of its digits is divisible by 9. Ex. Number 2736, sum of its digit is 2 + 7 + 3 + 6 = 18 which is divisible by 9, hence 2736 is divisible by 9**Divisibility by 4**– A number is divisible by 4 if number formed by its last two digits is divisible by 4. Ex. In number 4728 , its last 2 digits form a number 28 , which is divided by 4 hence 4728 is divisible by 4 !**Divisibility by 8**– A number is divisible by 8 if the number formed by its last 3 digits is divisible by 8 . Ex. In number 16495152, number formed by last 3 digits is 152 , which is divisible by 8, hence the number 16495152 is divisible by 8 !**Divisibility by 11**– A number is divisible by 11 if the difference between sum of its digits at odd places and the sum of digits at even places is either 0 or divisible by 11. Ex. Consider the number 29435417 -> (Sum of digits at odd place ) – ( Sum of digits at even place) = (2 +4+5+1) -(9 + 3+4+7) is equal to 11 , which is divisible by 11 , hence 29435417 is divisible by 11.**Divisibility by 6**– A number is divisible by 6, if it is divisible by both 2 and 3.**Divisibility by 12**– A number is divisible by 12, if it is divisible by both 3 and 4.**Divisibility by 15**– A number is divisible by 15, if it is divisible by both 3 and 5.**Divisibility by 18**– A number is divisible by 18, if it is divisible by both 2 and 9.**Divisibility by 14**– A number is divisible by 14, if it is divisible by both 2 and 7.**Divisibility by 24**– A number is divisible by 24, if it is divisible by both 3 and 8.

## 3. HCF & LCM Tips and Maths Formula

- Product of 2 numbers = Product of their H.C.F. and L.C.M.
- HCF and LCM of Fractions —
- HCF = HCF of Numerators/LCM of Denominators
- LCM = LCM of Numerators/HCF of Denominators

## 4. Profit and Loss Maths Formula and Tips

Cost priceorC.P.- The price at which an article is purchasedSelling priceorS.P.- The price at which an article is sold.

- Gain or profit = S.P. — C.P.
- Loss or gain is always reckoned on Cost price
- Gain % = \( {\frac{Gain * 100}{C.P.}} \)
- Loss % = \( {\frac{Loss * 100}{C.P.}} \)
- S.P. = \( {C.P. ({\frac{100 + Gain Percentage}{100}})} \)
- S.P. = \( {C.P. ({\frac{100 – Loss Percentage}{100}})} \)
- C.P. = \( {S.P. ({\frac{100}{100 + Gain Percentage}})} \)
- C.P. = \( {S.P. ({\frac{100}{100 – Loss Percentage}})} \)
- If an article is sold at a gain of 10 %, then S.P. = 110% of C.P.
- If an article is sold at a loss of 10 %, then S.P. = 90% of C.P.
- If a trader sells two similar items, one at a gain of x% and another at loss of x%, then seller always incur a loss given by Loss % = \( ({\frac{x}{10}})^2 \)

## 5. Pipes and Cisterns Maths Tips

- If a pipe can fill a tank in x hours, then part filled in 1 hour is (1/x).
- If a pipe can empty a tank in x hours, then part emptied in 1 hour is (1/y).
- If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x),then on opening both the pipes, the net part filled in 1 hour is \(( {\frac{1}{x} – \frac{1}{y}}) \)
- If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where x > y),then on opening both the pipes, the net part filled in 1 hour is \(( {\frac{1}{y} – \frac{1}{x}}) \)