Quantitative Aptitude Important Formulas

Numbers - Important Formulas,Tricks and Examples

The common number system is decimal number system.
The Decimal number system used base (or radix) as 10 . This means that the system has ten symbols or numerals to represent any quantity. These symbols are called Digits and they are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Types of Numbers

Natural Numbers:The numbers that are used for counting called Natural Numbers.These are infinite and start from the number 1 .
Ex : 1, 2, 3, 4, 5, 6 ........

Whole numbers:The whole numbers are just all the natural numbers plus zero.
Ex : 0, 1, 2, 3, 4, 5 .............

Integers: Integers incorporate all positive and negative numbers with zero.
Ex : .... –3, –2, –1, 0, 1, 2, 3 .....

Even Numbers: An even number is one that can be divided evenly by two leaving no remainder, such as 2, 4, 6, and 8.

Odd Numbers: An odd number is one that does not divide evenly by two, such as 1, 3, 5, and 7.

Rational Numbers: All numbers of the form p/q where p and q are integers (q ≠ 0) called Rational numbers.
Ex : 4, 3/4, 0, ….

Irrational Numbers: Irrational numbers are the opposite of rational numbers. An irrational number cannot be written as a fraction as p/q where a and b are integers.
the decimal values for irrational numbers never end and do not have a repeating pattern in them.please note ‘pi’ has never ending decimal places, is irrational.
Ex : pi, 2^1/2 , 3^1/2, 5^1/2 , 7^1/2 ..........

Real numbers: Real numbers include counting numbers, whole numbers, integers, rational numbers and irrational numbers.
Ex : 8, 6, 2, (3)^1/2 , 3/5 etc.

Prime Number: A prime number is a number which can be divided only by 1 and itself. The prime number has only two factors, 1 and itself.
Ex : 2, 3, 7, 11, 13, 17, …. are prime numbers.

Composite Number: A Composite Number is a number which can be divided evenly. Any composite number has additional factors than 1 and itself.
Ex : 4, 6, 8, 9, 10 …..

Co-primes or Relatively prime numbers: A pair of numbers not having any common factors other than 1 or –1. (Or alternatively their greatest common factor is 1 or –1)
Ex : 15 and 28 are co-prime, because the factors of 15 (1,3,5,15) , and the factors of 28 (1,2,4,7,14,28) are not in common (except for 1) .

Twin Primes: A pair of prime numbers is said to be twin primes if they differ by 2.
Ex : (3,5) , (5,7) , (11,13) , …

Algebra

(a+b)2 = a2 + 2ab + b2
(a-b)2 = a2 - 2ab + b2

(a+b)2 - (a-b)2 = 4ab
(a+b)2 + (a-b)2 = 2 (a2 + b2)

a2-b2 = (a-b)(a+b)

(a+b)3 = a3+b3+3ab(a+b) = a3+b3+3a2b+3ab2
(a-b)3 = a3-b3-3ab(a-b) = a3-b3-3a2b+3ab2

a3+b3 =(a+b)3-3ab(a+b) = (a+b)(a2-ab+b2)
a3-b3 =(a-b)3+3ab(a-b) = (a-b)(a2+ab+b2)

Test of Divisibility

Divisibility By 2 : A number is divisible by 2, if its unit's digit is zero or even (2, 4, 6, 8..).

Divisibility By 3 : A number is divisible by 3, if the sum of its digits is divisible by 3.

Divisibility By 4 : A number is divisible by 4, if the number formed by the last two digits is divisible by 4.

Divisibility By 5 : A number is divisible by 5, if its unit's digit is either 0 or 5.

Divisibility By 6 : A number is divisible by 6, if it is divisible by both 2 and 3.

Divisibility By 8 : A number is divisible by 8, if the number formed by the last three digits of the given number is divisible by 8.

Divisibility By 9 : A number is divisible by 9, if the sum of its digits is divisible
by 9.

Divisibility By 10 : A number is divisible by 10, if it ends with 0.

Divisibility By 11 : A number is divisible by 11, if the difference of the sum of its digits at odd places and the sum of its digits at even places, is either 0 or a number divisible by 11.

Divisibility By 12: A number is divisible By 12 if the number is divisible By both 4 and 3.

Divisibility By 13: A number is divisible By 13 if its unit’s place digit is multiplied By 4 and added to the remaining digits and the number obtained is divisible By 13.

Divisibility By 14: A number is divisible By 14 if the number is divisible By both 2 and 7.

Divisibility By 15: A number is divisible By 15 if the number is divisible By both 3 and 5.

Divisibility By 16: A number is divisible By 16 if its last 4 digits is divisible By 16 or if the last four digits are zeros.

Divisibility By 17: A number is divisible By 17 if its unit’s place digit is multiplied By 5 and subtracted from the remaining digits and the number obtained is divisible By 17.

Divisibility By 18: A number is divisible By 18 if the number is divisible By both 2 and 9.

Divisibility By 19: A number is divisible By 19 if its unit’s place digit is multiplied By 2 and added to the remaining digits and the number obtained is divisible By 19.

Divisibility By 20: A number is divisible by 20 if it is divisible by 10 and the tens digit is even.

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General Knowledge of India

Which of the following dance forms was introduced by the great Vaishnava saint and reformer Mahapurusha Sankaradeva ?

Which of the following is the only classical dance of india having links with Muslim culture and represents a unique synthesis of Hindu and Muslim genius in art ?

Time and Distance

Starting from the same point at the same time, Ruhan and Yuvan had to reach the same destination. While Ruhan drove at 45 km/hr, Yuvan was slower by 5 km/hr. If Yuvan arrived at the destination an hour after Ruhan did, the distance covered by each, in Kilometres, was ?

Simple Interest

A sum of money was invested at a certain rate of simple interest for 4 years. Had the sum been invested at a rate 3% higher than the actual rate, the interest earned would have been 720 Rs more. Find the sum initially invested?

Ratio and Proportion

A bag contains red, blue and black balls. The ratio of red to blue balls is 3 : 5. The ratio of black to red balls is 3 : 4. What is the ratio of blue to black balls?

Profit and Loss

Selling a pack of incense sticks for 136 Rs resulted in a loss of 15%. To make a profit of 10%, the selling price should be ?

Percentage

23% of a bucket full of diluted milk was water. If the quantity of pure milk in the bucket was 15.4 liter, then the capacity of the bucket was ?

Average

The average of the marks obtained by three girls in a test was twice the average of the marks obtained by eight boys in that test. If the total marks obtained by all these examinees was 168, find the average marks each of the girls obtained ?

Pipes and Cistern

44 pipes can fill a large water tank in 27 hours. How many hours it take for 66 pipes to fill four such tanks ?

HCF and LCM

A natural number, when divided by 3, 4, 5, 6, and 7 respectively, leaves corresponding remainder of 2, 3, 4, 5 and 6. What is the smallest of all such numbers fulfilling the above condition ?

Coding-Decoding

If in a certain code language, PRINT is written as 34825 and TRUE is written as 5479. Then, how will TENURE be written in that language?

Order Sequence

Arrange the given words from smallest to biggest-
1.Jug
2.Mug
3.Bucket
4.Drum
5.Cup

Statement and Conclusion

Statements
All socks are shoes
Some shoes are black

Conclusions
I. Some shoes are socks.
II. No scoks is black

Numbers

The difference between the place value of 4 and 2 in the number 833749502 is ?

Analogy

GIKM : HJLN :: PRTV : .........?

Order Sequence

In a row of girls, Nanda is eighth from the left and Chanda is nineteenth from right. When Nanda and Chanda interchange their positions, Chanda becomes twnty-third form right. How many girls are there in the row?

Analogy

Summer: Day :: Winter : ........?

Bird:Winges :: Fish:........?