Quantitative Aptitude Important Formulas

Volume & Surface Area - Important Formulas,Tricks and Examples

Cuboid:
Volume = lbh
Surface Area = 2(lb + bh + hl)
Diagonal =√(l2 +b2 +h2)

Cube:
Volume = a3
Surface Area = 6a2
Length of diagonal = a√3

Sphere:
Volume = (4/3)πr3
Surface Area = 4πr2

Hemisphere:
Volume = (2/3)πr3
Curved Surface Area = 2πr2
Total Surface Area = 2πr2+ πr2 = 3πr2

Cylinder:
Volume = πr2h
Curved Surface Area = 2πrh
Total Surface Area = 2πrh + 2πr2 = 2πr(h + r)

Cone:
Volume = (1/3)πr2h
Curved Surface Area = πrl
Total Surface Area = πrl + πr2 = πr(l + r).

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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.

Latest Updates

Agriculture

Which gas is fixed by Rhizobium bacteria present in the root nodules of a pea plant ?

Chemistry

The formation of sulphurous acid involves ?

The acid present in soft drinks is ?

The cathode of a dry cell is made of ?

The number of atoms present in the molecule of an element is known as its?

Physics

If the angle of incidence formed by a ray of light on a plane mirror is 37°, then the angle of refraction is?

A dynamo converts ?

If the time taken for hearing the echo of a girl's voice after reflection from a cliff is 6 seconds, calculate the distance of the girl from cliff ?

The physical quantity corresponding to the rate of change of displacement is..............?

Work done is said to be zero when an object moves at an angle of ............with respect to the force applied ?

Indian Geography

In terms of area, India is the ........largest country in the world ?

Indian Politics

How many members from the Anglo Indian community are nominated to the Lok Sabha?

Which of the following parts of the Constitution of India provides fundamental rights ?

Time and Work

Ram could complete a job alone in 6 days but Sunil would take thrice the time to do it alone.They started the work together but Ram had to leave a few days before the completion of the work and Sunil had to complete the remaining task by himself. If as a result , it took 6.75 days in all to complete the job, for how many days did the duo work together?

Profit and Loss

The cost price of 20 articles is equal to the selling price of 16 articles. Find the gain or loss percent?

Discount

Successive discount of 10% and 10% are equivalent to a single discount of ?

A discount series of 10%, 20% and 40% is equal to single discount of ?

Pepsi and Coke, there are two companies, selling the packs of cold­drinks. For the same selling price Pepsi gives two successive discounts of 10% and 25% on marked price, while Coke sells it by giving two successive discounts of 15% and 20% on marked price. What is the ratio of their marked price?