Quantitative Aptitude Important Formulas

Simple Interest - Important Formulas,Tricks and Examples

Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then,

Simple Interest (SI) = (P*R*T )/100

Amount, A = P + SI = P + (P*R*T)/100

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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.

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In which year was the battle of ‘Koregaon Bhima’ fought?

The approach that is very useful in organizing the content in history is.

General Knowledge of India

NITI Aayog stands for _____.

General Knowledge of MP

India’s first Ramayan art museum was established at?

Errors Identification

Read the sentence carefully and choose the option that has an error in it:
The management’s trusted employee was suspected of stealing large sum of money.

Read the sentence carefully and choose the option that has an error in it:
The teacher asked the child to repeat again because he spoke feebly.

Fill in the blank

Fill in the blank with the most appropriate preposition in the given sentence.
Let’s sit _________ the shade of this beautiful tree.

Choose the most appropriate determiner for the given sentence.
________of what he said was very sensible.

Substitution

Choose the option that substitutes the given phrase appropriately.
A work of art made by carving

Correct sentence

Choose the option that best transforms the sentence into its Indirect form:
‘What country do you come from?’ said the police officer.

Alternative Phrase

Choose the option that best explains the highlighted expression:
All human beings have feet of clay.

Fill in the blank

Choose an appropriate modal for the given sentence:
My doctor said that I_____ stop smoking as one of my lungs got infected.

Choose the appropriate prepositions for the given sentence:
My parents have been married ________ forty-nine years, but you can still see the love ________ their eyes.

Choose the appropriate conjunction for the given sentence:
______ it rains, the college will declare the holiday.

Antonyms

Choose the appropriate antonym for the highlighted word in the given sentence.
The family protracted their visit by several days.

Tenses

Choose the appropriate tenses to fill in the blanks in the given sentence:
Please _________ a noise. Ritu __________ to sleep.

Synonyms

Choose the appropriate synonym for the highlighted word in the given sentence.
Does he really expect us to believe such a flimsy excuse?

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