## Numbers Aptitude Concepts and Formulas## Points to remember:1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15)
For example: The unit digit of 156
The unit digit of 4 It shows if the power of 4 is even, the unit digit is 6, and if the power is an odd number, the unit digit is 4. Rule for 9: 9 It shows if the power of 9 is even, the unit digit is 1, and if the power is an odd number, the unit digit is 9.
2
So, the possible unit digit of 2 has 4 different numbers 2, 4, 8, and 6.
3
Same logic for 7 and 8: The numbers have 4 possible different numbers as their possible unit digits. The 7 has 7, 9, 3, 1 and 8 has 8, 4, 2, 6 respectively. ## Notes:1.) The number 1 is not a prime or composite number. 2.) The number 2 is the only even number which is a prime number. 3.) There are 25 prime numbers between 1 and 100, e.g. 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89 and 97.
- Select the least positive integer 'n' so that n
^{2}> given number. - Find out all the prime numbers less than n and check if the given number is divisible by any of these prime numbers.
- If the given number is not divisible by any of the prime numbers, it will be a prime number. See the example given below;
As (28) (29) Prime numbers less than 29 are 2, 3, 5, 7, 11, 13, 17, 19, 23 We find that 823 is not divisible by any of these prime numbers so it is a prime number. ## Tests for divisibility or divisibility rules:
## Some Important Formulae:i. (a+b) ii. (a - b) iii. (a+b) iv. (a+b) v. (a vi. (a vii. a viii. a.( b + c) = ab + ac ix. a.( b - c) = ab - ac x. (a+b) xi. (a - b) ## Quick multiplicatoin methods :1.) Multiplying a number by 9, 99, 999, 9999 or 10 a.) 2789 * 99 = ? 2789 (multiplicand) x 99 (multiplier) = 278900-2789= 276111 b.) 234 * 999 = 234000 - 234 = 233766 2. Multiplying a number by 11, 101, 1001, 10001 or 10 a.) 234 * 11 (10 b.) 234 * 101 (10 3.) Multiplying a number by 5, 25, 125, 625 or by a number which is some power of 5: Place as many zeros to the right of the multiplicand equal to the power of 5 in the multiplier then divide it by 2 raised to the power of 5. See the examples given below; ## Some quiker methods:o A number when divided by d = (d o Two numbers when divided by a given divisor leaves remainders r = r o If the sum and difference of two numbers (x and y) is given, then their product is given by; o And, the two numbers are given by;
Let us understand it with an example; find the number of numbers up to 432 which are divisible by 15.
432 = 28 (quotient) * 15 + 12 The quotient obtained is the required number of numbers up to 432 which are divisible by 15.
o The sum of first n natural numbers is given by; o The sum of first n odd numbers is given by; Sum = n o The sum of first n even numbers is given by; Sum = n (n+1) o The sum of squares of first n natural numbers is given by; o The sum of cubes of first n natural numbers is given by;
The first term in an arithmatic progression is denoted by 'a' , n Therefore, an Arithmetic progression with first term 'a' and common difference d is given by; a, (a+d), (a+2d), (a+3d), o The nth term of an arithmetic progression is given by; T o The sum of first n terms of an arithmetic progression is given by; o The number of terms in an arithmetic progression is given by;
The first term in an geometric progression is denoted by 'a' , n Therefore, a geometric progression with first term 'a' and common ratio 'r' is given by; a, ar, ar o The n = ar o The sum of first n terms in a geometric progression is given by; ## Numbers Aptitude Test PaperNumbers Aptitude Test Paper 1Numbers Aptitude Test Paper 2 Numbers Aptitude Test Paper 3 Numbers Aptitude Test Paper 4 Numbers Aptitude Test Paper 5 Numbers Aptitude Test Paper 6 Numbers Aptitude Test Paper 7 Next TopicNumbers Aptitude Test Paper 1 |