# Numeral (Odd Man Out)

In **Numeral (Odd Man Out)** questions we have to find the odd man out from a series of numbers. These numbers can be single digit numbers, in which case the solution tends to be fairly easy. However, when the numbers are bigger, it does get increasingly more difficult to pick the odd one out. Some guidelines you can follow are,

- We will see if there is any obvious relation in those numbers
- we will next check if one specific number is in some way related to all the other numbers.
**Odd number/Even number/Prime numbers :**The series may consist of odd numbers /even numbers or prime numbers except one number, which will be the odd man out. Hence, before solving numerical on this topic must revise all basic concepts.**Difference or sum of numbers:**The difference between two consecutive numbers may increase or decrease**Perfect squares/Cubes:**we will also Check for squares and cubes of the numbers**Multiple or Divisibility of numbers:**we will also try other mathematical possibilities like divisibility by the same number, or multiples of the same number etc.**Numbers in A.P./G.P. :**Geometric progression: x, xr, xr^{3}, xr^{4}

Arithmetic progression: x, x + y, x + 2y, x + 3y are said to be in A.P.

The terms in series may be arithmetic or geometric progression.**Cumulative series:**In this type, the third number is the addition of previous two numbers.**Power series:**In this type, the terms are defined on the basis of powers of numbers; the number may be expressed in the form of ${n}^{3}$ – n.- The middle digit is the sum of other two digits.
- Sometimes we will find, there is interrelation between the digits of the number rather than the number itself. our last step should be to check for this.

Example : Find the odd man out.

8, 27, 64, 100, 125, 216, 343

Solution : 100

The pattern is 2^{3}, 3^{3}, 4^{3}, 5^{3}, 6^{3}, 7^{3}. But, 100 is not a perfect cube.

Example : Find the odd man out.

396, 462, 572, 427, 671, 264

Solution : 427

In each number except 427, the middle digit is the sum of other two.

Example : Find out the wrong number in the given sequence of numbers.

22, 33, 66, 99, 121, 279, 594

Solution : 279

Each of the number except 279 is a multiple of 11.

Example : Find out the wrong number in the given sequence of numbers.

1, 2, 6, 15, 31, 56, 91

Solution : 91

1, 1 + 1^{2} = 2, 2 + 2^{2} = 6, 6 + 3^{2} = 15, 15 + 4^{2} = 31, 31 + 5^{2} = 56, 56 + 6^{2} = 92

Example : Insert the missing number.

16, 33, 65, 131, 261, (....)

Solution : 523

Each number is twice the preceding one with 1 added or subtracted alternatively.

So, the next number is (2 x 261 + 1) = 523.

Last number of given series must be 92 not 91.

Example : Insert the missing number.

2, 4, 12, 48, 240, (....)

Solution : 1440

Go on multiplying the given numbers by 2, 3, 4, 5, 6.

So, the correct next number is 1440.

Example : Find out the wrong number in the series.

1, 1, 2, 6, 24, 96, 720

Solution : 96

Go on multiplying with 1, 2, 3, 4, 5, 6 to get next number. So, 96 is wrong.

Example : Find out the wrong number in the series.

445, 221, 109, 46, 25, 11, 4

Solution : 46

Go on subtracting 3 and dividing the result by 2 to obtain the next number. Clearly, 46 is wrong.