## Odd one out and series

This topic depends upon all basic concepts we have studied till now in this aptitude session. Numbers, A.P./G.P., Squares and cube roots, binomial theorem, etc.

Being logical and increasing your intelligence will help in solving the problems of odd man out and series. Your perspective in solving these types of problems should be unique. Different problems related to alphabets, numbers, metals, etc can be asked, hence different rules, differences should be figured out quickly to solve because time is limited.

**Quick Tips and Tricks**

**Series: **

The terms or elements follow a definite law in series but it cannot be generalized. You should know, what is the definite relationship between numbers which make the set of given terms in series. Addition, subtraction, multiplication, division, transposition of terms and series generally form such series. The different questions asked may depend upon the following:

**1) 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.

**2) Perfect squares/Cubes: **

Squares: 9, 16, 49, 81 ….

Cubes: 27, 64, 125, 216 ….

**3) Multiple of numbers: **

The series contains numbers which are multiple of different numbers.

**Example: **4, 8, 12, 16, 20…..

**4) 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.

**5) Difference or sum of numbers: **

The difference between two consecutive numbers may increase or decrease

**6) Cumulative series: **

In this type, the third number is the addition of previous two numbers.

**Example: **2, 4, 6, 10, 16, 26 ……

**7) 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 n3 – n.

**Example: **

If n = 4, n^{3} – n = 60

If n = 5, n^{3} – n = 120…

**Series: **60, 120, 210, 336 …

**8) **The middle digit is the sum of other two digits.

**Example: **165, 121, etc

**9) **The series of numbers may follow different sequence as shown below:

(n^{2} – 1), (n^{2} + 1), (n^{2} – n), (n^{3} – n), (n^{2} – n + 1), (n^{2} – n – 1), etc

**a) If numbers in the series are 1,5, 11, 19, 29…. then the relation is (n ^{2} – n – 1) **

**b) If numbers in the series are 21, 31, 43 then the relation is (n ^{2} – n + 1) **

**Example:**

If n = 5, (5

^{2}– 5 + 1) = 21

If n = 6, (6

^{2}– 6 + 1) = 31

If n = 7, (7

^{2}– 7 + 1) = 43

**How to find odd object**

*different one*or odd one out by following categories:

- Even or Odd
- Gender
- Use and the applicability of the object.

*This concept could be understood by following examples*:

**Directions**

*for questions 1 to 7:**In each of following examples, four words have been given of which three are alike in some way and one is different. Choose the*odd one out

*.*

**Example No. 1**: pen, pencil, marker, eraser

**Solution**: Except eraser, rest all are used for writing.

**Example No. 2**: 71, 73, 79, 91

**Solution:**Except 91, rest all are prime numbers. Hence odd one is 91.

**Ex**

**ample No. 3**: Book, eraser, pen and compass.

**Solution:**Book is not stationery item while rest all are stationery items. Hence book is the odd one out.

**Example No. 4**: Onions, garlic, radish, cauliflower

**Solution**: Here all the vegetables grow underground except cauliflower

**.**Therefore cauliflower is the answer.

**Example No. 5**: Agra, Vrindavan, Ambala, Bhopal.

**Solution**: Only Bhopal is Capital. Thus Bhopal is the answer.

**Example No. 6**: Jacket, Sweater, Coat, Tshirt

**Solution**: Except Tshirt all are winter wears.

**Example No. 7**: Cabbage, Apple, Apricot, Banana

**Solution**: Here all the objects are fruits except Cabbage, which is a vegetable.