## Odd man 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 â€¦.

Cubes: 27, 64, 125, 216 â€¦.

**3) Multiple of numbers:**

The series contains numbers which are multiple of different numbers.

**Example:**4, 8, 12, 16, 20â€¦..

**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 â€¦â€¦

**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 â€“ n.

**Example:**

If n = 4, n

^{3}â€“ n = 60

If n = 5, n

^{3}â€“ n = 120â€¦

**Series:**60, 120, 210, 336 â€¦

**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}â€“ 1), (n

^{2}+ 1), (n

^{2}â€“ n), (n

^{3}â€“ n), (n

^{2}â€“ n + 1), (n

^{2}â€“ n â€“ 1), etc

**a) If numbers in the series are 1,5, 11, 19, 29â€¦. then the relation is (n**

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

^{2}â€“ n + 1)**Example:**

If n = 5, (5

^{2}â€“ 5 + 1) = 21

If n = 6, (6

^{2}â€“ 6 + 1) = 31

If n = 7, (7

^{2}â€“ 7 + 1) = 43

**Types of questions**

Type 1: Find the missing number

**Q 1.**8, 16, 32, 64, 128, 256, ___, 1024

a. 423

b. 512

c. 896

d. 980

View solution

Correct Option: (b)**Hint: **Each preceding number is multiplied by 2

8 × 2 = 16, 16 × 2 = 32, 32 × 2 = 64, 64 × 2 = 128, 256 × 2 = 512 and 512 × 2 = 1024**Hence, the missing number is 512**

**Q 2.**11, 13, 17, 19, 23, 29, _____

a. 31

b. 33

c. 51

d. None of the above

View solution

Correct Option: (a)**Hint: **Numbers 11, 13, 17, 19, 23 and 29 are all prime numbers. **Therefore, next prime number is 31**

**Q 3.**15, 33, 69, 141, ___, 573, 1149

a. 151

b. 169

c. 285

d. 456

View solution

Correct Option: (c)**Hint: ****Each number is twice the previous number with 3 added to the answer. **

15 × 2 = 30, 30 + 3 = 33

33 × 2 = 66, 66 + 3 = 69

69 × 2 = 138, 138 + 3 = 141

141 × 2 = 282, 282 + 3 = 285

285 × 2 = 570, 570 + 3 = 573

573 × 2 = 1146, 1146 + 3 = 1149**Hence, the missing number is 285**

**Q 4.**6, 24, ___ , 120, 210, 336

a. 36

b. 60

c. 72

d. 95

View solution

Correct Option: (b)**Hint: **

Power series: n^{3} â€“ n

2^{3} â€“ 2 = 6

3^{3} â€“ 3 = 24

4^{3} â€“ 4 = 60

5^{3} â€“ 5 = 120

6^{3} â€“ 6 = 210

7^{3} â€“ 7 = 336**Hence, the missing number is 60**