Odd Man Out Questions

The given number series is 180, 90, 60, 40, 36

It follows a pattern that,

180 x 1/2 = 90

90 x 2/3  = 60

60 x 3/4  = 45 (NOT 40)

45 x 4/5  = 36

Hence, the wrong number in the given series is 40.

In each term second two numbers are multiples of the first number. But in 4-15-24 15 is not multiple of 4.

Arithmetic Series ::

An Arithmetic Series is a series of numbers in which each term increases by a constant amount.

How to find the sum of the Arithmetic Sequence or Series for the given Series ::

When the series contains a large amount of numbers, its impractical to add manually. You can quickly find the sum of any arithmetic sequence by multiplying the average of the first and last term by the number of terms in the sequence.

That is given by Sn = n(a1 + an)2 Where n = number of terms, a1 = first term, an = last term

Here Last term is given by an = a1 + n-1d where d = common difference

Now given Arithmetic Series is 

2, 5, 8, 11,...

Here a1 = 2,  d = 3, n = 36 

Now, $$\begin{gathered} an= a1 + n - 1d \\ a36= 2 + 36 - 13 = 105 + 2 = 107 \end{gathered}$$

Now, Sum to 36 terms is given by

S36 = 36(2 + 107)2 = 36 x 1092 = 39242 = 1962

Therefore, Sum to 36 terms of the series 2, 5, 8, 11,... is 1962.

2.5 × 1 + 1 = 3.5

3.5 × 2 + 2 = 9

9 × 4 + 4 = 40

40 × 8 + 8 = 328

Here the given series 28, 12, 4, 2, -2 follows a pattern that

$$\begin{gathered} 28 \\ 28 - 24 = 28 - 16 = 12 \\ 12 - 23 = 12 - 8 = 4 \\ 4 - 22 = 4 - 4 = 0 (NOT 2) \\ 0 - 21 = 0 - 2 = -2 \end{gathered}$$

Hence, the odd man in the given series is 2.

The given series is 8, 14, 24, 60, 180

8

8 x 1.5 = 12 (NOT 14)

12 x 2 = 24

24 x 2.5 = 60

60 x 3 = 180

Hence, the odd man in the given series is 12.

The given number series follows a pattern that,

56

56 + 8 = 64

64 - 16 = 48

48 + 32 = 80 (Not equal to 90)

80 - 64 = 16

16 + 128 = 144 

Hence, the odd number in the given number series is 90.

Given number series is 514   470   ?   415   404

Here the pattern it follows is

514

514 - 44 = 470

470 - 33 = 437

437 - 22 = 415

415 - 11 = 404

Hence, the missing number in the given number series is 437.