Odd Man Out Questions

The given number series is 720, 732, 708, 742, 696

720

720 + 12 = 732

732 - 24 = 708

708 + 36 = 744 (Not 742)

744 - 48 = 696

Hence, the odd man in the given number series is 742.

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 follows a pattern that, multiplying the number with odd numbers in decreasing order starting with 13. That is,

6 × 13 = 78

65 × 11 = 858

858 × 9 = 7722

7722 × 7 = 54054

54054 × 5 = 270270

Hence, the wrong number is 54055

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.

The given number series 410, 409, 413, 404, ? , follows a pattern that 

410

$$\begin{gathered} 410 - 13 = 409 \\ 409 + 22 = 413 \\ 413 - 33 = 404 \\ 404 + 42 = 420 \end{gathered}$$

Hence, the next number in the given series is 420.

48, 54, 63, 81 and 105 are divisible by 3 but not 35.

Given Number series is :

3   4   14   48   576   27648

It follows a pattern that,

3

4

4 x 3 = 12   but not 14

12 x 4 = 48

48 x 12 = 576

576 x 48 = 27648

Hence, the odd one in the given Number Series is 14.