Question Discussion & Solution

Given:

2, 10, 18, 54, 162, 486, 1458

Calculation:

The pattern of the number series is:

2 × 3 = 6 ≠ 10

6 × 3 = 18

18 × 3 = 54

54 × 3 = 162

∴ 10 is Wrong Number

The series follows the following pattern:

5.5 × 2 - 2 = 9

9 × 2 - 2 = 16

16 × 2 - 2 = 30

30 × 2 - 2 = 58

58 × 2 - 2 = 114

9 × 5 + 1 = 46

10 × 6 + 1 = 61

11 × 7 + 1 = 78

12 × 8 + 1 = 97

13 × 9 + 1 = 118

Given:

144, 288, 576, 1008, 1594, 2304, 3168

Calculation:

The logic behind the given series is as follows

144 + 144 × 1 = 288

⇒ 288 + 144 × 2 = 576

⇒ 576 + 144 × 3 = 1008

⇒ 1008 + 144 × 4 = 1584

⇒ 1584 + 144 × 5 = 2304

⇒ 2304 + 144 × 6 = 3168

∴ The wrong number in the given series is 1594.

The series follows the following pattern:

12 × 2 - 1 = 23

23 × 2 - 1 = 45

45 × 2 - 1 = 89

89 × 2 - 1 = 177

177 × 2 - 1 = 353