Question Discussion & Solution

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.

CALCULATIONS:

⇒ 5² + 10 = 35

⇒ 6² + 12 = 48

⇒ 7² + 14 = 63

⇒ 8² + 16 = 80

⇒ 9² + 18 = 99

⇒ 10² + 20 = 120

The series follows the following pattern:

12 × 1 + 1 = 13

13 × 2 + 1 = 27

27 × 3 + 1 = 82

82 × 4 + 1 = 329

329 × 5 + 1 = 1646

CALCULATIONS:

21² - 21 = 441 - 21 = 420

22² - 22 = 484 - 22 = 462

23² - 23 = 529 - 23 = 506

24² - 24 = 576 - 24 = 552

25² - 25 = 625 - 25 = 600

26² - 26 = 676 - 26 = 650

Given: 

4          6          12        30        90        315      ? 

Calculation:

The pattern of given series may be evaluated as:

⇒ 4

⇒ 4 × 1.5 = 6

⇒ 6 × 2 = 12

⇒ 12 × 2.5 = 30

⇒ 30 × 3 = 90

⇒ 90 × 3.5 = 315

Hence the next number in series

⇒ 315 × 4

⇒ 1260