Question Discussion & Solution

CALCULATIONS:

(14 ÷ 2) + 1 = 8

⇒ (8 ÷ 2) + 2 = 6

⇒ (6 ÷ 2) + 1 = 4

⇒ (4 ÷ 2) + 2 = 4

⇒ (4 ÷ 2) + 1 = 3

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:

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

The pattern followed in this question is:

2³ + 2 = 10

3³ + 2 = 29

4³ + 2 = 66

5³ + 2 = 127

6³ + 2 = 218

Calculation:

The given series is the cube of prime numbers

2³ = 8

3³ = 27

5³ = 125

7³ = 343

11³ = 1331

13³ = 2197

∴ The value of ? is 343.