Correct Answer - Option 1 : 34

**Given**

Average of the square of the first and the last consecutive positive even number = 778

**Formula Used **

Average = Sum of observation/No. of observation

**Calculation**

Let the eight consecutive positive even numbers are x, x + 2, x + 4, x + 6, x + 8, x + 10, x + 12, x + 14

So according to question

The average of the square of the first and the last number = 778

⇒ [x^{2 }+ (x + 14)^{2}]/2 = 778

⇒ x^{2 }+ (x + 14)^{2 }= 1556

⇒ 2x^{2 }+ 196 + 28x = 1556

⇒ 2x^{2 }+ 28x = 1556 - 196

⇒ x^{2 }+ 14 x = 680

⇒ x^{2 }+ 14 x – 680 = 0

⇒ x(x + 34) - 20(x + 34) = 0

⇒ (x + 34) (x - 20) = 0

⇒ x = - 34, 20

⇒ x = 20 (- 34 is a negative number)

So the largest positive number will be = x + 14 = 20 + 14 = 34

**∴ The largest positive number is 34**