LIC AAO 05 Mar 2016 Paper

Consecutive odd numbers ⇒ x, x+ 2, x+ 4, x+ 6 and x + 8
According to the question
${\left(\frac{\mathit{x}+6+\mathit{x}+8}{2}\right)}^2$ - ${\left(\frac{\mathit{x}+\mathit{x}+2}{2}\right)}^2$ = 588
⇒ ${\left(\mathit{x}+7\right)}^2-{\left(\mathit{x}+1\right)}^2$ = 588
⇒ ${\mathit{x}}^2$ + 14x + 49 - ${\mathit{x}}^2$ - 2x - 1
= 588
⇒ 12x + 48 = 588
⇒ 12x = 588 - 48 = 540
⇒ x = $\frac{540}{12}$ = 45