LIC AAO 06 Mar 2016 Paper

Five consecutive odd numbers = x x+ 2. x+ 4. x + 6 and x+ 8
According to the question.
${\left(\frac{\mathit{x}+6+\mathit{x}+8}{2}\right)}^2$ - ${\left(\frac{\mathit{x}+\mathit{x}+2}{2}\right)}^2$ = 492
⇒ ${\left(\frac{2\mathit{x}+14}{2}\right)}^2$ - ${\left(\frac{2\mathit{x}+2}{2}\right)}^2$ = 492
⇒ ${\left(\mathit{x}+7\right)}^2-{\left(\mathit{x}+1\right)}^2$ = 492
⇒ ${\mathit{x}}^2$ + 14x + 49 - ${\mathit{x}}^2$ - 2x - 1
= 492
⇒ 12x + 48 = 492
⇒ 12x = 492 - 48 = 444
⇒ x = $\frac{444}{12}$ = 37
= Smallest odd number