Madhya Pradesh Police Exam Model Paper 2

Given:
The difference of the square of two consecutive even numbers = 164
Concept used:
${\left(\mathit{a}+\mathit{b}\right)}^2={\mathit{a}}^2+2\mathit{a}\mathit{b}+{\mathit{b}}^2$
Calculations:
Let the first even number be x
So, second even number $=\mathit{x}+2$
According to the question
${\left(\mathit{x}+2\right)}^2\mathit{–}{\mathit{x}}^2=164$
$\Rightarrow {\mathit{x}}^2+2\times 2\times \mathit{x}+2^2\mathit{–}{\mathit{x}}^2=164$
$\Rightarrow 4\mathit{x}+4=164$
$\Rightarrow 4\mathit{x}=160$
$\Rightarrow \mathit{x}=40$
Second number $=\mathit{x}+2=42$
Sum of consecutive even numbers $=40+42=82$
∴ The sum of consecutive even numbers is 82