Question

What is the sum of two consecutive even numbers,the difference of whose squares is 84?

• A. 34
• B. 38
• C. 42
• D. 46
• E. 47

Answer 1

The correct option is C

42

Let the numbers be x and x+2

Then, ${\left(x+2\right)}^2-x^2=84\iff 4x+4=84\iff 4x=80\iff x=20.$

$\therefore \mathrm{Re}quiredsum=x+\left(x+2\right)=2x+2=42.$