Question

The product of two consecutive even numbers is 40 less than the square of the larger number. Find the larger number.

• A. 18
• B. 20
• C. 22
• D. 24

Answer 1

The correct option is B 20

Let the first number be x.
Hence, the consecutive even number = x+2.
Given, the product of two consecutive even numbersis 40 less than the square of the larger number
Hence, x(x+2) = (x+2)${}^2$ - 40
$\Rightarrow$ x${}^2$ + 2x = x${}^2$ + 4x + 4 - 40
$\Rightarrow$ 2x = 36
$\Rightarrow$ x = 18
$\Rightarrow$ x + 2 = 18 + 2 = 20.
Hence, the larger number is 20.