Question

The difference of the squares of two consecutive even natural numbers is $92$. Find the larger of the two numbers.

• A. $24$
• B. $43$
• C. $56$
• D. $86$

Answer 1

The correct option is A $24$

Let $x$ and $x+2$ be the two consecutive natural numbers.
Then according to question, we have
$(x+2{)}^2-(x{)}^2=92$
$\Rightarrow x^2+4x+4-x^2=92$
$\Rightarrow 4x+4=92\Rightarrow x=22$
Therefore, the required numbers are $22$ and $24$.
Hence, larger of two is $24$.