Question

If the sum of three consecutive odd numbers is a perfect square between 200 and 400, then the root of this sum is

• A. $15$
• B. $16$
• C. $18$
• D. $19$

Answer 1

The correct option is A $15$

Let three consecutive odd numbers be $x-1,x+1,x+3$

$200<(x-1)+(x+1)+(x+3)<400$

$200<(3x+3)<400$
$200<3(x+1)<400$
From squares lying between $200$ and $400-225,256,289,324,362$, $225$ is multiple of $3$.
$\therefore \sqrt{225}=15$