Question

Two natural numbers $x$ & $y$ are chosen at random. Find the probability that $x^2+y^2$ is divisible by $10$.

• A. $9/50$
• B. $1/100$
• C. $1/50$
• D. $4/25$

Answer 1

The correct option is A $9/50$

$y^2/x^2$	0	1	4	5	6	9
0	$✓$
1						$✓$	$P\left(0\right)=\frac{1}{10}=P\left(5\right)$
4					$✓$		$P\left(1\right)=P\left(4\right)=P\left(6\right)$
5				$✓$
6			$✓$				$P\left(9\right)=\frac{2}{10}$
9		$✓$

$P(00+19+91+55+64+46)$
$=\frac{1}{100}+\left(\frac{4}{100}\right)4+\frac{1}{100}=\frac{18}{100}$