A number is said to be a 'zeroth number' if the sum of the squares of

Question

A number is said to be a 'zeroth number' if the sum of the squares of its digits ends in a zero. How many two-digit 'zeroth numbers' are there?

Answer: Option D
:
D
Let the number be 10x + y.
Then,

1 \leq x \leq 9, 0, \leq y \leq 9

and

x^{2} + y^{2} = 10 k .

\begin{matrix} x & x^{2} & y^{2} m u s t e n d i n & P o s s i b l e v a l u e o f y 1 & 1 & 9 & 3, 7 2 & 4 & 6 & 4, 6 3 & 9 & 1 & 1, 9 4 & 16 & 4 & 2, 8 5 & 25 & 5 & 5 6 & 36 & 4 & 2, 8 7 & 49 & 1 & 1, 9 8 & 64 & 6 & 4, 6 9 & 81 & 9 & 3, 7 \end{matrix}

The required number = 17, hence option (d).

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