if we know the unit digit of the power the number is raised to, we can answer for the unit digit of a.

For statement 1\(100<y^2<x^2<169\) can be read as \(10^2<y^2<x^2<13^2\)

Which means y has to be 11 and x has to be 12. Thus, we can figure out the unit digit.

For statement 2\(x^2-y^2=23\)

We can either do it by adding perfect squares to 23 and see when we reach another perfect square (it's going to take precious time, of course) or we could solve it with \((x+y)(x-y)=23\) and get the values for x and y. Thus, figuring out the unit digit of a.

Answer: D
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