C. x and y are place holder values. Let the first number be A and the second number be B.
A = 10x+y, B= 10y+x
(for example 57 = 10(5) +7(1), 957 = 100(9)+10(5)+7(1))
A-B = 10x+y-(10y+x)
= 10x+y-10y-x
= 10x-x+y-10y
=9x-9y
We are told 9x-9y >10 and is a perfect square
9x-9y = 9(x-y)
= 3^2( x-y)
x-y must also be a perfect square. Of all the options given, only 4 is the perfect square.
9(x-y) = 9*4 = (3^2)(2^2)
A = 10x+y, B= 10y+x
(for example 57 = 10(5) +7(1), 957 = 100(9)+10(5)+7(1))
A-B = 10x+y-(10y+x)
= 10x+y-10y-x
= 10x-x+y-10y
=9x-9y
We are told 9x-9y >10 and is a perfect square
9x-9y = 9(x-y)
= 3^2( x-y)
x-y must also be a perfect square. Of all the options given, only 4 is the perfect square.
9(x-y) = 9*4 = (3^2)(2^2)