2012 AMC 10B Problems/Problem 8

Problem 8

What is the sum of all integer solutions to $1<(x-2)^2<25$ ?

$\textbf{(A)}\ 10\qquad\textbf{(B)}\ 12\qquad\textbf{(C)}\ 15\qquad\textbf{(D)}\ 19\qquad\textbf{(E)}\25$ (Error compiling LaTeX. Unknown error_msg)

$(x-2)^2$ = perfect square.

1< perfect square< 25

Perfect square can equal: 4, 9, or 16

Solve for x:

$(x-2)^2=4$

$x=4$

and

$(x-2)^2=9$

$x=5$

and

$(x-2)^2=16$

$x=6$

What is the sum of all integer solutions

$4+5+6=\boxed{15}$

OR

$\textbf{(C)}$