Difference between revisions of "2012 AMC 10B Problems/Problem 8"

Revision as of 17:44, 24 February 2012

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:

$(x-2)^2=4$

$x=4,0$

and

$(x-2)^2=9$

$x=5,-1$

and

$(x-2)^2=16$

$x=6,-2$

What is the sum of all integer solutions

$4+5+6+0+(-1)+(-2)=\boxed{12}$

OR

$\textbf{(B)}$

@@ Line 22: / Line 22: @@
 <math>(x-2)^2=4</math>
-<math>x=4</math>
+<math>x=4,0</math>
 and
@@ Line 28: / Line 28: @@
 <math>(x-2)^2=9</math>
-<math>x=5</math>
+<math>x=5,-1</math>
 and
@@ Line 34: / Line 34: @@
 <math>(x-2)^2=16</math>
-<math>x=6</math>
+<math>x=6,-2</math>
 ''What is the sum of all integer solutions''
-<math>4+5+6=\boxed{15}</math>
+<math>4+5+6+0+(-1)+(-2)=\boxed{12}</math>
 OR
-<math> \textbf{(C)}</math>
+<math> \textbf{(B)}</math>