During AMC testing, the AoPS Wiki is in read-only mode. No edits can be made.

2012 AMC 10B Problems/Problem 8

Revision as of 15:50, 24 February 2012 by Rguan (talk | contribs) (Created page with "== Problem 8 == What is the sum of all integer solutions to <math>1<(x-2)^2<25</math>? <math> \textbf{(A)}\ 10\qquad\textbf{(B)}\ 12\qquad\textbf{(C)}\ 15\qquad\textbf{(D)}\ 19...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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. ! Undefined control sequence.)

Solution



Solutions

$(x-2)^2$ = 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

$\textbf{(C)}$

Invalid username
Login to AoPS