Difference between revisions of "2005 AMC 12B Problems/Problem 20"

Revision as of 15:10, 4 February 2011

Let $a,b,c,d,e,f,g$ and $h$ be distinct elements in the set $\{-7,-5,-3,-2,2,4,6,13\}.$

What is the minimum possible value of $(a+b+c+d)^{2}+(e+f+g+h)^{2}?$

$\mathrm{(A)}\ 30 \qquad \mathrm{(B)}\ 32 \qquad \mathrm{(C)}\ 34 \qquad \mathrm{(D)}\ 40 \qquad \mathrm{(E)}\ 50$

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 == Problem ==
+Let <math>a,b,c,d,e,f,g</math> and <math>h</math> be distinct elements in the set <math>\{-7,-5,-3,-2,2,4,6,13\}.</math>
+What is the minimum possible value of <math>(a+b+c+d)^{2}+(e+f+g+h)^{2}?</math>
+<math>
+\mathrm{(A)}\ 30     \qquad
+\mathrm{(B)}\ 32     \qquad
+\mathrm{(C)}\ 34     \qquad
+\mathrm{(D)}\ 40     \qquad
+\mathrm{(E)}\ 50
+</math>
 == Solution ==