1989 AJHSME Problems/Problem 1

Revision as of 18:44, 26 May 2009 by 5849206328x (talk | contribs) (New page: ==Problem== <math>(1+11+21+31+41)+(9+19+29+39+49)=</math> <math>\text{(A)}\ 150 \qquad \text{(B)}\ 199 \qquad \text{(C)}\ 200 \qquad \text{(D)}\ 249 \qquad \text{(E)}\ 250</math> ==Solu...)
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Problem

$(1+11+21+31+41)+(9+19+29+39+49)=$

$\text{(A)}\ 150 \qquad \text{(B)}\ 199 \qquad \text{(C)}\ 200 \qquad \text{(D)}\ 249 \qquad \text{(E)}\ 250$

Solution

We make use of the associative and commutative properties of addition to rearrange the sum as \begin{align*} (1+49)+(11+39)+(21+29)+(31+19)+(41+9) &= 50+50+50+50+50 \\ &= 250 \Longrightarrow \boxed{\text{E}} \end{align*}

See Also

1989 AJHSME (ProblemsAnswer KeyResources)
Preceded by
First
Problem
Followed by
Problem 2
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All AJHSME/AMC 8 Problems and Solutions