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1987 AJHSME Problems/Problem 12

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Problem

What fraction of the large 12 by 18 rectangular region is shaded?

draw((0,0)--(18,0)--(18,12)--(0,12)--cycle);draw((0,6)--(18,6));for(int a=6; a<12; ++a) {  draw((1.5a,0)--(1.5a,6)); }fill...

\text{(A)}\ \frac{1}{108} \qquad \text{(B)}\ \frac{1}{18} \qquad \text{(C)}\ \frac{1}{12} \qquad \text{(D)}\ \frac29 \qquad \...

Solution

The shaded region makes up \frac13 of the quarter rectangle. The quarter rectangle is then \frac14 of the large rectangle, so the shaded region takes up \frac{1}{3}\times \frac{1}{4}=\frac{1}{12} of the large rectangle.

\boxed{\text{C}}

See Also

1987 AJHSME (ProblemsResources)
Preceded by
Problem 11
Followed by
Problem 13
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Looking for a challenging geometry text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.
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