1990 AJHSME Problems/Problem 3

Problem

What fraction of the square is shaded?

$[asy] draw((0,0)--(0,3)--(3,3)--(3,0)--cycle); draw((0,2)--(2,2)--(2,0)); draw((0,1)--(1,1)--(1,0)); draw((0,0)--(3,3)); fill((0,0)--(0,1)--(1,1)--cycle,grey); fill((1,0)--(1,1)--(2,2)--(2,0)--cycle,grey); fill((0,2)--(2,2)--(3,3)--(0,3)--cycle,grey); [/asy]$

$\text{(A)}\ \frac{1}{3} \qquad \text{(B)}\ \frac{2}{5} \qquad \text{(C)}\ \frac{5}{12} \qquad \text{(D)}\ \frac{3}{7} \qquad \text{(E)}\ \frac{1}{2}$

Solution

Reflecting the square across the diagonal drawn, we see that the shaded region covers exactly the unshaded region in the original square, and thus makes up $1/2$ of the square $\rightarrow \boxed{\text{E}}$ .

1990 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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1990 AJHSME Problems/Problem 3

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