Difference between revisions of "1995 AHSME Problems/Problem 6"
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The figure shown can be folded into the shape of a cube. In the resulting cube, which of the lettered faces is opposite the face marked x? | The figure shown can be folded into the shape of a cube. In the resulting cube, which of the lettered faces is opposite the face marked x? | ||
| − | + | <asy> | |
| + | defaultpen(linewidth(0.7)); | ||
| + | path p=origin--(0,1)--(1,1)--(1,2)--(2,2)--(2,3); | ||
| + | draw(p^^(2,3)--(4,3)^^shift(2,0)*p^^(2,0)--origin); | ||
| + | draw(shift(1,0)*p, dashed); | ||
| + | label("$x$", (0.3,0.5), E); | ||
| + | label("$A$", (1.3,0.5), E); | ||
| + | label("$B$", (1.3,1.5), E); | ||
| + | label("$C$", (2.3,1.5), E); | ||
| + | label("$D$", (2.3,2.5), E); | ||
| + | label("$E$", (3.3,2.5), E);</asy> | ||
<math> \mathrm{(A) \ A } \qquad \mathrm{(B) \ B } \qquad \mathrm{(C) \ C } \qquad \mathrm{(D) \ D } \qquad \mathrm{(E) \ E } </math> | <math> \mathrm{(A) \ A } \qquad \mathrm{(B) \ B } \qquad \mathrm{(C) \ C } \qquad \mathrm{(D) \ D } \qquad \mathrm{(E) \ E } </math> | ||
Revision as of 19:47, 18 August 2011
Problem
The figure shown can be folded into the shape of a cube. In the resulting cube, which of the lettered faces is opposite the face marked x?
![[asy] defaultpen(linewidth(0.7)); path p=origin--(0,1)--(1,1)--(1,2)--(2,2)--(2,3); draw(p^^(2,3)--(4,3)^^shift(2,0)*p^^(2,0)--origin); draw(shift(1,0)*p, dashed); label("$x$", (0.3,0.5), E); label("$A$", (1.3,0.5), E); label("$B$", (1.3,1.5), E); label("$C$", (2.3,1.5), E); label("$D$", (2.3,2.5), E); label("$E$", (3.3,2.5), E);[/asy]](http://latex.artofproblemsolving.com/c/d/2/cd26443e7d52459f1c3554f595e6832511d1d1f7.png)
Solution
The marked side is the side with the x. We imagine it folding up. First, we fold the x upwards. Now we fold the A upwards, and thus x is touching B on it's left side. We now fold B up, and we realize that x won't be touching 
at all.
See also
| 1995 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
