Difference between revisions of "1995 AHSME Problems/Problem 6"

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(Problem)
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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?  
  
[[Image:1995 AHSME num. 6.png]]
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<asy>
 +
defaultpen(linewidth(0.7));
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path p=origin--(0,1)--(1,1)--(1,2)--(2,2)--(2,3);
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draw(p^^(2,3)--(4,3)^^shift(2,0)*p^^(2,0)--origin);
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draw(shift(1,0)*p, dashed);
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label("$x$", (0.3,0.5), E);
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label("$A$", (1.3,0.5), E);
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label("$B$", (1.3,1.5), E);
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label("$C$", (2.3,1.5), E);
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label("$D$", (2.3,2.5), E);
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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]

$\mathrm{(A) \ A } \qquad \mathrm{(B) \ B } \qquad \mathrm{(C) \ C } \qquad \mathrm{(D) \ D } \qquad \mathrm{(E) \ E }$

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 $\boxed{\mathrm{(C)}}$ at all.

See also

1995 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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All AHSME Problems and Solutions
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