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

(New page: ==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 ? Image:1995 AHSME num. 6.png <ma...)
 
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==Problem==
 
==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 ?  
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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?  
  
[[Image:1995 AHSME num. 6.png]]
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<asy>
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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>
  
 
==Solution==
 
==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 <math>\boxed{\mathrm{(C)}}</math> at all.
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The marked side is the side with the <math>x.</math> We imagine it folding up. First, we fold the <math>x</math> upwards. Now we fold the <math>A</math> upwards, and thus <math>x</math> is touching <math>B</math> on it's left side. We now fold <math>B</math> up, and we realize that <math>x</math> won't be touching <math>\boxed{\mathrm{(C)}}</math> at all.
  
 
==See also==
 
==See also==
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{{AHSME box|year=1995|num-b=5|num-a=7}}
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{{MAA Notice}}

Latest revision as of 00:49, 14 October 2013

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
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

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