Difference between revisions of "2023 AMC 8 Problems/Problem 2"

(Solution 2)
(Solution 2 (Similar to Solution 3 but without pictures))
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-apex304
 
-apex304
  
==Solution 2 (Similar to Solution 3 but without pictures)==
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==Solution 2 (Vague)==
  
 
Notice how the paper is folded. The bottom right corner of the twice-folded paper has to be the middle of the unfolded paper. So if you cut it in the way that it is shown in the problem, you find (it has to be symmetrical) that the cuts make an equilateral rhombus [tilted square] centered in the middle of the paper.
 
Notice how the paper is folded. The bottom right corner of the twice-folded paper has to be the middle of the unfolded paper. So if you cut it in the way that it is shown in the problem, you find (it has to be symmetrical) that the cuts make an equilateral rhombus [tilted square] centered in the middle of the paper.

Revision as of 11:19, 25 January 2023

Problem

A square piece of paper is folded twice into four equal quarters, as shown below, then cut along the dashed line. When unfolded, the paper will match which of the following figures?

2023 AMC 8-2.png

Solution 1

Take a paper and fold it using the given conditions to see the resulting answer -apex304

Solution 2 (Vague)

Notice how the paper is folded. The bottom right corner of the twice-folded paper has to be the middle of the unfolded paper. So if you cut it in the way that it is shown in the problem, you find (it has to be symmetrical) that the cuts make an equilateral rhombus [tilted square] centered in the middle of the paper.

-claregu

Solution 3 (Thorough)

Notice that when we unfold the paper from the vertical fold line, we get

Screenshot 2023-01-25 8.11.20 AM.png

Then, if we unfold the paper from the horizontal fold line, we result in

Screenshot 2023-01-25 8.14.41 AM.png

It is clear that the answer is $\boxed{\textbf{(E)}}$

~MrThinker

See Also

2023 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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
All AJHSME/AMC 8 Problems and Solutions

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