<p>(Remove spaces)</p>
<p><a href="http://i.imgur">http://i.imgur</a>. com/MNf739c.png
Answer: B</p>
<p><a href="http://i.imgur">http://i.imgur</a>. com/lcUhnC8.png
Answer: A
For future reference, how would you go about solving problems like these? It's very hard to imagine questions like that in my head, involving folding boxes along lines and whatnot.</p>
<p><a href="http://i.imgur">http://i.imgur</a>. com/NTT7iUw.png
Answer: D</p>
<p>I will give you some hints:</p>
<p>Q#1: What is the relationship between the lengths of side PT and PQ? Can they be related via the dimensions of the cube. Here P is the mid point of the edge of the cube.</p>
<p>Q#2: This can be visually tricky. I used to have trouble visualizing them as well. I would recommend cutting out pieces of paper and making the folds where the dotted lines are, and then try to see if you create an enclosed box. This would help you on other similar problems as well. I think Q#1 also requires a similar visualization.</p>
<p>Q#3: The two triangles are similar which means their internal angles are identical. Use that information to find the internal angles of triangle DEF, then use the familiar ratios. </p>
<p>Q2 is a little tricky, but note that (A) can form a closed rectangular box. Thus the answer is (A).</p>
<p>It is easy to see why (B) is impossible; (B) only has five faces (the rectangular solid is closed). (D) and (E) are impossible because the six faces are congruent. Can you have a rectangular prism with six congruent faces that is <em>not</em> a cube? (C) is also impossible because if we were to fold it, two of the faces would be overlapping.</p>