Tuesday, March 27, 2012

this week's MGRE Math Beast Challenge: blind edition

MGRE's website is undergoing some sort of facelift, which is playing havoc with certain parts of the site. This week's Math Beast Challenge has been affected: I can no longer see the illustration that accompanies the problem, nor can I see most of the answer choices, except for the first choice, which is 8. So this week, we're going to fly blind and just use our imagination to try to draw the illustration accompanying the problem. The problem itself is pretty clearly worded, and we needn't worry about the unseeable answer selections: we'll just figure things out on our own.

A solid cube with edge length 2 is sliced by a plane passing through two opposite corners of the cube. This creates a cut surface, the shaded rhombus shown [below]. What is the perimeter of the shaded rhombus?

I've attempted to make an illustration, which you see below. Note that the illustration is in two parts: a drawing based on the above description, plus a "closeup" that will help us analyze the problem.

I'm of the opinion that the perimeter of the rhombus in question is 4√5. Segment AC is the hypotenuse of a right triangle whose legs measure, respectively, 2 (Segment AB) and 1 (Segment BC). We can check visually that all the other edges of the rhombus are the same length, so this rhombus is a square with perimeter 4√5.

I bet that, once MGRE's site is back in order, one of the answer choices will indeed be 4√5.

By the way, here's a horizontally squished version of what I currently see at the MGRE page:

As you see, there's no illustration, and only one visible answer choice.


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