Quant Foundation – Session 4 Homework

Admittedly, Greg approaches a couple questions as a GRE expert rather than a mathematician. Can anyone give me the “mathematician’s” explanation for:

  1. #30 concerning the dimensions of the rug that takes up half of the floor space, correct answer D, 6√2
  2. The two alloys question concerning ratio concepts, correct answer A, 1:1

I, also, answered it with some trickery and workarounds, but I’d love to know the way to solve these “by the books” rather than shoehorned. Any thoughts? I had an interesting approach to the latter that I’d be willing to bounce off someone.

Can you give relevant screenshots?