Great explanation, winnie! On a question like this, all you have to do is find one situation in which the conditions are satisfied, so really they're challenging you to push the limits of number properties.
Strategically, I'd look at something like this this way - for 1 and 3, I want x to be the biggest in both cases: the given x > y > z AND the proposed case. So I don't want to worry about x - I want it to be huge. x could be 1,000,000,000 in either case and then I'm done with it - I won't reach it. Now I'm just looking at whether:
1) can y^2 be bigger than z^4 while y > z? Sure - let's slot y in at something also big like 100, and z in at something small like 1.
3) can z be bigger than y while y^2 is bigger than z^4? Like you showed, with pretty-close fractions the one taken to the higher power will get a lot smaller, so 1/4 and 1/3 will do it. 1/3 is bigger, but becomes 1/81 when taken to the 4th whereas 1/4 only becomes 1/16 when squared.
Now with 2, we can repeat the logic of #3 - we want the biggest value to become the smallest when it's taken to the highest exponent...the only way for that to happen is with fractions, and if we keep the fractions for all three relatively close: 1/3, 1/4, 1/5, then the higher the exponent the lower the value, so the order will reverse to 1/5, 1/16, 1/81.
A question like this really hinges on "what is your goal", so identify that first before you start plugging in numbers and you can save quite a bit of time (and maximize your opportunity for accuracy).
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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