If x is an integer, then without even reading the rest of the question none of the answer choices could possibly be right ('between' means 'strictly between' unless you add the word 'inclusive').
I don't know if there's a typo in the original question - I guess so, considering how the OE reads - but the question makes no sense as written. I suppose it makes sense if you take out the word 'integers' and just require x and y to be positive.
edit: or perhaps the question means to say "If x^2
are positive integers..." Then the solution is right.
Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.
Private GMAT Tutor based in Toronto