the above solution is valid, yes.

this is an extremely clever problem; in fact, i like it quite a bit. however, i'm afraid it's not at all like anything i've ever seen in an official problem.
not at all like anything.

this is more like the sort of thing that would show up on a junior-high or high school Math Olympiad for gifted kids. if there's a standardized-test connection, i'd say that this problem bears some resemblance to the "logic games" problems that show up on the LSAT, except it's been hammered into the shape of a math problem.

in any case, it's far too formal-logic-heavy and "proof"-like to be a legitimate candidate for a gmat problem.
where'd you get it?

Vemuri wrote:I hope I don't see such a question on the D day

you won't. see my post above.

this is just not the style of the questions that show up on the test.