FOR ALL POSITIVE INTEGERS m, m(there is a box around m)= 3m(no box here m) when m is odd and m(there is a box around m)=1/2m(no box around m here) when m is even. Which of the following is equivalent to 9 times 6(there is a box around each 9 and 6).

The answer is 27.

What's the best way to solve this problem

wow. what a question. Thanks Ron for that explanation. i would have never seen it.

GMAT folks are evil....

interestingly, the gmat doesn't really feature questions that could be honestly classified as “trick questions”.
there are certainly questions that require the reader to read the problem carefully, noting any instances of notation or any specific wordings -- such as this one -- but one thing that the gmat writers DO NOT do, in general, is write problems that play on words in unusual ways, or demand that you understand unusual definitions.

Very tricky - thanks Ron!

for instance, in technical mathematical speak, it's perfectly okay to speak of "the sum of all numbers in a set" even if there is only one number in the set. for instance, if set T contains only the number 16, then “the sum of all numbers in set T” is 16.
the gmat will not do this to you.
also, such numbers as 0, -5, etc. are technically multiples of 5, but the gmat will also stay away from testing you on that sort of thing, too.

so the problem writers aren't really as evil as you might think -- you just have to be really careful when you go over the problems.