For any integer k greater than 1, the symbol k* denotes the

I don't know that there are any 'alternative approaches' here. This is one of the GMAT 'function' questions. We've never seen this * function before, and we can't really have any idea how to simplify an expression that includes it. We don't have much choice; we need to:

a) figure out what the * function does;
b) if asked to evaluate some expression involving the *, we need to get rid of the *, using the definition we worked out in step a).

5* = (1/1)*(1/2)*(1/3)*(1/4)*(1/5) = 1/5!
4* = 1/4!

Now we know 5*/4* = (1/5!)/(1/4!) = 4!/5! = 1/5

_________

Some may be tempted to choose 5/4 here, either because it looks similar to the question, or because they will incorrectly divide their fractions near the end of the calculation. I imagine others may find the definition of the * function somewhat abstract. Still others might make the incorrect 'deduction' that 5*/4* = (5/4)*, which would lead to confusion. Those are the 'traps' I can see in the question; perhaps there are others.

If forced to guess an answer within three seconds of reading the question, I'd notice that the question involves reciprocals ("fractions of the form 1/t"), so I'd choose something with 5 in the denominator- C or E. I'd rule out B because it looks too similar to the expression in the question.