The answer is D.

You need to solve for the ratio of Students in 2004 to Faculty in 2004 (# students in 2004 (or #_s henceforth) / # faculty in 2004 (or #_f henceforth)). #_s is the original 5500 * (100% - S%) (because the number of students is decreasing). #_f is the # of faculty in '99 * (100% + F%) (because the number of faculty is increasing). Next you would solve for the # of faculty in '99, which is 5500 students / R (R = # students/#faculty so 1/R = #faculty/#students).

Overall this means that your equation is 5500 (100-S) / (5500 / R * (100+F). Do a small bit of factoring and you get ((100-S)/(100+F)) * R.

I don't have a lot of experience answering math questions on forum boards so my thinking may come across a bit scattered. I hope this makes sense.

You are right.

but it is E at mba.com - (100+S)/(100+F)R !!!!!

The answer to the question at mba.com is correct. It should be R*(100+S)/(100+F).

Remember that S and F both are %age change. They also give the definition of F and S, for the same reason. S= 100*(S_new-S_old)/S_old. This means that S itself is negative as we are given that student enrollment decreases. Therefore we don't subtract S%, we just add it the usual way.

1999: Students = 5500;
1999: Faculty = 5500/R
2004: Students change by S% so S_new = 5500*(1+S%) = 5500*(100+S)/100;
2004: Faculty changes by F% so F_new = 5500/R * (1+F%) = 5500*(100+F)/(100R)

So Answer for second part is S_new/F_new = R*(100+S)/(100+F)

Let me know if this helps