Hi, Can anyone explain the answer to second column for the question posted at the following URL:
https://www.mba.com/thegmat/nexgen/sam ... 6?next=yes
Two part analysis  Sample question
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 bubbliiiiiiii
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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 (100S) / (5500 / R * (100+F). Do a small bit of factoring and you get ((100S)/(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 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 (100S) / (5500 / R * (100+F). Do a small bit of factoring and you get ((100S)/(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.

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 eagleeye
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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_newS_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
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_newS_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