Over a period of 5 academic years from Fall 1999 through Spring 2004,

Lets list the variables to make this problem easier to keep track of:

F = % change of faculty
S = % change of students
R = Stu(1999) / Fac(1999)
R(2004) = Stu(2004) / Fac(2004)
Stu(1999) = 5500


We are asked to find:
1.) Fac(1999) = ?
2.) R(2004) = ?

1.)
R = Stu(1999) / Fac(1999)

Fac(1999) = Stu(1999) / R

Fac(1999) = 5500 / R

2.) R(2004) = Stu(2004) / Fac(2004)
OR R(2004) = the previous Student / Faculty ratio times the change over the past 5 years.

The change is given: S, and F respectively.

Thus (100+S) / (100+f) NOTE: the 100 represents 100%, so 100% the ratio from 1999 +/- the change in the past 5 years (which is S and F)

R(2004) = R * (100+S) / (100+f)

The trick in this problem is the sign of the S and F. These variables should be added. Even though the problem states that the number of students is decreasing, while number of faculty is increasing, when you calculate out the rates, they should still be added. If the rate was negative, adding a negative rate is still subtracting it. Meanwhile if you subtracted the negative rate, it would flip the sign and mess up the calculation.

why should we consider "faculty" and "faculty member" the same? i did not know.

As per my understanding, essentially they’re the same.

If it were Factulty it would meant something else, for example the Faculty of business.

But here it talks about members rather than a division of knowledge.

Posted from my mobile device

But it saya Faculty not member after once

Hi faltan Faculty by definition means faculty members or a division of knowledge.

I don’t think the question implies in anyway that they are introducing new “divisions”.

The question talks about faculty members and students.

Posted from my mobile device

I thought since no. of students is decreasing should use a -ve sign for percent change "S". What a silly mistake.

Expecting test takers to use -ve sign for S, in my view is silly and leaving the question too ambiguous..
it's rare in my view to write: student population decreased.... and then after another sentence.. it changed by -20%!, you usually write changed by 20%, because you already said it decreased. I am not saying you won't see that in real world, but then you would use real numbers so will be clear. Under a timer, you can't put candidates through this sort of ambiguity.. what will it test really!

hello BrentGMATPrepNow can you pls provide your algebraic solution to the second question. official solution by gmat prep is kinda confusing...

Dear dave13
I agree the the official answer is cumbersome; take into consideration the explanation provided by subsauce.

The question has asked Students per faculty in Spring 2004 or \(\frac{#Students (2004)}{#Faculty (2004)}\)
How to find the number of students ? Old value *( 100% + % changes)
Pursuant to the prompt F and S represent the percent changes. So, you do not need to compute them.

100 = 100%
S = S% or S/100
F = F% or F/100
Number of Faculty in 1999 = 5500R
Number of student in 1999 = 5500

Now substitute in the equation for Student: Old value *( 100% + % changes) = 5500 (100 + S )
and in the equation for Faculty: Old value *( 100% + % changes) = 5500R (100 + F )
Therefore, final equation is \(\frac{#Students (2004)}{#Faculty (2004)}\) = \(\frac{5500 (100 + S )}{5500R (100 + F )}\) =\(\frac{(100 + S )}{R (100 + F )}\)

Hope it helps