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

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.

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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.

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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

The correct answer choice should include "R" not "one over R"?

Bunuel GMATNinja is there a smart way to solve this since OG explanation is very hard to understand

A quick method would be to assign certain values as the expression should be valid for all values.

To ease my calculations, I’ll take a hypothetical situation that all students moved out and the faculty still increased from 55 to 66.
% Change in students = S = (0-5500)/5500 *100 = -100
% Change in faculty = F = (66-55)/55 * 100 = 20
R = 5500/55 = 100
We are looking for the options that give us F(1999) = 55 and S(new)/faculty (new) = 0/66 = 0

1) Now, faculty in fall 1999 = 55……option 5500/R gives 5500/100 or 55….Correct
2) we are looking for value 0. Clearly only 100+S in numerator will give 100+(-100) = 0.
Option (100+S)/(100+F) * R

 
I'm not sure whether I can improve on Chetan's explanation, but I'll give it a shot, anyway!

To find the number of faculty members in 1999, we can use two pieces of information that we're given: there were 5500 students in 1999 and R represents the ratio of students/facultymembers in 1999.

Starting with: \(R = \frac{students}{facultymembers}\)

Then rearranging it for faculty members in 1999: \(facultymembers = \frac{students}{R}\)

Subsituting the number of students in 1999 into the equation: \(facultymembers= \frac{5500}{R ­}\)­

And we have our answer. The number of faculty members in 1999 is \(\frac{5500}{R}\)­

Next, we're looking for the number of students per faculty member in 2004. It makes sense to start with R -- our ratio of students per faculty member in 1999 -- and then adjust it to account for the changes from 1999 to 2004. The changes are S and F for students and faculty, respectively.

(Note that both S and F represent the percentage change, so even though S is a decrease, it needs to be added. For example if S is -5%, then 100%+S would give us 95%.)

So we can start with R and its adjustments: \(studentsperfaculty2004 = R*\frac{100+studentschange}{100+facultychange}\)

Then we place S and F in their respective spots: \(studentsperfaculty2004 = R*\frac{100+S}{100+F}\)

And we have our answer! The number of students per faculty in 2004 is \(R*\frac{100+S}{100+F}\)­

I hope that helps!­

 
­But we have a decreasing number of students. Hence, we can infer that there will be a sign change. By placing the larger number in front of the smaller when subtracting the difference we would get:

S1999 - S2004/S1999 = S%/100

And we would then need to deduct this number from 100 to get the correct ratio, or not?!

Best
Sergej

Bunuel GMATNinja, this might be a repetitive question, but could you please explain why it is (100+s) rather than (100-s)? went through the above explanations but still very confused.

Male in 2020 - 3300
ratio of female/ Male in 2020 =R

Hence female in 2020 =3300 R

=11pt=12.0ptAnser-1 A

Using above formula -
Number of Male in 2020 - 3300 (100+M)/100
Number of Female in 2020 - 3300R(100+F)/100

ration of Female & male in 2020 = R(100+F)/(100+M)

answer-2 C

Final Answer is - Option - AC

 ­

­I feel your pain here. Think about it like this. If Tim had $100 in his account on Day 1 and has $90 in day two, there are two ways we might describe this change in value:

1. Tim experienced a 10% DECREASE in his account.

2. Tim experienced a -10% CHANGE in his account.

If we use interpretation two, then we wouldn't want to subtract the variable representing the % change, because the negative is already in there. Rather, we'd add a variable that represents a negative value.

That appears to be what's going on in this question, since S represents the percent change rather than the percent decrease, and so the negative component is already accounted for within the variable, the same way it is in scenario 2 above.

For the record, I don't think I've ever seen another official GMAT question come down to this sort of thing, so don't lose your mind trying to memorize broader takeaways about percents here. It's possible that you'll never see anything quite like this again.

I hope that helps a bit!