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

Question

Over a period of 5 academic years from Fall 1999 through Spring 2004, the number of faculty at a certain college increased despite a decrease in student enrollment from 5,500 students in Fall 1999,

In the given expressions, F and S represent the percent change in the number of faculty and students, respectively, over the 5 academic years, and R represents the number of students per faculty member in Fall 1999. The percent change in a quantity X is calculated using the formula

\frac{X_{New} - X_{Old}}{X_{Old}}(100)

Select the expression that represents the number of faculty in Fall 1999, and select the expression that represents the number of students per faculty member in Spring 2004. Make only two selections, one in each column.

subsauce · Accepted Answer

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.

Sajjad1994 · Answer

Official Explanation https://gmatclub.com/forum/download/file.php?mode=view&id=61349 2.jpg

faltan · Answer

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

Salsanousi · Answer

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

faltan · Answer

But it saya Faculty not member after once

Salsanousi · Answer

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

Sanchitdd · Answer

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

gmatlayman · Answer

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!

dave13 · Answer

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

BLTN · Answer

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

PepperBot · Answer

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

Deepam10 · Answer

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

chetan2u · Answer

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

GMATNinja · Answer

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!

SergejK · Answer

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

mollyweasley · Answer

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.

riturajsingh21 · Answer

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

Hence female in 2020 =3300 R

=11pt=12.0pt Anser-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

GMATNinja · Answer

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!

siddhantvarma · Answer

There’s an easy way to do this if you can spot the pattern

Number of faculty in Fall 1999	Students per faculty member in Spring 2004	-----------------
		5,500 R
		\(\frac{5,500}{R}\)
		\(\frac{1}{R}\)
		\((\frac{100+S}{100+F})R\)
		\((\frac{100-S}{100+F})\frac{1}{R}\)
		\((\frac{100+F}{100-S})\frac{1}{R}\)

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

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