Problem Solving

Right now, the number of students per faculty member is R. In 5 years, the number of faculty members will be increased by F% and the number of students will be decreased by S%. Which of the following represents the number of students per faculty member after the change?

A)R
B)R^-1
C)(100+S)/(100+F) * R
D)(100-S)/(100+F) * R
E)(100+F)/(100-S) * R

Answer is B

Are you sure its [spoiler]{B}? [/spoiler] ; I got [spoiler]{D}[/spoiler]

student : faculty = R : 1

S/F = R/1

Faculty will increase by f% ==> F + Ff/100 ==> F (1 + f/100)

Students will decrease by S% = S - Ss/100 ==> S ( 1 - s/100)

S ( 1 - s/100) / F (1 + f/100)

R ( 100 - s)/(100 + f)

amirhakimi wrote:Right now, the number of students per faculty member is R. In 5 years, the number of faculty members will be increased by F% and the number of students will be decreased by S%. Which of the following represents the number of students per faculty member after the change?

A)R
B)R^-1
C)(100+S)/(100+F) * R
D)(100-S)/(100+F) * R
E)(100+F)/(100-S) * R

Answer is B

Current number of students = x
Current number of teachers = y

x/y = R

In 5 years,
number of students = x * (100-S)/100
number of teachers = y * (100+F)/100

New ratio = [x * (100-S)/100] / [y * (100+F)/100]
= x/y * (100-S)/(100+F)
= R * (100-S)/(100+F)

Choose [spoiler]D?[/spoiler]

Cheers

Using Assumption Method:

S / F => 100/10 = 10 = R

Faculty = F = 10% = 11

Students = S = 1% = 99

New S/F = 9

{A} 10 NO
{B} 1/10 NO
{C} 101/111 * 10 NO
{D} 99/110 * 10 YES
{E} 110/99 * 10 NO

theCodeToGMAT wrote:Are you sure its [spoiler]{B}? [/spoiler] ; I got [spoiler]{D}[/spoiler]

student : faculty = R : 1

S/F = R/1

Faculty will increase by f% ==> F + Ff/100 ==> F (1 + f/100)

Students will decrease by S% = S - Ss/100 ==> S ( 1 - s/100)

S ( 1 - s/100) / F (1 + f/100)

R ( 100 - s)/(100 + f)

I myself reached the choice D but GMAC says that the answer is B and there is no explanation. That's why I've posted it here.
Here is the link: https://www.mba.com/the-gmat/nex-gen/samples/Sample-806
It's part of an IR problem.

amirhakimi wrote: I myself reached the choice D but GMAC says that the answer is B and there is no explanation. That's why I've posted it here.
Here is the link: https://www.mba.com/the-gmat/nex-gen/samples/Sample-806
It's part of an IR problem.

Both questions ask different things..
The question you posted says : Which of the following represents the number of students per faculty member after the change?

but, the Question on URL says: Find Percentage change..

amirhakimi wrote:

theCodeToGMAT wrote:Are you sure its [spoiler]{B}? [/spoiler] ; I got [spoiler]{D}[/spoiler]

student : faculty = R : 1

S/F = R/1

Faculty will increase by f% ==> F + Ff/100 ==> F (1 + f/100)

Students will decrease by S% = S - Ss/100 ==> S ( 1 - s/100)

S ( 1 - s/100) / F (1 + f/100)

R ( 100 - s)/(100 + f)

I myself reached the choice D but GMAC says that the answer is B and there is no explanation. That's why I've posted it here.
Here is the link: https://www.mba.com/the-gmat/nex-gen/samples/Sample-806
It's part of an IR problem.

The answer that GMAC has provided is correct.

Their answer is (100+S)/(100+F) * R.

In that problem, S and F represent the percentage change in numbers.

Whereas, in your problem, S represents percentage decrease and F represents percentage increase.

So, for the question that you've provided here, the answer is D.

Cheers

Oh, I've missed that

Yeah, I have proved to myself over and over that the answer is D (R * (100-S)/(100+F)) as follows:

R = n/m

where n = initial number of students
and m = initial number of faculty members

R new = [n(100-S)%]/[m(100+F)%] = R * (100-S)/(100+F)

Answer D