Funding per student

Question

Hello,

Can you please assist with this:

In a local school district, the high school and middle school each received r dollars toward funding for the student arts program. The high school enrolled 300 students and the middle school enrolled 200 students. Later, the middle school transferred s dollars to the high school so that they would have received the same funding per student. Which of the following is equivalent to s?

A) r/2
B) r/3
C) r/4
D) r/5
E) r/6

Sorry I don't have the OA.

I tried to solve as follows:

The high school received r/300 dollars for 1 student
The middle school received r/200 dollars for 1 student

The question says:

Later, the middle school transferred s dollars to the high school so that they would have received the same funding per student.

I was not sure how to proceed from here. I tried the following:

(r/300) + s = (r/200) - s

but I don't think this is correct. Can you please help? Thanks a lot.

Best Regards,
Sri

Rich.C@EMPOWERgmat.com · Answer

Hi gmattesttaker2,

This is a great question to TEST Values.

The prompt tells us there are 500 total students. Later on, we're told that money has to move transferred, so that the end result is the same funding PER student. Let's TEST $1 per student, so

500 students
$1 each
$500 total

The question further states that the two schools each received $R each, so each school received the same amount. That means…

R = $250

So, the High School got $250 for 300 students
and the Middle School got $250 for 200 students

Later, the middle school transferred $S to the High School to make it $1 per student, so the Middle School would have transferred $50

S = $50

Now, the High School has $300 for 300 students
and the Middle School has $200 for 200 students

Plug in R = 250 and find the answer that equals 50

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Kundan.xlri · Answer

Another way to solve easily:
MS has r dollars
HS has r dollars
After MS has transferred s dollars to HS
MS has r-s dollars
HS has r+s dollars
For MS, dollar per student=(r-s)/200
For HS, dollar per student=(r+s)/300
Equating
(r-s)/200 = (r+s)/300
>300(r-s)= 200(r+s)
dividing both side by 100
>3(r-s)=2(r+s)
>3r-2r=3+2s
>r=5s
>s=r/5

Kundan.xlri · Answer

Another way to solve easily:
MS has r dollars
HS has r dollars
After MS has transferred s dollars to HS
MS has r-s dollars
HS has r+s dollars
For MS, dollar per student=(r-s)/200
For HS, dollar per student=(r+s)/300
Equating
(r-s)/200 = (r+s)/300
>300(r-s)= 200(r+s)
dividing both side by 100
>3(r-s)=2(r+s)
>3r-2r=3+2s
>r=5s
>s=r/5

Bill@VeritasPrep · Answer

Rich.C@EMPOWERgmat.com wrote:Hi gmattesttaker2, This is a great question to TEST Values. The prompt tells us there are 500 total students. Later on, we're told that money has to move transferred, so that the end result is the same funding PER student. Let's TEST $1 per student, so 500 students $1 each $500 total The question further states that the two schools each received $R each, so each school received the same amount. That means… R = $250 So, the High School got $250 for 300 students and the Middle School got $250 for 200 students Later, the middle school transferred $S to the High School to make it $1 per student, so the Middle School would have transferred $50 S = $50 Now, the High School has $300 for 300 students and the Middle School has $200 for 200 students Plug in R = 250 and find the answer that equals 50 Final Answer: D GMAT assassins aren't born, they're made, Rich That's how I would do it. A single variable that appears in all of the answer choices? Pick an easy value and go to town!

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