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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## In a local school district, the high school and middle... tagged by: BTGmoderatorLU ##### This topic has 3 expert replies and 1 member reply ### Top Member ## In a local school district, the high school and middle... In a local school distirct, 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 The OA is D. I'm really confused with this PS question. Experts, any suggestion? Why D is the correct answer? Thanks in advance. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15352 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 Top Reply LUANDATO wrote: In a local school distirct, 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 Since each student must have the same funding, let the funding per student =$1.

Since the high school has 300 students, the amount required by the high school = 300*1 = $300. Since the middle school has 200 students, the amount required by the middle school = 200*1 =$200.
Total amount distributed to the two schools = 300+200 = $500. Since each school originally received r dollars, and the total amount distributed was$500, r = $250. Since the middle school originally had$250 and gave away s dollars to end with only $200, s =$50.

The question stem asks for the value of s (50). This is the target value.
Now plug r=250 into the answers to see which yields the target value of 50.
Only D works:
r/5 = 250/5 = 50.

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### GMAT/MBA Expert

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LUANDATO wrote:
In a local school distirct, 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

The OA is D.

I'm really confused with this PS question. Experts, any suggestion? Why D is the correct answer? Thanks in advance.
Alternatively, you can say that each school receives $600 to start. (So r = 600.) If the middle school gives the high school s dollars, the middles school will have 600 -s dollar sand the high school will have 600 + s dollars. Average funding for middle school. = (600 -s)/200 Average funding for high school. = (600 + s)/300 These values should be equal. (600 -s)/200 = (600 + s)/300 Multiply both sides by 600 to get 3(600-s) = 2(600 +s) 1800 -3s = 1200 + 2s 600 = 5s s = 120. When we plug in '600' for 'r,' the correct answer will yield 120, our target. Only D works. 600/5 = 120. _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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### GMAT/MBA Expert

Legendary Member
Joined
14 Jan 2015
Posted:
2667 messages
Followed by:
122 members
1153
GMAT Score:
770
LUANDATO wrote:
In a local school distirct, 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

The OA is D.

I'm really confused with this PS question. Experts, any suggestion? Why D is the correct answer? Thanks in advance.
If the high school received r dollars, and it has 300 students, then the funding per student would be r/300

If the middle school received r dollars, and it has 200 students, then the funding per student would be r/200.

If the middle school transfers s dollars to the high school, the total funding of the high school would be r + s, and the funding per student would be (r + s)/300
Similarly the middle school would have total funding of r -s and funding per student of (r-s)/200
We know those two values are equal so (r+s)/300 = (r-s)/200
Multiply both sides by '600' to get 2(r+s) = 3(r-s).

(Note: 600 is a nice number to use as it's a multiple of both 300 and 200. 600/300 = 2 and 600/200 = 3.)

2r + 2s = 3r -3s
5s = r
s = r/5. The answer is D

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Save $100 off any live Veritas Prep GMAT Course Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! Senior | Next Rank: 100 Posts Joined 15 Jan 2018 Posted: 83 messages For each dollar a student gets, then collectively the schools get$500 split equally between them = $250 per school. Transferring$50 will create $200 and$300 as required.
$250 /$50 = 5
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