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OG - PS - #106

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bmcshane
 Post subject: OG - PS - #106
 Post Posted: Wed Jul 18, 2007 11:29 pm 
My question is from OG 11th edition, page 166, question # 106. How do you do this problem?
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Guest
 Post subject:
 Post Posted: Thu Jul 19, 2007 8:57 am 
Please post the problem text.
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bmcshane
 Post subject: ratio Problem
 Post Posted: Thu Jul 19, 2007 9:43 pm 
The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?

A. 5
B. 8
C. 10
D. 12
E. 15
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GMAT_scares_me
 Post subject:
 Post Posted: Thu Jul 19, 2007 10:30 pm 
THis is not a bad problem.


1. ------- S/T = 30/1

or S = 30T

2. ---------- (S+50)/(T+5) = 25/1

or (S+50) = 25T+125

from 1. ( 30T+50) = 25T+125

or T = 15

(E)

(Please verify the answer)
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StaceyKoprince
 Post subject:
 Post Posted: Fri Jul 20, 2007 6:41 pm 
Offline
ManhattanGMAT Staff


Posts: 6077
Location: San Francisco
Yep, you got it. That's the algebraic way. You can also try the answer choices; choose whatever method is best for you.

If you try the answers, start with C (because they are in ascending order). If C) 10 is right, then there are currently 10 teachers. That would mean 30(10) = 300 students. Then the new numbers would be 300+50=350 students and 10+5=15 teachers, for a ratio of 350:15 or 70:3. Which isn't 25:1, so C is wrong. In addition, 70:3 is not quite high enough, so we can eliminate A and B; we need more teachers.

D) 12 = teachers, 360 = students now. 17 = teachers, 410 = students after. 410:17 doesn't simplify. Wrong.

E) 15 = teachers, 450 = students now. 20 = teachers, 500 = students after. 500:20 = 25:1. Bingo.

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
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bmcshane
 Post subject: ration problem
 Post Posted: Sat Jul 21, 2007 3:39 pm 
E is correct. Thank you for your help.
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