At a certain college, 25 percent of the students pay : PS Archive
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# At a certain college, 25 percent of the students pay

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Director
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At a certain college, 25 percent of the students pay [#permalink]

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05 Dec 2004, 05:19
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At a certain college, 25 percent of the students pay out-of-state tuition while the other 75 percent pay in-state tuition. Half of the students are enrolled in the College of Arts and Sciences while the other half are enrolled in technical schools. If 10 percent of the students are enrolled in technical schools and pay out-of-state tuition, what percent of the students enrolled in the College of Arts and Sciences pay in-state tuition?

A. 15%
B. 30%
C. 40%
D. 50%
E. 70%
Director
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05 Dec 2004, 05:48
B - 30%

Assume total # of students = 100
Students paying out-of-state tuition = 25
Students paying in-state tuition = 75
Students in Arts & Science = 50
Students in Tech = 50

Student in tech scool paying out-of-state = 10% of 50 =5
Students in tech school paying in-state = 50-5 = 45
Students in art school paying in-state = 75-45 = 30 (=30%)
Director
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06 Dec 2004, 07:23
Nope. You may want to try again. For such problems, just draw a quick matrix and fill in numbers in them. It would be quick and easy. Try it. I will explain when more people try.
Manager
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06 Dec 2004, 07:39
E. 70%

100 students in total.

50 in Technical school and 50 in Art stuff.
10 in technical & out-of-state -> 50-10 = 40 in technical & in-state
it yields 35 are in Art & out-of-state

35 = 70% of 50 attending college of arts
Director
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06 Dec 2004, 07:48
gayathri wrote:
B - 30%

Student in tech scool paying out-of-state = 10% of 50 =5
Students in tech school paying in-state = 50-5 = 45
Students in art school paying in-state = 75-45 = 30 (=30%)

I see that I made two mistakes

1) I interpreted that 10% of the students enrolled in tech are out-of-state whereas the question says 10% of the entire student population is enrolled in tech AND is out-of-state

2) My final answer was: (art students paying in-state/ total students) *100
whereas the question asks for: (art students paying in-state/ total art students)*100

Manager
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06 Dec 2004, 07:51
for clarity

________________| College of Arts | Technical schools __| Total

# in state_______ | 35 _________|_____ 40__________ | 75

# of out of state__ | 15_________|_____ 10__________ | 25

Total___________ | 50_________|_____ 50__________ | 100

calculated
hypotheses
VP
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06 Dec 2004, 19:01
Out-State In-State Total
Art&Sci 15.00% 35.00% 50.00%
Tech 10.00% 40.00% 50.00%
Total 25.00% 75.00% 100.00%

In-state Art&Sci student as a % of total Art&Sci student
= 35.00%/50.00% = 70.00%

Last edited by MA on 08 Dec 2004, 23:29, edited 1 time in total.
Director
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06 Dec 2004, 19:05
Excellent. 70% it is.

Oxon, thanks for drawing the grid and explaining. Great!
06 Dec 2004, 19:05
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