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Last year at a certain small college

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Last year at a certain small college

by darlingriyarai » Tue Nov 27, 2012 2:48 am
Last year at a certain small college, the ratio of the number of faculty members to the number of students was 1 to 13. This year, there are 14 more faculty members and 74 more students than there were last year. If this year the ratio of the number of faculty members to the number of students is 1 to 12, how many students are at the college this year?

A. 1,272
B. 1,296
C. 1,320
D. 1,344
E. 1,368
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by Brent@GMATPrepNow » Tue Nov 27, 2012 8:19 am
darlingriyarai wrote:Last year at a certain small college, the ratio of the number of faculty members to the number of students was 1 to 13. This year, there are 14 more faculty members and 74 more students than there were last year. If this year the ratio of the number of faculty members to the number of students is 1 to 12, how many students are at the college this year?

A. 1,272
B. 1,296
C. 1,320
D. 1,344
E. 1,368
Let F = # of faculty members last year
Let S = #of students last year

Last year, the Faculty to Students ratio was 1: 13
We get F/S = 1/13

This year: faculty up 14, and students up 74. The ratio becomes 1: 12
(F+14)/(S+74) = 1/12

We have a system of equations that we can solve for F and S
F/S = 1/13
(F+14)/(S+74) = 1/12

Cross multiply both to get:
13F = S
12(F+14) = S + 74

In the 2nd equation, replace S with 13F to get:
12(F+14) = 13F + 74

Now solve for F:
12F + 168 = 13F + 74
94 = F

Plug F=94 into either of the original equations to get S=1222.
So there were 1222 students last year

This year's student population is 1222+74 = [spoiler]1296 = B[/spoiler]

Cheers,
Brent
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by nisagl750 » Tue Nov 27, 2012 8:20 am
darlingriyarai wrote:Last year at a certain small college, the ratio of the number of faculty members to the number of students was 1 to 13. This year, there are 14 more faculty members and 74 more students than there were last year. If this year the ratio of the number of faculty members to the number of students is 1 to 12, how many students are at the college this year?

A. 1,272
B. 1,296
C. 1,320
D. 1,344
E. 1,368
LEt there are F faculty last year
So, No. of students 13F

This year 14 more faculty members are there F+14
This year srudents 13F + 74

According to given conditions

(F+14)/(13F+74) = 1/12
F=94

This is no. of Faculty members last year.
No. of students = 13F = 1222

This year no. of students increased by 74

Add and get the answer B
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