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At College X, the faculty-to-student ratio is 1:9. If two-th

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At College X, the faculty-to-student ratio is 1:9. If two-th [#permalink] New post 03 Oct 2009, 17:22
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At College X, the faculty-to-student ratio is 1:9. If two-thirds of the students are female and one-quarter of the faculty is female, what fraction of the combined students and faculty are female?

(A) 11/24
(B) 5/8
(C) 25/56
(D) 11/12
(E) It cannot be determined from the information given.

[Reveal] Spoiler:
Does someone know how to solve this one without picking numbers? This is how far I got:

p/s=1/9
f/s=2/3
f/p=1/4

Equation 2 and 3 give us:

f=2s/3
f=1p/4

Set equal 2s/3=1p/4; Reducing: s/p=3/8 (which does not agree with equation 1). Where did I go wrong?

Thanks
Steve
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Apr 2014, 00:31, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: Ratio: System of Equation (Kaplan) [#permalink] New post 03 Oct 2009, 17:32
enfinity wrote:
At college x, the ratio of students to students is 1:9. If two thirds of the students are female and one quarter of faculty is female, what fraction of the combined students and faculty are female?

a) 11/24
b) 5/8
c) 23/47
d) 3/4
e) 2/3

Does someone know how to solve this one without picking numbers? This is how far I got:

p/s=1/9
f/s=2/3
f/p=1/4

Equation 2 and 3 give us:

f=2s/3
f=1p/4

Set equal 2s/3=1p/4; Reducing: s/p=3/8 (which does not agree with equation 1). Where did I go wrong?

Thanks
Steve


Can you please recheck if this is correct question?
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Re: Ratio: System of Equation (Kaplan) [#permalink] New post 03 Oct 2009, 17:35
Sorry, that's the right question:

At college x, the ratio of faculty to students is 1:9. If two thirds of the students are female and one quarter of faculty is female, what fraction of the combined students and faculty are female?
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Re: Ratio: System of Equation (Kaplan) [#permalink] New post 03 Oct 2009, 17:48
enfinity wrote:
Sorry, that's the right question:

At college x, the ratio of faculty to students is 1:9. If two thirds of the students are female and one quarter of faculty is female, what fraction of the combined students and faculty are female?


Faculty/Students = 1/9
Female Faculty = ff = F/4
Female Students = fs = 2S/3

So combined ratio = (ff+fs)/(F+S) = (1/4 + 2*9/3)/(1+9)
ratio = 5/8

Answer is B.
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Re: Ratio: System of Equation (Kaplan) [#permalink] New post 04 Oct 2009, 06:20
i simply picked 100 but faculty came in fraction....so picked up 200 in nxt interval

125/200 = 5/8 ...i didint take more than a minute to conclude option answer
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Re: Ratio: System of Equation (Kaplan) [#permalink] New post 05 Oct 2009, 09:12
faculty = x

Students = 9x.

Female (faculty) = x/4 and female(students) = 6x.

So fraction is = 25x/40x = 5/8

I wud go with option B
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Re: Ratio: System of Equation (Kaplan) [#permalink] New post 05 Oct 2009, 19:34
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bhushan252 wrote:
i simply picked 100 but faculty came in fraction....so picked up 200 in nxt interval

125/200 = 5/8 ...i didint take more than a minute to conclude option answer
Just wanted to chime in here. I know I've been beaten to the math, and the OP wanted to avoid picking numbers. However, for this problem picking numbers will be easier for many test takers. Picking 100 can make it difficult, though. Fortunately, there's a trick to it! A 1:9 ratio has a total of ten parts, we're taking thirds of the the faculty, and quarters of the students. So we need a number divisible by 10, 3, and 4; multiply them out and we get 120. Start there, and things work out much better! 12 faculty, 3 female faculty, 108 students, 72 female students, 75 females gives us 75/120 = 15/24 = 5/8.
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Re: Ratio: System of Equation (Kaplan) [#permalink] New post 27 Apr 2014, 08:36
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Re: At College X, the faculty-to-student ratio is 1:9. If two-th [#permalink] New post 01 Jul 2015, 02:39
enfinity wrote:
At College X, the faculty-to-student ratio is 1:9. If two-thirds of the students are female and one-quarter of the faculty is female, what fraction of the combined students and faculty are female?

(A) 11/24
(B) 5/8
(C) 25/56
(D) 11/12
(E) It cannot be determined from the information given.

[Reveal] Spoiler:
Does someone know how to solve this one without picking numbers? This is how far I got:

p/s=1/9
f/s=2/3
f/p=1/4

Equation 2 and 3 give us:

f=2s/3
f=1p/4

Set equal 2s/3=1p/4; Reducing: s/p=3/8 (which does not agree with equation 1). Where did I go wrong?

Thanks
Steve


The Ratio F:S is 1:9
2/3 of the students are female: 2/3*9 = 6
1/4 of the faculty are female: 1/4*1 = 0.25

So we have a combined fraction of 6.25/10 >>> expand with *4 both the dividend and divisor to get to 25/40 = 5/8
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Re: At College X, the faculty-to-student ratio is 1:9. If two-th [#permalink] New post 01 Jul 2015, 04:35
Let F be Faculty, and S be Students.

F : S = 1x : 9x
Female_F = 1x/4
Female_S = 9x*2/3 = 6x

Total number of people at college X = 1x+9x = 10x.

Total Male = 3x/4 + 3x = 3x+12x/4 = 15x/4

Total Female = x/4 + 6x = x +24x/4 = 25x/4

Ratio of Total Female : Total Number of People at College X = 25x/4 : 10x = 25x : 40x = 5:8. Ans is B.
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Re: At College X, the faculty-to-student ratio is 1:9. If two-th   [#permalink] 01 Jul 2015, 04:35
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