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# Ratio: System of Equation (Kaplan)

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Manager
Joined: 12 May 2009
Posts: 54
Followers: 2

Kudos [?]: 41 [0], given: 18

Ratio: System of Equation (Kaplan) [#permalink]  03 Oct 2009, 17:22
00:00

Difficulty:

5% (low)

Question Stats:

100% (02:36) correct 0% (00:00) wrong based on 1 sessions
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?

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

Last edited by enfinity on 03 Oct 2009, 17:35, edited 1 time in total.
Senior Manager
Joined: 18 Aug 2009
Posts: 333
Followers: 6

Kudos [?]: 147 [0], given: 13

Re: Ratio: System of Equation (Kaplan) [#permalink]  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?
Manager
Joined: 12 May 2009
Posts: 54
Followers: 2

Kudos [?]: 41 [0], given: 18

Re: Ratio: System of Equation (Kaplan) [#permalink]  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?
Senior Manager
Joined: 18 Aug 2009
Posts: 333
Followers: 6

Kudos [?]: 147 [0], given: 13

Re: Ratio: System of Equation (Kaplan) [#permalink]  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

Manager
Joined: 18 Jul 2009
Posts: 171
Location: India
Schools: South Asian B-schools
Followers: 2

Kudos [?]: 54 [0], given: 37

Re: Ratio: System of Equation (Kaplan) [#permalink]  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
_________________

Bhushan S.
If you like my post....Consider it for Kudos

Manager
Joined: 15 Sep 2009
Posts: 141
Followers: 1

Kudos [?]: 14 [0], given: 2

Re: Ratio: System of Equation (Kaplan) [#permalink]  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
Kaplan GMAT Instructor
Joined: 25 Aug 2009
Posts: 644
Location: Cambridge, MA
Followers: 64

Kudos [?]: 164 [0], given: 2

Re: Ratio: System of Equation (Kaplan) [#permalink]  05 Oct 2009, 19:34
Expert's post
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] 05 Oct 2009, 19:34
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