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Intern  Joined: 12 May 2009
Posts: 48
At College X, the faculty-to-student ratio is 1:9. If two-th  [#permalink]

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1
12 00:00

Difficulty:   35% (medium)

Question Stats: 75% (02:20) correct 25% (02:33) wrong based on 372 sessions

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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.

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

Originally posted by enfinity on 03 Oct 2009, 18:22.
Last edited by Bunuel on 28 Apr 2014, 01:31, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Manager  Joined: 18 Aug 2009
Posts: 236
Re: Ratio: System of Equation (Kaplan)  [#permalink]

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1
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?
Intern  Joined: 12 May 2009
Posts: 48
Re: Ratio: System of Equation (Kaplan)  [#permalink]

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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?
Manager  Joined: 18 Aug 2009
Posts: 236
Re: Ratio: System of Equation (Kaplan)  [#permalink]

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2
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: 130
Location: India
Schools: South Asian B-schools
Re: Ratio: System of Equation (Kaplan)  [#permalink]

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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
Manager  Joined: 15 Sep 2009
Posts: 87
Re: Ratio: System of Equation (Kaplan)  [#permalink]

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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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Posts: 629
Location: Cambridge, MA
Re: Ratio: System of Equation (Kaplan)  [#permalink]

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3
1
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: At College X, the faculty-to-student ratio is 1:9. If two-th  [#permalink]

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1
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.

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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Joined: 28 Jun 2015
Posts: 277
Concentration: Finance
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Re: At College X, the faculty-to-student ratio is 1:9. If two-th  [#permalink]

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1
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]

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Female students: 2/3*9
Female faculty: 1/4
Ratio will be:(2/3*9+1/4)/10=25/40=5/8

Please let me know if my method is wrong!
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Re: At College X, the faculty-to-student ratio is 1:9. If two-th  [#permalink]

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Hi All,

This prompt gives us a few facts to work with:
1) The ratio of faculty to students is 1:9 (meaning that the number of students MUST be a multiple of 9)
2) 2/3 of the students are FEMALE
3) 1/4 of the faculty are FEMALE (meaning that the number of faculty MUST be a multiple of 4)

We're asked for the fraction of total people that are female. This question can be solved by TESTing VALUES.

IF....
Total faculty = 4, then we have 1 female faculty
Total students = 36, then we have 24 female students
Total females = 25
Total people = 40
The answer to the question is 25/40 = 5/8

The logical question to ask is whether this fraction stays the same if we change the total number of people, so let's TEST another value...

IF....
Total faculty = 8, then we have 2 female faculty
Total students = 72, then we have 48 female students
Total females = 50
Total people =80
You should notice that ALL of the values increased by the same percent, so the answer to the question will be the SAME...
The answer to the question is 50/80 = 5/8

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Re: At College X, the faculty-to-student ratio is 1:9. If two-th  [#permalink]

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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. ]

We can let the total faculty = f and the total students = n. Thus, (2/3)n are female students and (1/3)n are male. Also, (1/4)f is female faculty and (3/4)f is male.

We also know that 1/9 = f/n, so n = 9f.

Thus, (2/3)(9f) = 6f are female students and (1/3)(9f) = 3f are male.

So the total students and faculty is:

9f + f = 10f, and the combined female students and female faculty is 6f + (1/4)f = 6.25f.

Thus, females are 6.25f/10f = 6.25/10 = 625/1000 = 5/8 of the total students and faculty at College X.

Alternate Solution:

Let 4x represent the number of faculty in College X. Since faculty-to-student ratio is 1:9, there are 36x students in College X. Since 1/4 of the faculty are females, there are x female faculty members. Since 2/3 of the students are females, there are (36x)(2/3) = 24x female students. In total, there are x + 24x = 25x females and 4x + 36x = 40x people in College X, giving us a ratio of 25x/40x = 5/8.

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Re: At College X, the faculty-to-student ratio is 1:9. If two-th  [#permalink]

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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.

We can express the ratio of faculty to students as x : 9x.

Since two-thirds of the students are female:

(9x)(2/3) = 6x = female

Since one-quarter of the faculty is female:

(1/4)x = x/4 = female

Thus, the fraction of the combined students and faculty who are female is:

(6x + x/4)/(9x + x) = (24x/4 + x/4)/(10x) = (25x/4)/10x = 25x/40x = 5/8

_________________

# Jeffrey Miller

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Re: At College X, the faculty-to-student ratio is 1:9. If two-th  [#permalink]

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Total number of people = 400
Total number of faculty = 40
Total number of students = 360

Female faculty members = 10
Female students = 240

So, 250/400 = 5/8 , our answer Manager  B
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Re: At College X, the faculty-to-student ratio is 1:9. If two-th  [#permalink]

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Re: At College X, the faculty-to-student ratio is 1:9. If two-th  [#permalink]

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Total no. of people at college X = 1x+9x = 10x

M = 3x/4 + 3x = 3x+12x/4 = 15x/4

F = x/4 + 6x = x +24x/4 = 25x/4

F : F+M = 25x/4 : 10x = 25x : 40x = 5:8.

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Re: At College X, the faculty-to-student ratio is 1:9. If two-th  [#permalink]

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