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

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.

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

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

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

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.

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!

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

Final Answer:
GMAT assassins aren't born, they're made,
Rich

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.

Answer: B

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

Answer: B

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

Sent from my Redmi Note 3 using GMAT Club Forum mobile app

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.

IMO B.

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