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At College X, the faculty-to-student ratio is 1:9

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by Vincen » Sat Oct 21, 2017 5:32 pm
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) 25/56
(D) 11/12
(E) It cannot be determined from the information given.

The OA is B.

All the questions that involves "ratio" are difficult to me. Experts, could you please help me here? Thanks.
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by sakali » Tue Oct 24, 2017 10:28 am
Not an expert but here's my take on this:

Using sample numbers:

Faculty to Student is 1:9
2/3 of students are female and 1/4 of faculty is female, so we need to pick a number that is easy to divide by those fractions

Suppose there are 4 faculty memebers, then there are 36 students

1/4 of 4 = 1
2/3 of 36 = 24

Total of 25 females out of 40 (4 faculty and 36 students) = 25/40 =>5/8
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by [email protected] » Tue Oct 24, 2017 10:33 am
Hi Vincen,

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: B

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by Jeff@TargetTestPrep » Sun Oct 29, 2017 6:39 am
Vincen wrote: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) 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

Answer: B

Jeffrey Miller
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[email protected]

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