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.
At College X, the faculty-to-student ratio is 1:9
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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
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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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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We can express the ratio of faculty to students as x : 9x.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.
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
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