At College X, the faculty-to-Student Ratio is 1:9 GMAT Problem Solving

Question: 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.


Correct Answer
:
B

Solution and Explanation
Approach Solution 1:

There's a trick to solve this question

A 1:9 ratio has a total of ten parts,
we're taking thirds of the faculty, and quarters of the students.
So we need a number divisible by 10, 3, and 4;
multiply them out and we get
10 x 3 x 4 = 120

Lets Start there,
12 faculty, 3 female faculty, 108 students, 72 female students,

Total females = 72 + 3 = 75
Total student and faculty = 12 + 108 = 120
Which will gives us

\(=\frac{75}{120}\)

\(=\frac{15}{24}\)

\(=\frac{5}{8}\)

The answer is B , \(\frac{5}{8}th\) of the combined students and faculty are female.

Approach Solution 2:

Let's try to solve this with arithmetic process

Let us take the Total number of people be 400
The faculty-to-student ratio is 1:9.
Total number of faculty will be 40
Total number of students will be 360

Female faculty members are 10
Female students are 240

So,total females= 250

The fraction of females will be

\(\frac{total female}{total people}\)

\(=\frac{250}{400}\)

\(=\frac{25}{40}\)

\(=\frac{5}{8}\)

The answer is B , \(\frac{5}{8}th\) of the combined students and faculty are female.

Approach Solution 3:
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

“At College X, the faculty-to-student ratio is 1:9.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT 800". To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.


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