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Bunuel
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x = number of female
number of male = 100-x
combining 1,2. we get the equation 0.05X/ 0.12(100-x)+0.05X

is this equation not enough?
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x = number of female
number of male = 100-x
combining 1,2. we get the equation 0.05X/ 0.12(100-x)+0.05X

is this equation not enough?

No. Firstly, we don't know whether there are 100 students in total, so it is incorrect to assume that if x represents the number of females, then the number of males is 100 - x.

Instead, let's assume that there are n students in total, with f representing the percentage of females and 1 - f representing the percentage of males. Then, we can calculate the percentage of females in math courses as:

\(\frac{0.05fn}{0.12(1 - f)n + 0.05fn}\)

Simplifying this expression by reducing by n gives:

\(\frac{0.05f}{0.12(1 - f) + 0.05f} \)

If f is close to 1 (100%), this expression approaches 1, indicating that the percentage of females in math courses is almost 100%. Similarly, if f is close to 0 (0%), the expression approaches 0, indicating that the percentage of females in math courses is almost 0%.

Note that the percentage of females in math courses does not depend on the total number of students in the university, but rather on the ratio of males to females in the university.

However, it is important to note that the algebraic calculations above are not necessary and can be avoided if one thinks logically before jumping to algebra, as demonstrated in the official solution.
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Bunuel
joe123x
x = number of female
number of male = 100-x
combining 1,2. we get the equation 0.05X/ 0.12(100-x)+0.05X

is this equation not enough?

No. Firstly, we don't know whether there are 100 students in total, so it is incorrect to assume that if x represents the number of females, then the number of males is 100 - x.

Instead, let's assume that there are n students in total, with f representing the percentage of females and 1 - f representing the percentage of males. Then, we can calculate the percentage of females in math courses as:

\(\frac{0.05fn}{0.12(1 - f)n + 0.05fn}\)

Simplifying this expression by reducing by n gives:

\(\frac{0.05f}{0.12(1 - f) + 0.05f} \)

If f is close to 1 (100%), this expression approaches 1, indicating that the percentage of females in math courses is almost 100%. Similarly, if f is close to 0 (0%), the expression approaches 0, indicating that the percentage of females in math courses is almost 0%.

Note that the percentage of females in math courses does not depend on the total number of students in the university, but rather on the ratio of males to females in the university.

However, it is important to note that the algebraic calculations above are not necessary and can be avoided if one thinks logically before jumping to algebra, as demonstrated in the official solution.

sorry I meant 100%, not 100. so x is the total percentage of females out of the 100% number of students.

huge thank you for this clarification, I understand now why we can't answer this question.
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Hello,

I'm failing to understand here, are we talking about what percentage of all the students in this university are female studying math, or what percentage of the students studying math are female?
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Adhish7
Bunuel
Official Solution:


At Wisconsin University, what percentage of students enrolled in math courses are female?

(1) Of the female students at the university, 5% are enrolled in math courses.

Clearly insufficient.

(2) Of the male students at the university, 12% are enrolled in math courses.

Clearly insufficient.

(1)+(2) We are given that 5% of the female students and 12% of the male students are enrolled in math courses. However, we cannot determine the exact percentage of female students enrolled in math courses without knowing the male to female student ratio at the university. This is because the percentage of female students enrolled in math courses depends on the proportion of male to female students at the university. For instance, if the university has a very high percentage of female students, then the percentage of female students enrolled in math courses would also be close to 100%. Conversely, if the university has a very low percentage of female students, then the percentage of female students enrolled in math courses would be close to 0%. Therefore, the answer is E.


Answer: E

Hello,

I'm failing to understand here, are we talking about what percentage of all the students in this university are female studying math, or what percentage of the students studying math are female?

There is a university. It has a math course, and there are students enrolled in that course. The question asks about the percentage of females among all the students enrolled in that math course.

Hope it's clear.
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I think this is a high-quality question and I agree with explanation.
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