A certain college party is attended by both male and female students.

m/f = 3/5
Assume constant = x
m=3x, f=5x

Now, 3x-5/5x =1/2
=> 6x-10 = 5x
=> x=10
total students = 8x = 80

Answer E

Ratio of males:females=3:5 or 3x:5x
Now, (3x-5)/5x=1:2
6x-10=5x
x=10
3x=30
5x=50
Total No of males=30 and Total no of females=50
Total no of students=80
Answer E

\(\frac{M}{F}\) =\(\frac{3}{5}\)
This means, 5M=3F
Now after 5 male leave the party,
\(\frac{(M-5)}{F}\) = \(\frac{1}{2}\)
Substitute F= \(\frac{5M}{3}\)
\(\frac{(M-5)}{(5M/3)}\)= \(\frac{1}{2}\)
2(3M -15) = 5M
M= 30
\(\frac{3}{8}\)* Total = 30
Total = 80 students

MANHATTAN GMAT OFFICIAL SOLUTION:

Of course, we could set up equations for the unknowns in the problem and solve them algebraically. However, it may be easier just to test the answer choices. Give this approach a try:

(A) 24 students implies 9 male and 15 female students. If 5 male students left the party, the remaining ratio would be 4/14 = 2/7. INCORRECT.

(B) 30 students implies 11.25 male and 18.75 female students. These numbers must be integers. INCORRECT.

(C) 48 students implies 18 male and 30 female students. If 5 male students left the party, the remaining ratio would be 13/30. INCORRECT.

(D) 64 students implies 24 male and 40 female students. If 5 male students left the party, the remaining ratio would be 19/40. INCORRECT.

(E) 80 students implies 30 male and 50 female students. If 5 male students left the party, the remaining ratio would be 25/50 = 1/2. CORRECT.

We proved that the correct answer must be (E) without doing any algebra at all. A nice thing about Testing Answer Choices is that it doesn't require any fundamental knowledge or theory. You don't need to know a special formula. Instead, it forces you to concentrate on the available answer options. It also steadily reduces your uncertainty, since you eliminate wrong answer choices one by one. A question might contain a phrase such as “Which of the following…” This is a great time to test choices

Can you please explain how we are choosing values here?

Hello anairamitch1804,

Here are the detailed steps for option A. Rest follow the same approch

Given: Male : Female = 3:5. Lets assume actual numbers to be 3x and 5x. Total students = 3x+5x = 8x.

Now from the answer choices we get

A. 8x = 24 => x = 3 => Male = 3x = 9 and female = 5x = 15. If 5 Male left, the new values of male = 9-5 = 4. There is no change in females. New Ratio of Male : Female = 4:15 ≠ 1:2. So, A is incorrect.

I think the highlighted portion below is a Typo error.

Hope this helps and this not too late a response

We can let the ratio of male to female = 3x to 5x and create the following equation:

(3x - 5)/5x = 1/2

2(3x - 5) = 5x

6x - 10 = 5x

10 = x

So, there are 3(10) + 5(10) = 80 total students at the party.

Answer: E

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