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

Question

A certain college party is attended by both male and female students. The ratio of male to female students is 3 to 5. If 5 of the male students were to leave the party, the ratio would change to 1 to 2. How many total students are at the party?

(A) 24
(B) 30
(C) 48
(D) 64
(E) 80

Kudos for a correct solution.

(A) 24 
(B) 30 
(C) 48 
(D) 64 
(E) 80

Kudos for a correct  solution .

jugglerG2 · Accepted Answer

Correct answer to this question would be divisible by  8 (3+5)  and correct answer subtracted by  5  would be divisible by  3 . Now lets put answer choices to solve the question:

(A) 24 => Divisible by  8  but  24-5=19  is not divisible by  3 . Incorrect
(B) 30 => No divisible by  8 . Incorrect
(C) 48 => Divisible by  8  but  48-5=43  is not divisible by  3 . Incorrect
(D) 64 => Divisible by  8  but  64-5=59  is not divisible by  3 . Incorrect
(E) 80 => Divisible by  8  and  80-5=75  is divisible by  3 . We have a winner.

E is the correct answer.

Naina1 · Answer

M/F = 3/5
5M = 3F-------1
Also, (M-5)/F = 1/2
 2M-10 = F
Multiply by 3 both sides
3F=6M-30--------2
from 1 and 2
M=30
F=50
Total=80
E is the answer

akhilbajaj · Answer

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

KS15 · Answer

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

ritigl · Answer

\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

Bunuel · Answer

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

anairamitch1804 · Answer

Can you please explain how we are choosing values here?

susheelh · Answer

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

ScottTargetTestPrep · Answer

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

bumpbot · Answer

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

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