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Math Expert V
Joined: 02 Sep 2009
Posts: 64222
A certain college party is attended by both male and female students.  [#permalink]

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Difficulty:   5% (low)

Question Stats: 83% (01:29) correct 17% (02:29) wrong based on 181 sessions

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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.

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GPA: 3.65
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Re: A certain college party is attended by both male and female students.  [#permalink]

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6
1
Bunuel wrote:
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.

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.

##### General Discussion
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A certain college party is attended by both male and female students.  [#permalink]

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3
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
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Re: A certain college party is attended by both male and female students.  [#permalink]

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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

Director  P
Joined: 21 May 2013
Posts: 611
Re: A certain college party is attended by both male and female students.  [#permalink]

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2
Bunuel wrote:
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.

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
Intern  B
Joined: 19 Jan 2014
Posts: 19
Concentration: Marketing, Economics
GPA: 3.81
Re: A certain college party is attended by both male and female students.  [#permalink]

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1
$$\frac{M}{F}$$ =$$\frac{3}{5}$$
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
Math Expert V
Joined: 02 Sep 2009
Posts: 64222
Re: A certain college party is attended by both male and female students.  [#permalink]

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Bunuel wrote:
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.

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
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Re: A certain college party is attended by both male and female students.  [#permalink]

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Bunuel wrote:
Bunuel wrote:
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.

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?
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Anaira Mitch
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Joined: 12 Jun 2016
Posts: 199
Location: India
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Re: A certain college party is attended by both male and female students.  [#permalink]

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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 anairamitch1804 wrote:
Bunuel wrote:
Bunuel wrote:
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.

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?

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Joined: 14 Oct 2015
Posts: 10590
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Re: A certain college party is attended by both male and female students.  [#permalink]

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Bunuel wrote:
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

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.

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Re: A certain college party is attended by both male and female students.  [#permalink]

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_________________ Re: A certain college party is attended by both male and female students.   [#permalink] 18 Jun 2019, 18:19

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