If the ratio of men to women in a class is 3:5 and the class has 24 p

Question

If the ratio of men to women in a class is 3:5 and the class has 24 people, how many additional men would have to enroll to make the ratio of men to women 1:1?

(A) 3

(B) 6

(C) 9

(D) 12

(E) 15

Hatakekakashi · Answer

total =24
ratio of men:women = 3:5

total = 3+5 = 8

24/8 =3

men = 9
women=15

15-9 =6

(B) imo

Cyborg9969 · Answer

3 men : 5 women
6 men : 10 women
9 men : 15 women = 24 
So, correct answer is (B) 6.

GMATinsight · Answer

Total people = 24

ratio of Men and women = 3:5

Men =  *24 = (3/8)*24 = 9
WoMen =  *24 = (3/8)*24 = 15

Needed ratio of men and women = 1:1 i.e. equal number of men and women are needed

hence men needed = 15-9 = 6

Answer: option B

BrentGMATPrepNow · Answer

The first 2 solutions are similar to my approach. However, we can also solve this question  algebraically .

Let M = # of men in the class
Let W = # of women in the class

The class has 24 people  
We can write:  M + W = 24

The ratio of men to women in a class is 3:5   
We can write: M/W = 3/5
Cross multiply to get:  3W = 5M

We now have the following system: 
 M + W = 24 
 3W = 5M

REWRITE  M + W = 24  as  M = 24 - W 
Take  3W = 5M  and replace M with 24 - W
We get: 3W = 5(24 - W)
Expand: 3W = 120 - 5W
Add 5W to both sides: 8W = 120
W = 15
So, there are 15 women in the class. 
Since there are 24 people altogether, then there must be 9 men.

Wow many additional men would have to enroll to make the ratio of men to women 1:1?   
If 6 men were to enroll, there would be 15 women and 15 men

Answer: B

Cheers,
Brent

generis · Answer

Ratio of men to women:   \frac{3x}{5x}  
Total of ratio parts: 3x + 5x = 8x
Total number of persons: 24
  8x = 24 
 x = 3   = multiplier that yields the actual number of men and women from the original ratio
Men =   3x = (3)(3) = 9  
Women =   5x = (5)(3) = 15

To get a 1:1 ratio, we need the same number of men and women. We need 15 men. There are 9. We need 6 more men.

Answer B

KSBGC · Answer

Total = 24 people 
men to women ratio is 3: 5
so men=9
women=15

now we don't knw how many men have to be enrolled in order to make the ratio 1:1
one thing has to be noticed here that 1: 1 means both men and women will be equal in no. 
so, we have 15 women. 
men 5
we need ( 15-9) men to make men and women equal in no. 
so, 6 men would have to enroll.

approach 2: assign variable:

let's assume the no. of men will X that must have to enroll to keep the ratio 1: 1

9+x/15=1:1
9+x=15
x=6.

rishabhmishra · Answer

solu  IMO B  3x+5x=24
8x=24, x=3
now men are 3*3=9 and women are 5*3=15 now to make ratio equal and increase boys equation will be 9+x/15=1/1 so x=6 and B is the correct option

ScottTargetTestPrep · Answer

We can first determine the number of men and women with the equation:

3x + 5x = 24

8x = 24

x = 3

So there are 9 men and 15 women.

Since we want the ratio of men to women to be 1:1, there must be an equal number of men and women. Therefore, 15 - 9 = 6 more men should enroll.

Answer: B

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If the ratio of men to women in a class is 3:5 and the class has 24 p

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If the ratio of men to women in a class is 3:5 and the class has 24 p

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards