At a certain soccer club, the number of players increased by 10 percen

Total number of players in 2015 = Men + Women \(= m + w\)

Total number of players increased by 10% in 2016 = 110% of (m + w) = \(\frac{110}{100} * (m + w) = 1.10 (m + w)\)

Number of male players decreased by 5% in 2016 = 95% of m = \(\frac{95}{100} * m = 0.95m\)

Number of female players increased by 15% in 2016 = 115% of w = \(\frac{115}{100} * w = 1.15w\)

Total number of players in 2016 is as given;

\(1.10(m + w) = 0.95m + 1.15w\)

\(1.10m + 1.10w = 0.95m + 1.15w\)

\(1.10m - 0.95m = 1.15w - 1.10w\)

\(0.15m = 0.05w\)

\(\frac{w}{m} = \frac{0.15}{0.05} = \frac{15}{5} = \frac{3}{1}\)

Required ratio of Female to Male players in 2016 \(= 3:1\) . Answer (E)...

Assume total number of players to be 1200(in 2015)
Since there is an increase of 10% in 2016, the number of players will be 1320
We have the increase of female players as 15% over the previous year
and the decrease of male players as 5% over the previous year.
Since evaluating the answer options, containing the ratio of female to male players :

Option A(1:3)
Initial Split : 900-Male,300-Female Total : 1200
Final Split : Male : 900-5%(45) = 855, Female: 300+15%(45) = 345 Total : 1200(not equal to 1320)

Option B(1:2)
Initial Split : 800-Male,400-Female Total : 1200
Final Split : Male : 800-5%(40) = 760, Female: 400+15%(60) = 460 Total : 1220(not equal to 1320)

Option C(3:2)
Initial Split : 480-Male,720-Female Total : 1200
Final Split : Male : 480-5%(24) = 456, Female: 720+15%(108) = 828 Total : 1284(not equal to 1320)

Option D(2:1)
Initial Split : 400-Male,800-Female Total : 1200
Final Split : Male : 400-5%(20) = 380, Female: 800+15%(120) = 920 Total : 1200(not equal to 1320)

Option E(3:1)
Initial Split : 300-Male,900-Female Total : 1200
Final Split : Male : 300-5%(15) = 285, Female:900+15%(135) = 1035 Total : 1320
Hence Option E is the correct answer option.

Bunuel
VeritasPrepKarishma

Hi, don't you think 3:1 is the ratio of female to male in 2015, and not in 2016?

Please confirm.

Yes that's my question The ratio mentioned in the options and calculated by everyone is for 2015. ratio for 2016 should be (115*3)/95

In 2015:
Let total be 100
No of males =x
No of females =100-x

In 2016
Total =110
Males =0.95x
Females =1.15(100-x)

0.95x + 1.15(100-x)=110

X=25

Now what is asked-

Females / males =0.95*25/1.15*75

Where I am going wrong
Bunuel?


Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app

Edited the question. It asks about the ration in 2015.

Veritas Prep Official Solution:

We can solve this one with the weighted average mapping strategy or with algebra. For the mapping strategy:

-5%...............10%......15%

M..........15...........5......F

This gives us a female:male ratio of 15:5, or 3:1.

To solve algebraically, we can set up the following equation:
\(1.1(f+m)=1.15f+.95m\). By manipulating, we can get to \(0.15m =0.05f\), or \(\frac{f}{m}=\frac{0.15}{0.05}=\frac{3}{1}\).

Answer: E.

Solution:

We can let x = the number of male players and y = the number of female players in 2015 and create the equation for 2016:

0.95x + 1.15y = 1.1(x + y)

0.95x + 1.15y = 1.1x + 1.1y

0.05y = 0.15x

5y = 15x

y/x = 15/5

y/x = 3/1

Answer: E

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.