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

Question

At a certain soccer club, the number of players increased by 10 percent between 2015 and 2016. If the number of male players decreased by 5 percent and the number of female players increased by 15 percent, what is the ratio of female players to male players in 2015?

A. 1:3
B. 1:2
C. 3:2
D. 2:1
E. 3:1

A. 1:3
B. 1:2
C. 3:2
D. 2:1
E. 3:1

quantumliner · Accepted Answer

Let number of Male players in 2015 = 100M
Let number of Female players in 2015 = 100F

Total number of players in 2015 = 100(M+F)

Given: the number of players increased by 10 percent between 2015 and 2016

Total number of players in 2016 = 100(M+F) * 1.1 = 110(M+F)

Given: number of male players decreased by 5 percent

Total number of Male players in 2016 = 0.95 * 100M = 95M

Given: number of female players increased by 15 percent

Total number of Female players in 2016 = 1.15 * 100F = 115F

Therefore

95M+115F = 110(M+F) = 110M+110F

5F = 15M
 F = 3M
F/M = 3/1

Answer is E. 3:1

mrdlee23 · Answer

Overall average +10%
Female +15% (difference of 5)
Male -5% (different of 15)

-5%-----------10%----15%
M-------------Avg-----F
5:15

Question asks F:M so answer is 3:1 (E)

sashiim20 · Answer

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)...

pushpitkc · Answer

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.

ShashankDave · Answer

Bunuel 
 VeritasPrepKarishma

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

Please confirm.

deepudiscover · Answer

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

lesner19 · Answer

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

Bunuel · Answer

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.

ScottTargetTestPrep · Answer

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

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

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