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

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Re: At a certain soccer club, the number of players increased by 10 percen [#permalink]
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Bunuel wrote:
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 2016?

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

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)...
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Re: At a certain soccer club, the number of players increased by 10 percen [#permalink]
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Kudos
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.
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Re: At a certain soccer club, the number of players increased by 10 percen [#permalink]
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Kudos
Bunuel wrote:
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 2016?

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

Bunuel
VeritasPrepKarishma

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

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Re: At a certain soccer club, the number of players increased by 10 percen [#permalink]
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Kudos
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
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Re: At a certain soccer club, the number of players increased by 10 percen [#permalink]
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Kudos
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

Females / males =0.95*25/1.15*75

Where I am going wrong
Bunuel?

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At a certain soccer club, the number of players increased by 10 percen [#permalink]
Bunuel wrote:
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

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 $$\frac{f}{m}=\frac{0.15}{0.05}=\frac{3}{1}$$.

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Re: At a certain soccer club, the number of players increased by 10 percen [#permalink]
Bunuel wrote:
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

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

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Re: At a certain soccer club, the number of players increased by 10 percen [#permalink]
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Re: At a certain soccer club, the number of players increased by 10 percen [#permalink]
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