Dodgers and Yankees

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Sun May 20, 2012 3:34 am

Every person in a certain group is either a Dodgers fan or a Yankees fan, but not both. The ratio of Yankees fans to Dodgers fans is 5 to 3. If 22 Yankees fans change teams to become Dodgers fans, the ratio of Dodgers fans to Yankees fans will be 1 to 1. How many people are in the group?

22
88
128
144
176

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Source: Beat The GMAT — Problem Solving | Sun May 20, 2012 3:34 am

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Sun May 20, 2012 3:49 am

GmatKiss wrote:Every person in a certain group is either a Dodgers fan or a Yankees fan, but not both. The ratio of Yankees fans to Dodgers fans is 5 to 3. If 22 Yankees fans change teams to become Dodgers fans, the ratio of Dodgers fans to Yankees fans will be 1 to 1. How many people are in the group?

22
88
128
144
176

Let the number of Yankee fans = 5x
Let the number of Dodgers fans = 3x

After the change,
The number of Yankee fans = 5x-22
The number of Dodgers fans = 3x+22
So (5x-22)/(3x+22) = 1/1
5x - 22 = 3x + 22
2x = 44
x = 22

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Sun May 20, 2012 3:51 am

neelgandham wrote:
GmatKiss wrote:Every person in a certain group is either a Dodgers fan or a Yankees fan, but not both. The ratio of Yankees fans to Dodgers fans is 5 to 3. If 22 Yankees fans change teams to become Dodgers fans, the ratio of Dodgers fans to Yankees fans will be 1 to 1. How many people are in the group?

22
88
128
144
176
Let the number of Yankee fans = 5x
Let the number of Dodgers fans = 3x

After the change,
The number of Yankee fans = 5x-22
The number of Dodgers fans = 3x+22
So (5x-22)/(3x+22) = 1/1
5x - 22 = 3x + 22
2x = 44
x = 22

OA is not A

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun May 20, 2012 4:41 am

GmatKiss wrote:Every person in a certain group is either a Dodgers fan or a Yankees fan, but not both. The ratio of Yankees fans to Dodgers fans is 5 to 3. If 22 Yankees fans change teams to become Dodgers fans, the ratio of Dodgers fans to Yankees fans will be 1 to 1. How many people are in the group?

22
88
128
144
176

We can plug in the answers, which represent the total number of people.

After 22 people switch from Yankees to Dodgers, Y : D = 1:1.
Thus, the resulting number of Yankees fans must be 1/2 of the correct answer choice, yielding the following options for the resulting number of Yankees fans after the switch:
11, 44, 64, 72, 88.

Thus, the original number of Yankees fans must have been 22 greater than one of the values above, yielding the following options for the original number of Yankees fans:
33, 66, 86, 94, 110.

Before the switch, Y : D = 5:3, implying that the original number of Yankees fans must be a multiple of 5.
Only answer choice E is viable.

The correct answer is E.

Other ratio problems that I solved with a similar approach:

https://www.beatthegmat.com/mgmat-abstra ... 89581.html

https://www.beatthegmat.com/please-simpl ... 90987.html

https://www.beatthegmat.com/ratio-from-g ... 08195.html

Last edited by GMATGuruNY on Sun May 20, 2012 7:14 am, edited 1 time in total.

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Sun May 20, 2012 5:35 am

Oops! I left it a x. The total number of people in the group = 5x + 3x = 8x = 8*22 = 176

Anil Gandham
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Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/

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