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Dodgers and Yankees

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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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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
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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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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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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
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