Problem Solving

Hi swerve,

We're told that in a certain town the ratio of NY Yankees fans to NY Mets fans is 3:2, the ratio of the NY Mets fans to Boston Red Sox fans is 4:5 and there are 300 total baseball fans in the town, each of whom is a fan of JUST ONE of those three teams. We're asked for the number of NY Mets in this town.

When dealing with ratios, it's important to remember that you can't have a 'fraction' of a person. Here, that means the number of NY Yankees fans MUST be a multiple of 3, the number of NY Mets fans MUST be a multiple of 2 and 4 and the number of Boston Red Sox fans MUST be a multiple of 5. Combining these facts into one big ratio, we have...
Y:M:R
6:4:5
This means that for every 6 NY Yankees fans, there are 4 NY Mets fans and 5 Boston Red Sox fans

For example....
Yankees = 6, Mets = 4, Red Sox = 5.... Total = 15
Yankees = 12, Mets = 8, Red Sox = 10.... Total = 30
Yankees = 18, Mets = 12, Red Sox = 15.... Total = 45
Notice that the TOTAL number of people will always be a multiple of 15, so we can use that deduction with the total that we're given (300 fans):

300/15 = 20 'groups' of fans:
(20)(6) = 120 Yankees fans
(20)(4) = 80 Mets fans
(20)(5) = 100 Red Sox Fans

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

swerve wrote:In a certain town in Connecticut, the ratio of NY Yankees fans to NY Mets fans is 3:2, and the ratio of the NY Mets fans to Boston Red Sox fans is 4:5. If there are 300 baseballs in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets are there in this town?

A. 75
B. 80
C. 90
D. 120
E. 133

We can create the ratios:

Yankees : Mets = 3 : 2

Multiplying by 2 we have:

Yankees : Mets = 6 : 4

and

Mets : Red Sox = 4 : 5

So we can create the ratio:

Yankees : Mets : Red Sox = 6x : 4x : 5x

Now we can create the equation:

6x + 4x + 5x = 300

15x = 300

x = 20

So there are 4 x 20 = 80 Mets fans.

Answer: B