In a certain town in Connecticut, the ratio of NY Yankees

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

In a certain town in Connecticut, the ratio of NY Yankees

by swerve » Sun Apr 15, 2018 10:03 am

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

The OA is B.

Please, can anyone explain this PS question? I can't get the correct answer. I appreciate your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Sun Apr 15, 2018 10:03 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Sun Apr 15, 2018 11:15 am

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

Contact Rich at [email protected]

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Tue Apr 17, 2018 3:39 pm

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

Jeffrey Miller
Head of GMAT Instruction
[email protected]