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

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In a certain town in Connecticut, the ratio of NY Yankees fans to NY  [#permalink]

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New post 02 Apr 2015, 05:34
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In a certain town in Connecticut, the ratio of NY Yankees fans to NY Mets fans is 3:2, and the ratio of NY Mets fans to Boston Red Sox fans is 4:5. If there are 300 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town?'

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


Kudos for a correct solution.

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Re: In a certain town in Connecticut, the ratio of NY Yankees fans to NY  [#permalink]

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New post 02 Apr 2015, 05:39
Bunuel wrote:
In a certain town in Connecticut, the ratio of NY Yankees fans to NY Mets fans is 3:2, and the ratio of NY Mets fans to Boston Red Sox fans is 4:5. If there are 300 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town?'

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


Kudos for a correct solution.


Y:M=3:2
M:B=4:5
Y:M:B=6:4:5

15x=300
x=20
4x=80

Answer: B
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Re: In a certain town in Connecticut, the ratio of NY Yankees fans to NY  [#permalink]

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New post 02 Apr 2015, 05:54
Bunuel wrote:
In a certain town in Connecticut, the ratio of NY Yankees fans to NY Mets fans is 3:2, and the ratio of NY Mets fans to Boston Red Sox fans is 4:5. If there are 300 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town?'

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


Kudos for a correct solution.


We have two ratios 3:2 and 4:5
for deciding this task we should find common ratio among these three groups
We have Mets fans in both ratios: 2 parts of Mets in first ratio and 4 parts of Mets in second ratio
LCM (2, 4) = 4
so we should multiply first ratio by 2 and get ratio 6:4

So in common for three groups we ratio:
Y M B
6 4 5

For now we should calculate how much people in one part:
for this we should calculate all parts: 6 + 4 + 5 = 15
and divide 300 people on 15 part: so we have 20 people in 1 part

We need to know how much people in NY Mets group and we know that this group have 4 parts (we should take parts from calculated coomon ratio, not from first ratio)
4 parts * 20 people = 80 people
So answer is B
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Re: In a certain town in Connecticut, the ratio of NY Yankees fans to NY  [#permalink]

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New post 02 Apr 2015, 15:07
Y/M=3/2; M/B=4/5; M+Y+B=300;
Rearranging above equation in terms of M gives; Y=3/2*M; B=5/4*M; and putting these value to final equation gives:
M+3/2*M+5/4*M= (15/4)M=300; therefore M=80

Hence Answer is B

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Re: In a certain town in Connecticut, the ratio of NY Yankees fans to NY  [#permalink]

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New post 02 Apr 2015, 17:54
Bunuel wrote:
In a certain town in Connecticut, the ratio of NY Yankees fans to NY Mets fans is 3:2, and the ratio of NY Mets fans to Boston Red Sox fans is 4:5. If there are 300 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town?'

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


Kudos for a correct solution.


(Yankees) Y:M (Mets) = 3:2

M:B (boston) = 4:5

Combining the ratios: 3:2:5/2 --> 6:4:5

Now total, 15x = 300
x = 20.

Therefore, Mets = 4x = 80

Answer:B
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Re: In a certain town in Connecticut, the ratio of NY Yankees fans to NY  [#permalink]

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New post 02 Apr 2015, 23:36
Answer = B = 80

Yankees ...................... Met ................ Boston

3 ............................... 2 ..................................

................................... 4 ........................... 5

6 ................................. 4 ............................ 5 (Resultant)

Total fans (6+4+5)x = 300

x = 20

Met fans = 20*4 = 80
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Re: In a certain town in Connecticut, the ratio of NY Yankees fans to NY  [#permalink]

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New post 03 Apr 2015, 00:37
Bunuel wrote:
In a certain town in Connecticut, the ratio of NY Yankees fans to NY Mets fans is 3:2, and the ratio of NY Mets fans to Boston Red Sox fans is 4:5. If there are 300 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town?'

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


Kudos for a correct solution.


Answer=B

NY Yankees/NY Mets=3:2 and NY Mets/Boston Red Sox=4:5
Rationalizing both the fractions
NY Yankees:NY Mets:Boston Reds=6:4:5
Therefore, No of NY Mets Fans=4/15*300=80
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Re: In a certain town in Connecticut, the ratio of NY Yankees fans to NY  [#permalink]

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New post 06 Apr 2015, 06:50
Bunuel wrote:
In a certain town in Connecticut, the ratio of NY Yankees fans to NY Mets fans is 3:2, and the ratio of NY Mets fans to Boston Red Sox fans is 4:5. If there are 300 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town?'

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


Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

The ratio of iniquitous Yankees fans to pure-hearted Mets fans is 3:2, and the ratio of these same noble Mets fans to the misguided Red Sox fans is 4:5. (The author acknowledges no preferences in this description.) We need to combine these into one ratio, but in order to do that, we need to make the common term, Mets fans, equal in both. Fortunately, Mets fans are represented by 2 in the #rst ratio and 4 in the second ratio, so we just have to multiply the #rst ratio by two—a 3:2 ratio is the same thing as a 6:4 ratio. Now we can combine these into a single 6:4:5 ratio—6 parts Yankees fans, 4 parts Mets fans, and 5 parts Red Sox fans. That's a total of 15 parts in the whole population. Well, there are 300 baseball fans, and if that's 15 parts, each part is worth 300/15 = 20 fans. The Mets fans comprise 4 parts, or 4 × 20 = 80 fans, answer = b. Fewer than the fans of the other two, less virtuous teams: many are called, few are chosen.

Answer: B.
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: In a certain town in Connecticut, the ratio of NY Yankees fans to NY  [#permalink]

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New post 07 Apr 2015, 04:43
Gimme a couple of these at the real test pls :).

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

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


Yankees : Mets : Boston Red Sox
Y:M = 3:2 or 6:4
M:B = 4:5

Y:M:B
6:4:5

6+4+5 = 15
300 / 15 = 20

Yankees: 6*20 = 120
Mets: 4*20 = 80
Boston Red Socks: 5*20 = 100

Answer is B.
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Re: In a certain town in Connecticut, the ratio of NY Yankees fans to NY  [#permalink]

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New post 17 Apr 2018, 16:29
Bunuel wrote:
In a certain town in Connecticut, the ratio of NY Yankees fans to NY Mets fans is 3:2, and the ratio of NY Mets fans to Boston Red Sox fans is 4:5. If there are 300 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans 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
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Re: In a certain town in Connecticut, the ratio of NY Yankees fans to NY &nbs [#permalink] 17 Apr 2018, 16:29
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