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Ratio question: Yankees and Dodgers

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Ratio question: Yankees and Dodgers

by suzeemunkee » Tue Jun 29, 2010 7:50 am
Hi,

I have a question from BTG's Smart GMAT practice.

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?

A) 22
B) 88
C) 128
D) 144
E) 176

The answer is E

I got 88... and I need help understanding what I did wrong. Why is it wrong write this equation?

22/x = 2/8

(x would be the total number of people.)

Can someone help me understand why my logic is faulty?

Thanks much!

P.S. I highly recommend BTG's Smart Practice!! It's fantastic!
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by albatross86 » Tue Jun 29, 2010 7:55 am
Y/D = 5/3

(Y - 22) / (D + 22) = 1 / 1

These are the two pivotal equations you need to solve.

You have basically added the ratios 1:1 and 5:3 up to get a new ratio of 2:8

This is conceptually wrong. I think you may have also misinterpreted the question a bit.

The total number of fans needs to be conserved which is why you remove them from the Yankees pool and add them to the Dodgers.
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by selango » Tue Jun 29, 2010 7:57 am
Y/D=5/3

3Y=5D--Eqn 1

22 peoples move from yankees to dodgers.So the new ratio is

Y-22/D+22=1/1

-->Y-22=D+22

Y-D=44

5y-5D=220

From eqn1,3Y=5D

5y-3Y=220

y=110 and D=66

Total=110+66=176
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by amising6 » Tue Jun 29, 2010 7:59 am
suzeemunkee wrote:Hi,

I have a question from BTG's Smart GMAT practice.

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?


It's fantastic!
let the total number of fan be 8x so dodger fan=3x and yankees fans=5x
22 yankees goes to dodgers so dogers now become 3x+22 and yankeees 5x-22
now given ratio=1:1
so equating
3x+22=5x-22
x=22
so total number of people =22*8=176
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by indiantiger » Tue Jun 29, 2010 8:04 am
Lets say the initial ratio is Y/D = 5/3 => Y = 5D/3 -----(1)

No 22 users change their loyalty From Yankee to Dodgers and the new ratio becomes 1/1

Yankees loose 22 fans and at the same time Dodgers get 22 fans
(Y - 22)/(D+22) = 1/1

Y-22 = D+22

From (1) we know that Y = 5D/3

5D/3 - 22 = D + 22

5D - 66 = 3D + 66
2D = 66 + 66
D = 66
Put the value of D back in --(1) we get 5*66/3 = 110 (yankee fans)

Total number of the fans = 110 + 66 = 176 (E)
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by globalcitizen » Tue Jun 29, 2010 8:08 am
Hmm...I don't quite understand how you got your equation...can you please write out your thought process? In the meantime, I can share how I got the answer.

So, we know that the ratio of Y:D is 5:3. I wrote it out as a fraction Y/D=5/3 and then cross-multiplied to get Y=(5/3)D. Lets put that aside for now as it will come in handy later.

Next, we are told that if 22 people leave the Yankee fan base to join that of the Dodgers', the ratio of Y:D will be 1:1. This can be expressed as:
(Y-22), because 22 people "leave"
(D+22) because D has 22 new fans join
So, (Y-22)/(D+22)=1/1. Cross multiply and you get Y-22=D+22 --> Y=D+44

Now we will refer back to our initial calculation of Y=(5/3)D and substitute it for Y.
(5/3)D=D+44
5D=3D+132
D=66

Plug 66 into Y=(5/3)D and you get 110 for Y. So 110+66=176

Hope that helps!
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by GMATGuruNY » Tue Jun 29, 2010 9:04 am
suzeemunkee wrote:Hi,

I have a question from BTG's Smart GMAT practice.

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?

A) 22
B) 88
C) 128
D) 144
E) 176

The answer is E

I got 88... and I need help understanding what I did wrong. Why is it wrong write this equation?

22/x = 2/8

(x would be the total number of people.)

Can someone help me understand why my logic is faulty?

Thanks much!

P.S. I highly recommend BTG's Smart Practice!! It's fantastic!
You can't just subtract one ratio from the other.

Let's say Y = Yankees fans, D = Dodgers fans.

If the original ratio is 5:3, then out of every 8 people, Y=5 , D=3. So Y=5/8 of the group. The rest will be Dodgers fans.

We know that the number of people in the group has to be one of the answer choices. We could just plug them in until we find the one that works. We should start with the answer choice right in the middle, answer choice C.

If there are 128 people in the group, Y= 5/8 * 128 = 80, D = 128-80=48.
If 22 people switch, Y=80-22=58, D=48+22=70.
Is 58/70 a 1:1 ratio? No. So answer choice C is incorrect.

Since Y ended up too small, we need a bigger answer choice. Let's try D.

If there are 144 people in the group, Y= 5/8 * 144 = 90, D = 144-90=54.
If 22 people switch, Y=90-22=68, D=54+22=76.
Is 68/76 a 1:1 ratio? No. So answer choice D is incorrect.

Since Y still ended up too small, we need a bigger answer choice. The correct answer must be E.

(Here's the math, in case you're wondering:

If there are 176 people in the group, Y= 5/8 * 176 = 110, D = 176-110=66.
If 22 people switch, Y=110-22=88, D=66+22=88.
Is 88/88 a 1:1 ratio? Yes. So answer choice E is correct.)
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by akdayal » Tue Jun 29, 2010 9:29 am
Hi,

I have a question from BTG's Smart GMAT practice.

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?

A) 22
B) 88
C) 128
D) 144
E) 176

The answer is E

I got 88... and I need help understanding what I did wrong. Why is it wrong write this equation?

22/x = 2/8

(x would be the total number of people.)

Can someone help me understand why my logic is faulty?

Thanks much!

P.S. I highly recommend BTG's Smart Practice!! It's fantastic!
@suzeemunkee

I think you misunderstood the question.
initial equation
Y/D = 5/3
Now you are trying to use componendo dividendo
Hence Now 1st equ will be

(Y - D)/(Y + D) = (5 -3)/(5 + 3) = 2/8
but here Y -D is not eq to 22. (think !!)
This mistake you are doing.
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by outreach » Tue Jun 29, 2010 10:44 am
Y-yankees
D=Dodgers


y/d=5/3
y=d*(5/3)

also
(y-22)/(d+22)=1
after sub value of y and solving d=66
y=110
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by suzeemunkee » Tue Jun 29, 2010 10:59 pm
Thank you everyone for all your replies! I truly appreciate it. I understand this question now - as some of you guys mentioned, you can't just subtract one ratio from the other. I also think I misunderstood the question in general.

Thanks again. You guys are the best! :)
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