In a certain district, the ratio of the number of registered republicans to the number of registered democrats was 3/5. After 600 additional republicans and 500 additional democrats registered , the ratio was 4/5. After these registrations, there were how many more voters in the district registered as democrats than as republicans.
A: 100
B: 300
C: 400
D: 1,000
E: 2,500
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Ratio- shorter method
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niketdoshi123
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So let the number of registered republicans be =3xThe ratio of the number of registered republicans to the number of registered democrats was 3/5
and the number of registered democrats be = 5x
total number of republicans = 3x+600After 600 additional republicans and 500 additional democrats registered , the ratio was 4/5
total number of democrats = 5x+500
the new ratio is 4/5, so (3x+600)/(5x+500)=4/5
equating this equation we get, x=200
5x+500-3x-600 = 2x-100 = 2*200 - 100 = 300After these registrations, there were how many more voters in the district registered as democrats than as republicans.
Hence the answer is B
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GMATGuruNY
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All of the values in the problem are multiples of 100.hey_thr67 wrote:In a certain district, the ratio of the number of registered republicans to the number of registered democrats was 3/5. After 600 additional republicans and 500 additional democrats registered , the ratio was 4/5. After these registrations, there were how many more voters in the district registered as democrats than as republicans.
A: 100
B: 300
C: 400
D: 1,000
E: 2,500
We can guess and check very quickly.
Let old r=300 and old d=500.
When 600 republicans and 500 democrats are added, we get:
new r: new d = 900:1000 = 9:10.
Doesn't work.
Let old r=600 and old d=1000.
When 600 republicans and 500 democrats are added, we get:
new r : new d = 1200:1500 = 4:5.
Success!
New d - new r = 1500-1200 = 300.
The correct answer is B.
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I did it like this, but did not get the correct answer:GMATGuruNY wrote: All of the values in the problem are multiples of 100.
We can guess and check very quickly.
Let old r=300 and old d=500.
When 600 republicans and 500 democrats are added, we get:
new r: new d = 900:1000 = 9:10.
Doesn't work.
Let old r=600 and old d=1000.
When 600 republicans and 500 democrats are added, we get:
new r : new d = 1200:1500 = 4:5.
Success!
New d - new r = 1500-1200 = 300.
The correct answer is B.
Let R be Registered Republicans and D be registered Democrats.
Now,
R/D=3/5 ---Given
5R = 3D ---(1)
(R+600)/(D+500) = 4/5 ---Given
5R+3000 = 4D+2000 ---(2)
Putting (1) in (2),
3D+3000 = 4D+2000
D = 1000 ---(3)
Putting (3) in (1),
R = 600
Difference = 400..!!
Please tell me where I am wrong. :!:
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[email protected]
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Hi ProGMAT,
You did everything correct except for the last couple of steps.
The question asks for how many more democrats are there than republicans AFTER the additional registrations.
You correctly calculated that D = 1000 and R = 600, but you have TO INCLUDE the additional registrations (+600 republicans, + 500 democrats)
We end up with...
Total Democrats = 1500
Total Republicans = 1200
Difference = [spoiler]300, Final Answer = B[/spoiler]
GMAT assassins aren't born, they're made,
Rich
You did everything correct except for the last couple of steps.
The question asks for how many more democrats are there than republicans AFTER the additional registrations.
You correctly calculated that D = 1000 and R = 600, but you have TO INCLUDE the additional registrations (+600 republicans, + 500 democrats)
We end up with...
Total Democrats = 1500
Total Republicans = 1200
Difference = [spoiler]300, Final Answer = B[/spoiler]
GMAT assassins aren't born, they're made,
Rich
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Scott@TargetTestPrep
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Solution:hey_thr67 wrote:In a certain district, the ratio of the number of registered republicans to the number of registered democrats was 3/5. After 600 additional republicans and 500 additional democrats registered , the ratio was 4/5. After these registrations, there were how many more voters in the district registered as democrats than as republicans.
A: 100
B: 300
C: 400
D: 1,000
E: 2,500
Since 3/5 means 3 : 5, we first set up this ratio of registered Republicans to registered Democrats using a variable multiplier:
Republicans : Democrats = 3x : 5x
We are given that 600 additional Republicans and 500 additional Democrats registered, and that the new ratio of Republicans to Democrats becomes 4 to 5. It follows that the new number of Republicans can be expressed as (3x + 600), and the new number of Democrats can be expressed as (5x + 500). We can put all this information into an equation:
R/D --> (3x + 600)/(5x + 500) = 4/5
After cross multiplying we have:
5(3x + 600) = 4(5x + 500)
15x + 3,000 = 20x + 2,000
1,000 = 5x
x = 200
Thus, after the registration we have the following:
Democrats = (5 × 200) + 500 = 1,500
Republicans = (3 × 200) + 600 = 1,200
There are 1,500 - 1,200 = 300 more Democrats than Republicans.
Answer: B
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nikhilgmat31
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By mistake, I also find the answer as D-R = 1000-600 = 400
but later realized that 1500-1200 = 300 is correct answer.
but later realized that 1500-1200 = 300 is correct answer.
