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Ratio- shorter method

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by hey_thr67 » Wed Jun 13, 2012 9:46 am
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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by niketdoshi123 » Wed Jun 13, 2012 10:33 am
The ratio of the number of registered republicans to the number of registered democrats was 3/5
So let the number of registered republicans be =3x
and the number of registered democrats be = 5x
After 600 additional republicans and 500 additional democrats registered , the ratio was 4/5
total number of republicans = 3x+600
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
After these registrations, there were how many more voters in the district registered as democrats than as republicans.
5x+500-3x-600 = 2x-100 = 2*200 - 100 = 300

Hence the answer is B
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by hey_thr67 » Wed Jun 13, 2012 11:07 am
Avoiding the direct method :)
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by GMATGuruNY » Wed Jun 13, 2012 12:57 pm
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
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.
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by ProGMAT » Sun Apr 06, 2014 4:34 am
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.
I did it like this, but did not get the correct answer:

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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by [email protected] » Sun Apr 06, 2014 12:26 pm
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]

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by Scott@TargetTestPrep » Sat Jun 27, 2015 5:15 am
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
Solution:

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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by nikhilgmat31 » Wed Jul 01, 2015 11:20 pm
By mistake, I also find the answer as D-R = 1000-600 = 400

but later realized that 1500-1200 = 300 is correct answer.
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