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In a certain district, the ratio of the number of registered Republica

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Walkabout
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In a certain district, the ratio of the number of registered Republica [#permalink] New post   12 Dec 2012, 04:38
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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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Re: In a certain district, the ratio of the number of registered Republica [#permalink] New post   12 Dec 2012, 04:47
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Walkabout 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


Old ratio: \(\frac{republicans}{democrats}=\frac{3x}{5x}\).

New ratio: \(\frac{3x+600}{5x+500}=\frac{4}{5}\) --> \(x=200\).

Current difference is \((5x+500)-(3x+600)=2x-100=300\).

Answer: B.
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Re: In a certain district, the ratio of the number of registered Republica [#permalink] New post   10 Jul 2013, 07:48
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If ever you're not seeing the math, you know one of the answers has to be correct, so you can just backsolve. Looking at the increase in numbers, it would make sense that the number of democrats MORE than republicans will probably be in the hundreds, so you'd likely start with B or C.

If you start with C: 400 is the difference between D's and R's in the new ratio: So there are 4x400 = 1600 Republicans and 5x400 = 2000 Democrats. If you subtract 600 from R and 500 from D, you get 1000 Republicans and 1500 Democrats, a 2/3 ratio. This isn't 3/5, but it's not far (66.7% vs 60%). The next attempt should be B since it's close but slightly too big:

B: 300 is the difference between D's and R's in the new ratio: So there are 4x300 = 1200 Republicans and 5x300 = 1500 Democrats. If you subtract 600 from R and 500 from D, you get 600 Republicans and 1000 Democrats, a 3/5 ratio. Bingo.

If you started with B, you got to the right answer quickly. If you started with A, D or E, your answer will be way off. While this is not a better solution than the algebraic one, sometimes it is easier to see.

Hope this helps!
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Re: In a certain district, the ratio of the number of registered Republica [#permalink] New post   19 Dec 2012, 02:46
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In a certain district, the ratio of the number of registered Republicans to the number of registered Democrats was 3/5. After 600 additional R and 500 additional D registered, the ratio was 4/5. After these registrations, the there were how many more voters in the district registered as D than as R?

When you solve the two given equations, you arrive at D = 1000, which is perfectly logical. As R = 3/5 D, R must be 600.

Now comes the thing I don't understand. In the sample solution, the newly registered voters are now added to the above numbers, which results in D = 1000 + 600 = 1500, respectively R = 600 + 600 = 1200. The difference is 300 now, which corresponds to the OA. But isn't it true that the numbers which result from solving the given equations must already be post the additions?
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Re: In a certain district, the ratio of the number of registered Republica [#permalink] New post   19 Dec 2012, 02:54
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Merging similar topics. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #8: Post Answer Choices for PS Questions

tomtom1610 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 R and 500 additional D registered, the ratio was 4/5. After these registrations, the there were how many more voters in the district registered as D than as R?

When you solve the two given equations, you arrive at D = 1000, which is perfectly logical. As R = 3/5 D, R must be 600.

Now comes the thing I don't understand. In the sample solution, the newly registered voters are now added to the above numbers, which results in D = 1000 + 600 = 1500, respectively R = 600 + 600 = 1200. The difference is 300 now, which corresponds to the OA. But isn't it true that the numbers which result from solving the given equations must already be post the additions?


As for your question: we are asked to find the difference between the numbers of Democrats and Republicans AFTER the registration of 600 additional Republicans and 500 additional Democrats, so it should be 1500-1200=300.

Hope it's clear.
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Re: In a certain district, the ratio of the number of registered Republica [#permalink] New post   10 Jul 2013, 05:03
Hi, just wondering what is wrong with my approach as follows:

3/5 republican voters = 0.6*x
Another 600 register as republican, with the total amount being 80% republican (4/5)
Total new voters is 1,100 (500+600)

So, 0.6x + 600 = 0.8(x+1,100)

0.6x + 600 = 0.8x + 880

However, this is where I go awry.

Could someone pls explain why I can't use the approach noted above?

Thanks in advance
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Re: In a certain district, the ratio of the number of registered Republica [#permalink] New post   10 Jul 2013, 06:37
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insidertrader wrote:
Hi, just wondering what is wrong with my approach as follows:

3/5 republican voters = 0.6*x
Another 600 register as republican, with the total amount being 80% republican (4/5)
Total new voters is 1,100 (500+600)

So, 0.6x + 600 = 0.8(x+1,100)

0.6x + 600 = 0.8x + 880

However, this is where I go awry.

Could someone pls explain why I can't use the approach noted above?

Thanks in advance


The ratio of Republicans to Democrats was 3:5, which means that Republicans were 3/(3+5)=3/8 of the total number (not 3/5 of the total number)

After 600 additional Republicans and 500 additional Democrats registered, the ratio was 4:5, which means that that Republicans were 4/(4+5)=4/9 of the total number (not 4/5 of the total number).

3/8*x+600=4/9(x+1100) --> x=1600 --> after registration = x+1100=2700 --> Republicans=4/9*1200 and Democrats=1500 --> the difference=300.

Hope it helps.
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Re: In a certain district, the ratio of the number of registered Republica [#permalink] New post   14 Oct 2013, 02:42
sorry for violating the rules.. I didn't really know them as this was my first post. Anyway, I still don't understand why we can not take the multiplier and multiply it by the new ration 4/5 (200*5)-(200*4)= 200 difference.
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Re: In a certain district, the ratio of the number of registered Republica [#permalink] New post   14 Oct 2013, 05:18
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mjb2 wrote:
sorry for violating the rules.. I didn't really know them as this was my first post. Anyway, I still don't understand why we can not take the multiplier and multiply it by the new ration 4/5 (200*5)-(200*4)= 200 difference.


Sorry but I don't understand the logic behind your approach.
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In a certain district, the ratio of the number of registered Republica [#permalink] New post   19 Jul 2015, 08:29
gmatser1 wrote:
Bunuel wrote:
mjb2 wrote:
sorry for violating the rules.. I didn't really know them as this was my first post. Anyway, I still don't understand why we can not take the multiplier and multiply it by the new ration 4/5 (200*5)-(200*4)= 200 difference.


Sorry but I don't understand the logic behind your approach.


After we find x = 200 as the multiplier, why can't we say that since AFTER these registrations the ratio is 4/5, then 4x/5x. Since x=200, 4x equals 800 registered Republicans, and 5x equals 1000 registered Democrats. Thats means that the difference after the registrations is 1000 Democrats - 800 Republicans is 200!
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In a certain district, the ratio of the number of registered Republica [#permalink] New post   19 Jul 2015, 09:26
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gmatser1 wrote:
Bunuel wrote:
mjb2 wrote:
sorry for violating the rules.. I didn't really know them as this was my first post. Anyway, I still don't understand why we can not take the multiplier and multiply it by the new ration 4/5 (200*5)-(200*4)= 200 difference.


Sorry but I don't understand the logic behind your approach.


After we find x = 200 as the multiplier, why can't we say that since AFTER these registrations the ratio is 4/5, then 4x/5x. Since x=200, 4x equals 800 registered Republicans, and 5x equals 1000 registered Democrats. Thats means that the difference after the registrations is 1000 Democrats - 800 Republicans is 200!


Because x = 200 is for the old ratio and you cannot use it for the new one.
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Re: In a certain district, the ratio of the number of registered Republica [#permalink] New post   10 Jun 2016, 11:48
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Walkabout 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


The fractional ratio indicates that for every 3 Republicans, there are 5 Democrats, a ratio of 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 was 4 to 5. This means 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 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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Re: In a certain district, the ratio of the number of registered Republica [#permalink] New post   27 Oct 2016, 09:20
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Bunuel Can you please guide where I am getting wrong ?

R/D = 3/5 -----(1)

R+600 / D+500 = 4/5 ----(2)

Solving (2) we get

1000 = 4D - 5R

Substitute value of R from (1)

1000 = 4D - 5* (3D/5)

D = 1000

Hence R = 600

So difference should be 400 ??
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Re: In a certain district, the ratio of the number of registered Republica [#permalink] New post   27 Oct 2016, 10:05
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The difference of 400 is before the new registrations. But the problems asks for "After these (new) registrations..." So the new number of registered Republicans is 600 + 600 = 1200, and the new number of registered Democrats is 1000 + 500 = 1500. So the difference is 300.

Does that make sense?
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Re: In a certain district, the ratio of the number of registered Republica [#permalink] New post   27 Oct 2016, 10:25
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ScottTargetTestPrep wrote:
The difference of 400 is before the new registrations. But the problems asks for "After these (new) registrations..." So the new number of registered Republicans is 600 + 600 = 1200, and the new number of registered Democrats is 1000 + 500 = 1500. So the difference is 300.

Does that make sense?


I agree to your explanation as its evident from the answer.

My query is algebraically where I am getting wrong? Is it that at the time if expressing a Q into ratios , we need to provide a constant 'k' or 'x' everytime
What is the significance of this constant?
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Re: In a certain district, the ratio of the number of registered Republica [#permalink] New post   31 Oct 2016, 08:46
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I think you're getting confused with the variables that you created. When you make up variables in your equation, you need to know what those variables stand for - what they represent.. For example, what does the variable D correspond to? Right? Otherwise, your algebra looks fine. You just have to be careful to answer the question that is being asked. I hope this helps...
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Re: In a certain district, the ratio of the number of registered Republica [#permalink] New post   21 Oct 2021, 04:15
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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Re: In a certain district, the ratio of the number of registered Republica [#permalink] New post   12 Oct 2023, 12:20
I am confused to how you came to x = 200
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Re: In a certain district, the ratio of the number of registered Republica [#permalink]
12 Oct 2023, 12:20
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