Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

In a certain district, the ratio of the number of registered [#permalink]

Show Tags

12 Dec 2012, 04:38

26

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

65% (03:02) correct
35% (02:06) wrong based on 1074 sessions

HideShow timer Statistics

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?

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

In a certain district, the ratio of the number of registered [#permalink]

Show Tags

19 Dec 2012, 02:46

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?

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.

Re: In a certain district, the ratio of the number of registered [#permalink]

Show Tags

06 Mar 2013, 11:45

why cant we write it down as R/D = 3/5 and go further with (R+600)/(D+500). If we combine them we get R = 600 and D = 1000. Difference = 400. Whats wrong with this logic. Thanks in advance

why cant we write it down as R/D = 3/5 and go further with (R+600)/(D+500). If we combine them we get R = 600 and D = 1000. Difference = 400. Whats wrong with this logic. Thanks in advance

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.

Re: In a certain district, the ratio of the number of registered [#permalink]

Show Tags

10 Jul 2013, 06:45

Bunuel wrote:

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.

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.

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

_________

My question is, why can't we take the multiplier which is 200, and multiply the new ratio 4/5 to get a difference of 200? Why is that wrong? that what was done In question 105 in the official guide. Thank you

Re: Official guide problem solving Q 113 [#permalink]

Show Tags

14 Oct 2013, 02:01

mjb2 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

_________

My question is, why can't we take the multiplier which is 200, and multiply the new ration 4/5 to get a difference of 200? Why is that wrong? In question 105 in the official guide that what was done. Thank you

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

_________

My question is, why can't we take the multiplier which is 200, and multiply the new ratio 4/5 to get a difference of 200? Why is that wrong? that what was done In question 105 in the official guide. Thank you

Merging similar topics. Please refer to the solutions above and ask if anything is unclear.

Re: In a certain district, the ratio of the number of registered [#permalink]

Show Tags

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.

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.
_________________

Re: In a certain district, the ratio of the number of registered [#permalink]

Show Tags

16 Oct 2014, 09:36

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: In a certain district, the ratio of the number of registered [#permalink]

Show Tags

06 Dec 2014, 08:32

R/D = 3x/5x

add the new voters: R/D = 3x+600/(5x+500) = 4/5 Solve for x to get x=200. Now put in original equation to get total Republicans as 1200, and the total number of democrats as 1500. difference= 300

Re: In a certain district, the ratio of the number of registered [#permalink]

Show Tags

19 Jul 2015, 08:29

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.

It's a shame this wasn't addressed, Bunuel. Let me follow up this question with the logic and you can let me know why it's wrong.

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!

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.

It's a shame this wasn't addressed, Bunuel. Let me follow up this question with the logic and you can let me know why it's wrong.

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.
_________________

Re: In a certain district, the ratio of the number of registered [#permalink]

Show Tags

08 Sep 2015, 03:43

Can we solve this somehow with the "change in ratio" method?

Starting ratio: 5R=3D Ending ratio: 5R=4D

Now we have a change in ratio of 1 unit in democrats corresponding to 500 democrats. This means, 1 unit in 5:4 represents 500. However I believe this just holds true as long as only one number changes. Since we also have changing numbers of republicans, we can not calculate it like that. Can anyone agree/disagree?
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

gmatclubot

Re: In a certain district, the ratio of the number of registered
[#permalink]
08 Sep 2015, 03:43

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...