GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 09 Dec 2019, 16:18

### GMAT Club Daily Prep

#### 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

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

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 173
In a certain district, the ratio of the number of registered  [#permalink]

### Show Tags

12 Dec 2012, 04:38
5
36
00:00

Difficulty:

55% (hard)

Question Stats:

71% (02:15) correct 29% (02:29) wrong based on 1156 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?

(A) 100
(B) 300
(C) 400
(D) 1,000
(E) 2,500
Math Expert
Joined: 02 Sep 2009
Posts: 59622
Re: In a certain district, the ratio of the number of registered  [#permalink]

### Show Tags

12 Dec 2012, 04:47
7
12
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 $$(5x+500)-(3x+600)=2x-100=300$$.

_________________
##### General Discussion
Intern
Joined: 12 Dec 2011
Posts: 1
In a certain district, the ratio of the number of registered  [#permalink]

### Show Tags

19 Dec 2012, 02:46
1
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?
Math Expert
Joined: 02 Sep 2009
Posts: 59622
Re: In a certain district, the ratio of the number of registered  [#permalink]

### Show Tags

19 Dec 2012, 02:54
1
1

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.
_________________
Intern
Joined: 28 Oct 2012
Posts: 1
Re: In a certain district, the ratio of the number of registered  [#permalink]

### Show Tags

06 Mar 2013, 11:45
1
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
Math Expert
Joined: 02 Sep 2009
Posts: 59622
Re: In a certain district, the ratio of the number of registered  [#permalink]

### Show Tags

07 Mar 2013, 02:29
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

Check my response here: in-a-certain-district-the-ratio-of-the-number-of-registered-143983.html#p1158046
_________________
Intern
Joined: 03 Mar 2013
Posts: 24
Re: In a certain district, the ratio of the number of registered  [#permalink]

### Show Tags

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?

Math Expert
Joined: 02 Sep 2009
Posts: 59622
Re: In a certain district, the ratio of the number of registered  [#permalink]

### Show Tags

10 Jul 2013, 06:37
2
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?

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.
_________________
Intern
Joined: 03 Mar 2013
Posts: 24
Re: In a certain district, the ratio of the number of registered  [#permalink]

### Show Tags

10 Jul 2013, 06:45
Bunuel 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?

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.

Thanks a lot, appreciate your help!
Veritas Prep GMAT Instructor
Joined: 11 Dec 2012
Posts: 312
Re: In a certain district, the ratio of the number of registered  [#permalink]

### Show Tags

10 Jul 2013, 07:48
3
1
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!
-Ron
_________________
Intern
Joined: 09 Sep 2013
Posts: 2
GPA: 3.53
Official guide problem solving Q 113  [#permalink]

### Show Tags

14 Oct 2013, 01:59
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
Current Student
Status: Chasing my MBB Dream!
Joined: 29 Aug 2012
Posts: 1096
Location: United States (DC)
WE: General Management (Aerospace and Defense)
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

Before posting please check whether the same question is discussed or not. In this case it is already discussed.
_________________
Become a GMAT Club Premium member to unlock discounts

MBA, Class of 2020,
Math Expert
Joined: 02 Sep 2009
Posts: 59622
Re: Official guide problem solving Q 113  [#permalink]

### Show Tags

14 Oct 2013, 02:03
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 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.

P.S. All OG13 questions with solutions are here: the-official-guide-quantitative-question-directory-143450.html
_________________
Intern
Joined: 09 Sep 2013
Posts: 2
GPA: 3.53
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.
Math Expert
Joined: 02 Sep 2009
Posts: 59622
Re: In a certain district, the ratio of the number of registered  [#permalink]

### Show Tags

14 Oct 2013, 05:18
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.
_________________
Manager
Joined: 30 Mar 2013
Posts: 101
Re: In a certain district, the ratio of the number of registered  [#permalink]

### Show Tags

06 Dec 2014, 08:32
R/D = 3x/5x

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
Manager
Joined: 07 Feb 2015
Posts: 60
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!
Math Expert
Joined: 02 Sep 2009
Posts: 59622
Re: In a certain district, the ratio of the number of registered  [#permalink]

### Show Tags

19 Jul 2015, 09:26
3
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.

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.
_________________
Retired Moderator
Joined: 29 Apr 2015
Posts: 816
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
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?
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8645
Location: United States (CA)
Re: In a certain district, the ratio of the number of registered  [#permalink]

### Show Tags

10 Jun 2016, 11:48
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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: In a certain district, the ratio of the number of registered   [#permalink] 10 Jun 2016, 11:48

Go to page    1   2    Next  [ 27 posts ]

Display posts from previous: Sort by