Ratio- shorter method

Expert replies

hey_thr67: Master | Next Rank: 500 Posts; Posts: 299; Joined: Tue Feb 15, 2011 10:27 amFollowed by: 2 members; Thanked: 9 times

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

Like this post

Source: Beat The GMAT — Problem Solving | Wed Jun 13, 2012 9:46 am

niketdoshi123: Master | Next Rank: 500 Posts; Posts: 210; Joined: Thu Mar 08, 2012 11:24 pmFollowed by: 3 members; Thanked: 62 times

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

Like this post

hey_thr67: Master | Next Rank: 500 Posts; Posts: 299; Joined: Tue Feb 15, 2011 10:27 amFollowed by: 2 members; Thanked: 9 times

by hey_thr67 » Wed Jun 13, 2012 11:07 am

Avoiding the direct method

Like this post

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Like this post

ProGMAT: Senior | Next Rank: 100 Posts; Posts: 35; Joined: Wed Jul 24, 2013 10:15 am; Thanked: 2 times

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. :!:

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

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]

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8138; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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 Ã— 200) + 500 = 1,500

Republicans = (3 Ã— 200) + 600 = 1,200

There are 1,500 - 1,200 = 300 more Democrats than Republicans.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

Like this post

nikhilgmat31: Legendary Member; Posts: 518; Joined: Tue May 12, 2015 8:25 pm; Thanked: 10 times

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.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review