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.
_________________
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.