Lesson: Introduction to Ratios

Rate this video: 

Comment on Introduction to Ratios

Awesome thanks for the lesson. I hear ratios is a big part of the gmat
gmat-admin's picture

Ratios are important, but I wouldn't say they're tested as often as the super popular concepts like percents, geometry, statistics, integer properties and overlapping sets.

I always mix up the ratios and my solution is always exactly the other way round, e.g. my solution is the ratio x:y but actually the right answer would be y:x. Do you have any idea what I am doing wrong?
gmat-admin's picture

This is a common error.

To help avoid making this mistake, it's useful to jot down the order in which you are presenting your info. Here's what I mean.

Let's say we're told that the ratio of girls to boys is 2 to 3.

Some students will take this information and write 2 : 3 (or 2/3) on their notepad. The problem with this is that it isn't clear what the two numbers represent.

Instead, I suggest that you first write: girls/boys to help you keep track of what each number represents. Then, when you write 2/3, you will be less likely to mix up the values.

You'll see that I do this throughout the videos.

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
. Please help can't figure out .
gmat-admin's picture

There are some nice approaches to that question here: http://www.beatthegmat.com/ratio-shorter-method-t114168.html and here https://gmatclub.com/forum/in-a-certain-district-the-ratio-of-the-number...

Let me know if you'd like me to solve as well.

I solved this problem and I figured out 400. What I'm doing wrong??
Let X = Registered Republicans
Let Y = Registered Democrats

X=(3/5)Y equation (1)

After Additional:
(X+600)/(Y+500)=4/5 Using (a/b)=(c/d) -> ad=bc
5X+3,000=4Y+2,000 equation (2)

Replacing equation (1) in equation (2)
Solving: Y=1,000
Putting Y in the equation (1): X = (3/5)*1,000


Help me to find what I'm doing wrong.


gmat-admin's picture

Everything is perfect . . . . . except we're not done yet.

You determined that X = 1000 and Y = 600.

However, X = Registered Republicans ORIGINALLY, and Y = Registered Democrats ORIGINALLY.

The question asks, "AFTER these registrations, there were how many more voters in the district registered as Democrats than as Republicans?"

So, AFTER the registrations...
X + 500 = number of Democrats, and...
Y + 600 = number of Republicans

So, AFTER the registrations...
1000 + 500 = 1500 = number of Democrats, and...
600 + 600 = 1200 = number of Republicans

So, there are 300 more Democrats than Republicans

Wow, I forgot to sum after the registrations!

Thank you.

Add a comment

Tweet about our course!

If you're enjoying our video course, help spread the word on Twitter.

Have a question about this video?

Post your question in the Comment section below, and we’ll answer it as fast as humanly possible.

Change Playback Speed

To watch our videos at faster speeds (e.g., 20% or 50% faster), download this free extension for your Chrome web browser.