Lesson: Introduction to Ratios

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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??
Solution:
Let X = Registered Republicans
Let Y = Registered Democrats

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

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

Replacing equation (1) in equation (2)
5[(3/5)Y]+3,000=4Y+2,000
3Y+3,000=4Y+2,000
Solving: Y=1,000
Putting Y in the equation (1): X = (3/5)*1,000
X=600

Y-X=1,000-600
Y-X=400

Help me to find what I'm doing wrong.

Thanks,
Pedro

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.

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