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.

Hey, thanks for all the awesome videos. I was wondering something though, at 01:20 it's said that ratio can be written in 3 ways. The two first ways of writing it makes sense, but the last one confuses me a little. When reading 2 divided on 5 (2 over 5) somehow that seems wrong to me. If I read it that way then I read it as 2 out of 5 being boys, and the remaining (3 out of 5) being girls. Instead of reading it as there being 2 boys for every 5 girls. Any simple explanation to keep me from getting it mixed up or for it to make sense to me?
gmat-admin's picture

Here's another way to look at the a/b notation.

Rather than say the ratio a/b represents "a out of b", we can say "For every b things there are a things"

For for example, if 2/3 of the students are girls, we can say "For every 3 students, 2 are girls"

In this case, the ratio of girls to total students is 2:3 (or 2/3)

Does that help?

Cheers,
Brent

For the reptiles and birds question, after you get 7/2 = R/28, you cannot cross simply 7 and 28 to get 1/2 = R/4 correct? I tried doing that and got 2 just to test this. I knew this was incorrect, but that makes me curious about cross multiplying and when it was okay to use that technique.
gmat-admin's picture

Good question.

Cross simplifying only works when we are multiplying fractions.

However, cross MULTIPLYING is something completely different.

If 7/2 = R/28, then we can solve for R by first cross multiplying to get: (2)(R) = (7)(28), and then solving this equation for R

Cheers,
Brent

Also for the cookies and nuts questions, I looked over the work you did to see if I could come up with a quicker way. I noticed, for example, in the cookie question, adding 2:1 to get 3, you can then divide 3 into 15 (the total amount of cookies) to get 5, which are the amount of cookies in each bag, then just multiply the corresponding number in the ratio to the person receiving the cookie by that 5, in this case, 10 for Kendra (2 times 5) and 5 for Patty (1 times 5). I tried this approach for the nuts questions and got the same result and found it quicker than drawing bags out.
gmat-admin's picture

Your approach is perfectly valid.

I start by drawing bags/buckets of values to show why the technique works. I imagine many students, once they're familiar with the related concepts, gradually transition away from drawing bags.

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