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## Comment on

Introduction to Ratios## Awesome thanks for the lesson

## Ratios are important, but I

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

## This is a common error.

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

(A) 100

(B) 300

(C) 400

(D) 1,000

(E) 2,500

. Please help can't figure out .

## There are some nice

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

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

## Everything is perfect . . . .

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

Thank you.

## Hey, thanks for all the

## Here's another way to look at

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

## Good question.

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

## Your approach is perfectly

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.

## Hi Brent, can you please

Yesterday, the ratio of males to females working at Gigacorp was 2:3. Today, Gigacorp hired an additional 81 employees, and the ratio of males to females is now 6:5 (no employees left or were fired). What is the least number of males that could have been working at Gigacorp yesterday?

A) 16

B) 24

C) 39

D) 40

E) 42

## Hi Jalal,

Hi Jalal,

Here's my step-by-step solution: https://gmatclub.com/forum/yesterday-the-ratio-of-males-to-females-worki...

Cheers,

Brent

## Hi Brent, I have a question

In a certain physics class, the ratio of the number of physics

majors to non-physics majors is 3 to 5. If two of the physics

majors were to change their major to biology, the ratio would

be 1 to 2. How many physics majors are in the class?

(A) 16

(B) 18

(C) 24

(D) 30

(E) 32

If I use the same approach of the others questions the answer I get that the answer is 16. A). Since:

(3x-2)/(5x+2) =1/2

x=6.

3*(6)-2= 16. They are asking how many physics majors ARE in the cl...OH.. I just realize the question is asking about actual physics and not physics in a theorical scenario.

Thank you anyway.

Cheers, Alex

## Nice catch!

Nice catch! You're certainly not the first person to confuse the hypothetical information with the given information :-)

## Hi Brent,

Regarding the portioning of ratios part, what should we do when we are unable to divide the quantity in equal parts?

For instance, in the nuts mix question, what if we had to find the proportion of walnuts in 47 pounds of nut mix?

## Great question!

Great question!

In general we can say:

If the terms of the ratio add to x, then the number of "things" to be distributed in that ratio must be divisible by x (otherwise the distribution is impossible).

Consider this example:

Someone wants to distribute cookies to Joe and Sue in a 1 : 2 ratio, in which Joe receives 1 cookie for every 2 cookies that Sue receives.

1 + 2 = 3

So, for every 3 cookies to be distributed, Joe receives 1 cookie and Sue receives 2 cookies.

For example, if there are 15 cookies in total, then Joe receives 5 cookies and Sue receives 10 cookies. Notice that our distribution works perfectly, since 15 is divisible by 3.

Conversely, if there are 4 cookies in total, it's impossible to distribute those 4 cookies in the 1 : 2 ratio. Notice that our distribution doesn't work in this case because 4 is NOT divisible by 3.

Does that help?

Cheers, Brent

## yes it does. Thank you.

## Hi Brent,

For the following question - https://gmatclub.com/forum/oil-vinegar-and-water-are-mixed-in-a-3-to-2-to-1-ratio-to-make-salad-273726.html

We have been asked the maximum number of cups of salad dressing he can make. If 6x makes ONE cup of salad dressing and x is 8/3 --> shouldn't we be able to make (1*8/3) cups of salad dressing?

I may be misinterpreting what the question is asking. Please help.

## Question link: https:/

Question link: https://gmatclub.com/forum/oil-vinegar-and-water-are-mixed-in-a-3-to-2-t...

The question: Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad dressing. If Larry has 8 cups of oil, 7 cups of vinegar, and access to any amount of water, what is the maximum number of cups of salad dressing he can make with the ingredients he has available, if fractional cup measurements are possible?

Given the notation in your question, I assume you're referring to Scott's solution (at https://gmatclub.com/forum/oil-vinegar-and-water-are-mixed-in-a-3-to-2-t...)

In his solution, Scott let's x = cups of water, 2x = cups of vinegar and 3x = cups of oil

So, x + 2x + 3x = 6x

So, 6x = the total CUPS of dressing.

So, if x = 8/3, then we're combining:

- 8/3 cups of water

- 16/3 cups of vinegar

- 24/3 cups of oil

For a total of 16 cups of dressing.

Does that help?

## I think I messed up in

## Hi Brent, thanks for previous

The ratio of cups of flour to cups of milk in a cake is 3:2. 6 cups of milk are added to the cake, and the new ratio is 3:4, how many cups of flour are there in the cake?

A) 6

B) 8

C) 9

D) 10

E) 12

## Let F = the number of cups of

Let F = the number of cups of flour in the mixture

Let M = the number of cups of milk in the mixture

So we can write: F/M = 3/2

Cross multiply to get: 2F = 3M

After we add 6 cups of milk...

F = the number of cups of flour in the mixture

M + 6 = the number of cups of milk in the mixture

So we can write: F/(M + 6) = 3/4

Cross multiply to get: 4F = 3(M + 6)

Expand: 4F = 3M + 18

We now have the following system of equations:

2F = 3M

4F = 3M + 18

Solve to get: F = 9

Answer: C

## https://gmatclub.com/forum

I think there are some ambiguity here because someone could understand it as "the original values add up to 117?

## Given: IF k is added to each

Given: IF k is added to each number the new ratio will be 4 to 5, and the sum of the numbers will be 117

The key words/phrases here are IF and WILL BE.

These words set up a hypothetical situation.

So, the sum of 117 refers to a hypothetical situation if it were true that k was added to each number.

While it's possible someone may misread the question, the words themselves are not ambiguous.