# Lesson: Combining Ratios

## Comment on Combining Ratios

### I used Strategy 1 to apply to

I used Strategy 1 to apply to the "GRE practice question (difficulty level: 160 to 170) - Magoosh" provided above, and I ended up with 9w:16y, which is the different than the solution explained in the video. Can you please confirm whether or not I got the wrong answer? Thank you.

The question requires us to determine the ratio w:y, or written another way, we want the ratio w/y.

I'm not sure how you got 9w:16y, since the ratio w/y shouldn't include the variables w and y.

Did you mean to say that you got the EQUATION 9w = 16y?

If so, then you're on the right track. In the Magoosh video, they also get the EQUATION 9w = 16y

From there we can divide both sides by y to get: 9w/y = 16

Then divide both sides by 9 to get: w/y = 16/9

We get..
QUANTITY A: 16/9
QUANTITY B: 1

### I too was confused. I

I too was confused. I confused 9w=12x=16y as 9w:12x:16y: 9/16 but its really 16/9

### Yes, I got the equation 9w

Yes, I got the equation 9w=16y, and I was mistaken when I thought that meant w/y = 9/16. Thanks for the quick clarification.

### Dear Brent,

Dear Brent,

does 13 count as a multiple of 26?

http://greprepclub.com/forum/a-jar-contains-marbles-of-3-colors-2545.html

To answer your question: No, 13 is not a multiple of 26

Multiples of 26 are in the form 26k, where k is an INTEGER

So, the multiples of 26 are as follows: {. . ., -78, -52, -26, 0, 26, 52, 78, 104, . . . }

### Can’t I have all the

Can’t I have all the reinforcement questions in one pdf or page, unit wise ?

### Hi Minisha,

Hi Minisha,

Sorry, but I don't have a consolidated list like that.
However, you can use GRE Prep Club's question filter (https://greprepclub.com/forum/viewforumtags.php) to filter out questions on a particular topic (Geometry, Statistics, etc).

I hope that helps.

Cheers,
Brent

### I have a couple of questions

I have a couple of questions I would like to get insight on.

1. Four different company boards consist of 7, 10 , 11, and 15 members respectively. If x is the total number of people of the 4 boards combined what is the least possible value of x?

2. A man has 28 pieces of fruit in a bag, with equal numbers of oranges, bananas, apples, and kiwi. What is the minimum number of fruit the man can pull out to ensure that he has at least 3 pieces of each fruit?

### Hi Terah.

Hi Terah.
I'm happy to help.

Question #1.
We can minimize the value of x by placing several people on MORE THAN 1 board each.

Given: 7 people on board A, 10 people on board B, 11 people on board C, and 15 people on board D.

Place 7 of these board D members on board A.
Now place 10 of the board D members on board B.
And place 11 of the board D members on board C.

So, we still have 15 people. All of these 15 people are on board D
Some of these 15 people are on boards A.
Some are on board B, and some are on board C.

Question #2:
Start by examining the MOST pieces of fruit we can have WITHOUT meeting the condition that we have at least 3 pieces of EACH fruit?
Well, we could have 7 oranges, 7 bananas, 7 apples, and 2 kiwi
7 + 7 + 7 + 2 = 23
It's possible to choose 23 pieces of fruit and NOT have at least 3 pieces of EACH fruit.
However, once we choose our 24th piece of fruit, it will definitely be a kiwi (since we already chose all of the other fruit)

So, to ENSURE that we have at least 3 pieces of EACH fruit, we must pull out 24 pieces of fruit.

Cheers,
Brent

Thank you

### When you take members from

When you take members from Board D are you creating the 7, 10 , and 11 members of Board A-C or are you adding 7, 10, and 11 to the already present members?

### Yes, that's exactly what I'm

Yes, that's exactly what I'm doing.

Given: 7 people on board A, 10 people on board B, 11 people on board C, and 15 people on board D.

So, for example, if the 15 members of Board D are names 1, 2, 3, 4, 5, ...., 13, 14 and 15, then we can list all of the boards each person is on:
Person #1: D, A, B, C
Person #2: D, A, B, C
Person #3: D, A, B, C
Person #4: D, A, B, C
Person #5: D, A, B, C
Person #6: D, A, B, C
Person #7: D, A, B, C
Person #8: D, B, C
Person #9: D, B, C
Person #10: D, B, C
Person #11: D, C
Person #12: D
Person #13: D
Person #14: D
Person #15: D

We can see that we've addressed all board members.
So, we can meet all of the criteria with as little as 15 people.

Cheers,
Brent

### Hey Brent!

Hey Brent!

Why is the answer not D? Since we aren't given exact numbers and only the ratios? I remember few questions in the last module having D as the answer due to this reason.

I think you might be confusing two different question types.

If we're only given only a ratio, then there's no way to determine actual values.
For example, if we're told that the ratio of cats to dogs is 2:1, there's no way to determine the NUMBER of cats or the NUMBER of dogs.

However, if we're told that the ratio of cats to dogs is 2:1, we know that there are twice as many cats as dogs.
This means we can definitely conclude that there are more cats than dogs.

Does that help?

### Hello Brent,

Hello Brent,

I was looking at our recorded sessions and there was a ratio question in regards to the numbers of total fans ( hockey vs. football) if you recall. In that problem apart from the multiplier way what else is another method we can use to solve that problem. Also I wanted to know in what ratio questions do we use the multiplier rule? Because I came across this question in Magoosh and wanted to know why the multiplier idea did not work here: The ratio of two positive numbers is 3 to 4. If k is added to each number the new ratio will be 4 to 5, and the sum of the numbers will be 117. What is the value of k? Please let me know your thoughts. Thanks!

### Hi Ravin,

Hi Ravin,

I believe this is the hockey/football question you're referring to: https://www.greenlighttestprep.com/module/gre-word-problems/video/908

For both questions we can use either approach.

Here's a solution to the Magoosh question that doesn't use the multiplier rule: https://gmatclub.com/forum/the-ratio-of-two-positive-numbers-is-3-to-4-i...

Likewise, we can solve the above hockey/football question by using the multiplier rule (let 2x = # of hockey fans and 3x = # of football fans)