Lesson: Combining Ratios

Comment on Combining Ratios

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.
greenlight-admin's picture

Question link: https://www.youtube.com/watch?v=3OklAxqfSF0

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..

Answer: A

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

Dear Brent,

does 13 count as a multiple of 26?

greenlight-admin's picture

Question link: http://gre.myprepclub.com/forum/a-jar-contains-marbles-of-3-colors-2545....

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 reinforcement questions in one pdf or page, unit wise ?
greenlight-admin's picture

Hi Minisha,

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

I hope that helps.


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?
greenlight-admin's picture

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.

Let's start with the 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.
Answer: 15

Question #2:
Start with 7 oranges, 7 bananas, 7 apples, and 7 kiwi
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.


Thank you

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?
greenlight-admin's picture

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.


Hey Brent!

I had a question on this: https://gre.myprepclub.com/forum/in-a-fruit-basket-containing-apples-pears-and-oranges-the-15743.html

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.
greenlight-admin's picture

Question link: https://gre.myprepclub.com/forum/in-a-fruit-basket-containing-apples-pea...

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,

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!
greenlight-admin's picture

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)

Hey Brent


The above question and below are similar


however the answer to above one is A and Below one IS D.....i do belive Above one should be D as well as the amount not told so we cant calculate the actucal number
greenlight-admin's picture

Question link 1: https://gre.myprepclub.com/forum/in-a-fruit-basket-containing-apples-pea...
Question link 2: https://www.youtube.com/watch?v=a-FvKXqLD5k

The questions aren't very similar.
Question 1 involves a three-part ratio, while question 2 involves two separate ratios from two separate populations.

For question 1, you are correct to say that we can't calculate the actual numbers.
However, that doesn't matter, since one quantity will always be greater than the other.

Here's what I mean:
We learn that the ratio Apples : Pears : Oranges = 15 : 20 : 12
There are infinitely many equivalent ratios.
For example, there could be 15 Apples, 20 Pears, and 12 Oranges.
OR there could be 30 Apples, 40 Pears, and 24 Oranges.
OR there could be 45 Apples, 60 Pears, and 36 Oranges.
OR there could be 60 Apples, 80 Pears, and 48 Oranges.

In ALL of these cases, the ratio is 15 : 20 : 12 each time.
However, the question doesn't require us to determine the actual numbers of each piece of fruit.

Instead, the two quantities are:
QUANTITY A: The number of apples in the fruit basket
QUANTITY B: The number of orange in the fruit basket

For every possible case (listed above), the number of apples is ALWAYS greater than the number of oranges.
So, the answer will be A.

The second question (the video question on YouTube) isn't dealing with a 3-part ratio.

Does that help?

Study Guide

The step-by-step Study Guide will help direct your studies and ensure that you cover everything that the GRE tests.

Let me Know

Have a suggestion to make the course even better? Email us today!

Free “Question of the Day” emails!