# Lesson: Double Matrix Method

## Comment on Double Matrix Method

### Thank you for this

Thank you for this straightforward method, it's really helpful.﻿

### Thanks for taking the time to

Thanks for taking the time to say that!

### Hi Brent!, Thanks for this

Hi Brent!, Thanks for this awesome approach.
i am confused in the below question

http://gre.myprepclub.com/forum/qotd-11-of-the-students-in-a-school-20-percent-are-in-the-2660.html
and
http://gre.myprepclub.com/forum/if-75-percent-of-the-employees-of-a-certain-company-take-a-w-2701.html

in first question, it ask for what percent of the students who are in the science club are not in the band?

i answered 15per, but in your explanation you have given 75 per. 15per is not even choices.

in second question, it ask for what percent of the employees take a summer vacation but not a winter vacation?

though i was thinking 5 per, i answered as (5/45) * 100, as i had gone through in last question's answer explanation.

what am i doing wrong?, what is the style difference between those question?

### For the first question (http:

For the first question (http://gre.myprepclub.com/forum/qotd-11-of-the-students-in-a-school-20-p...), you are answering a different question. You are answering a question that asks "What percent of the ENTIRE school population is in the science club but not in the band?"

The actual question asks "What percent of the SCIENCE CLUB STUDENTS are not in the band?"

There are 20 students in the science club. Of those 20 students, 15 are NOT in the band.

15/20 = 3/4 = 75%

In the second question (http://gre.myprepclub.com/forum/if-75-percent-of-the-employees-of-a-cert...), you answered a different question as well.

You answered the question "What percent of THE SUMMER VACATIONERS do not take a winter vacation?"

The actual question asks "What percent of ALL EMPLOYEES take a summer vacation but do not take a winter vacation?"

I can see how the first question could have thrown you off. It's a very common mistake. The difference is wording is quite subtle and easy to miss.

### Nice and clear method! Thanks

Nice and clear method! Thanks.

### Hi Brent, thanks for share

Hi Brent, thanks for share with us this great method. This method only works for problems that have Overlapping sets. For example can be used for the following problems ?http://gre.myprepclub.com/forum/set-a-consists-of-40-integers-1893.html and
Thanks so much.

### Hi Brent!

Hi Brent!

I have come across the below question in ETS quant guide

Set A has 50 members and set B has 53 members. At least 2 of the members in set A are not in set B. Which of the following could be the number of members in set B that are not in set A?

indicate all such numbers

a)3 b)5 c)13 d)25 e)50 f)53

my approach:
min number of members from A can be in B are : 2
max number of members from A can be in B are : 48

with min value 5 number of members of B who are not in A.
with max value 51 number of members of B who are not in A.

so answers would be B C D E

but in official guide F is also in answer, can you please explain.

### Hi yogasuhas,

Hi yogasuhas,

I have responded to this question here: http://gre.myprepclub.com/forum/set-a-has-50-members-and-set-b-has-53-me...

### Hello Brent,

Hello Brent,
In the following question, I confuse in understanding the statement ' the number of people who graduated from college in 1997 who did not both receive a degree in the applied sciences and graduate from a school in one of six northeastern states?'

I thought that we need to find the value of last square (Not AS & Not NES). However, we need to find the value of the three blue shaded squares.

Could you please once explain that statement for a better understanding ?

Thanks :-)

Let's say that, when you left for work, there WERE two pieces of pie in the fridge. When you came home, you found that both pieces are missing.

If ask your friend "Did you eat BOTH pieces of pie?" and he/she says, "No, I did NOT eat BOTH pieces of pie," what can you conclude from this answer?

Does it mean your friend did not eat ANY pie?

No. All you can conclude is that your friend did not eat BOTH pieces. However, if your friend ate ONE piece of pie, then he/she would be telling the truth when replying "No, I did NOT eat both pieces of pie."

So, when your friend says "I did NOT eat both pieces of pie," this means EITHER your friend ate zero pieces of pie OR your friend at one piece of pie.

The question asks us to determine "the number of people who did NOT BOTH receive a degree in applied sciences AND graduate from a school in one of six northeastern states"

This includes:
- the students who received a degree in applied sciences but did NOT attend a school in one of six northeastern states"
- the students who did NOT receive a degree in applied sciences but DID attend a school in one of six northeastern states"
- the students who did NOT receive a degree in applied sciences and did NOT attend a school in one of six northeastern states"

Does that help?

### pls solve the question in 3rd

pls solve the question in 3rd edition official gre guide 161(5)...i know its double matrix method

### hey brent Im having trouble

hey brent Im having trouble assigning names to the box hence the entire concept gets lost on me. help!

### To apply the Double Matrix

To apply the Double Matrix Method, we must identify that a certain population is such that each member has two characteristics associated with it.

So, for example, we may have a population of baseball players, and the two characteristics are:
- left-handed or right-handed
- speaks Spanish or does not speak Spanish

It may take time to identify (and label) the two characteristics.
I suggest that you carefully go through each of the linked questions above and try to identify the two characteristics.
Then review the responses of others.
This is the only way to master this technique.

Cheers,
Brent

### In a group of 100 homeowners,

In a group of 100 homeowners, x homeowners had an alarm security system and y homeowners had deadbolt locks. If z homeowners had neither an alarm security system nor deadbolt locks, how many homeowners had both an alarm security system and deadbolt locks?

### In a given finance lecture,

In a given finance lecture, 30% of the students are finance majors, and 40% of the students are female. The gender distribution for finance majors and non-finance majors is the same. What percent of the students are neither female nor a finance major?

A. 70%
B. 60%
C. 58%
D. 42%
E. 30%

I am a little confuse for this one would you plz clarify it for me? whereas we have 30%, not 30 students?

30% of the students are finance majors
So, 30 students are finance majors and 70 are not.

How we reach sum (70 ), not in finance?

Since the question asks us to find a certain PERCENT (and not actual numbers), can make things easy on ourselves and say that there is a TOTAL of 100 students in the lecture.

So if 30% of the students are Finance majors, the number of Finance majors = 30% of 100 = 30
This means that, 30 of the 100 students are Finance majors, the remaining 70 students are NOT Finance majors.

Does that help?

### Excellent method, although a

Excellent method, although a 3 x 3 grid would be much better so that you can accommodate the sums.

### I understand how the matrix

I understand how the matrix works but I am having hard time figuring out the columns. Is there any solution to that?

### We need to identify the TWO

We need to identify the TWO CHARACTERISTICS associated with the given population.
For example, we might have a population of students, and the two characteristics are:
- took French or did not take French
- took Geography or did not take Geography

To help you get better at this technique, you could start by going through all of the linked questions above and trying to identify the 2 characteristics.
Then check my solution to see whether you correctly identified the characteristics.

Once you've practiced identifying the characteristics, you can go back and answer each question.

Cheers,
Brent

### https://gre.myprepclub.com/forum

https://gre.myprepclub.com/forum/of-the-84-parents-who-attended-a-meeting-at-a-school-35-vol-18724.html

In this problem, how did you come up with 54 for the number of parents that were not supervising? I keep looking at it and since 84-35=49 I put 49 in that column.

### Good catch!!

Good catch!!
Fortunately that number doesn't affect the correct answer choice. Nevertheless, I have edited my response here: https://gre.myprepclub.com/forum/of-the-84-parents-who-attended-a-meetin...

### A marketing firm determined

A marketing firm determined that, of 200 households
surveyed, 80 used neither Brand A nor Brand B soap,
60 used only Brand A soap, and for every household
that used both brands of soap, 3 used only Brand B
soap. How many of the 200 households surveyed used
both brands of soap?

So for this question I made the matrix as follows
A ~A T
B x 60 3x
~B 80
T 60 140 200

Why is this wrong it seems to do with the word phrase only? not really sure. I am definitly stumped on this question. Please help me find my mistake. Thanks

Your mistake occurred when you translated "...for every household that used both brands of soap, 3 used ONLY Brand B soap"
The people who used only Brand B soap are people who used soap B and did NOT use soap A
So, the 3x should go in the top right corner of the matrix, where as you have as the total number of people who use soap B.
That is, the total number of people who use soap B includes people who use both soaps and people who use soap B but not soap A.

Does that help?

Here's my full solution: https://gre.myprepclub.com/forum/a-marketing-firm-determined-that-of-200...

### ok i got it. It seems to me

ok i got it. It seems to me the focus was on the word only. So words like that mean for ex ONLY A would mean A but not B right?

That's correct.

### Hey Brent can u tell me how

Hey Brent can u tell me how to solve this?

On a final exam, 75 percent of a class had scores that were greater than 70, and 60 percent of the class had scores that were less than 85. What percent of the class had scores that were greater than 70 but less than 85 ?

what i knw is there is an overlappting sets formula = a + b - both +neither? but i want to see your appraoch please!

### Here's how I would handle the

Here's how I would handle the question:

Let's first say there are 100 students in the class.

Given: 75% of the scores were greater than 70.
So, 75 scores are greater than 70.

Given: 60% of the scores were less than 85
This means 40% of the scores were greater than or equal to 85.
So, 40 scores are greater than or equal to 85.

Of the 75 scores that are greater than 70, we know that 40 of them are greater than or equal to 85.
This means the remaining 35 scores must be less than 85.

In other words, 35 scores will be greater than 70 but less than 85.