GMAT Ninja Quant Ep 13: Overlapping Sets

Summary

Charles from GMAT Ninja delivers an in-depth guide on overlapping sets, a minor GMAT quant topic, in episode 16 of his series. He introduces a double set matrix for efficient problem-solving, presents nine example questions with varying difficulties, and offers shortcuts for complex language in questions. The video is tailored for different skill levels, focusing on maximizing scores and minimizing study time on this 3% represented topic.

Takeaways

• 📚 Charles from GMAT Ninja introduces Episode 16, focusing on Overlapping Sets and Venn Diagrams, a minor topic in GMAT Quant.
• 🔢 The video covers nine example questions, including two and three overlapping sets, and provides a shortcut for solving them efficiently.
• 💡 A double set matrix is recommended over Venn diagrams for clarity and simplicity when dealing with complex overlapping sets.
• 👨‍🏫 The video is ideal for those new to GMAT, looking to improve efficiency in overlapping sets, or needing help with complex language in questions.
• 📉 Overlapping sets account for only about 3% of GMAT Quant questions, so Charles advises not to over-study this topic unless aiming for a very high score.
• 🧩 The script uses a step-by-step approach to solve problems, emphasizing the importance of understanding the question before attempting to answer.
• 🗣️ Language nuances are highlighted as crucial, especially when the question asks for percentages of different groupings within the sets.
• 📝 Data sufficiency in overlapping sets is addressed, with tips on how to avoid unnecessary re-drawing of diagrams and focus on the given information.
• 🤔 The video addresses the complexity of certain questions, suggesting that not all students need to master the most difficult variants unless aiming for a top score.
• 📈 Emphasis is placed on the importance of reading questions carefully, especially in the context of GMAT's overlapping sets, where subtle changes in language can alter the answer.
• 🏆 The final message is that while the video challenges viewers with complex examples, it is not necessary for all test takers to master these for a satisfactory GMAT Quant score.

Q & A

What is the main topic of episode 16 in GMAT Ninja's comprehensive quant series?

The main topic of episode 16 is overlapping sets, also known as Venn diagrams, which are a minor topic in the GMAT quant section.

What percentage of GMAT quant questions typically involve overlapping sets?

Approximately three percent of GMAT quant questions are expected to involve overlapping sets.

What is a recommended method for organizing information in overlapping sets problems according to Charles from GMAT Ninja?

Charles recommends using a double set matrix instead of a Venn diagram for organizing information in overlapping sets problems due to its simplicity and effectiveness.

What is a common mistake made by test takers when dealing with overlapping sets questions on the GMAT?

A common mistake is not reading the questions carefully, especially the denominators, which can lead to incorrect answers.

How many example questions are covered in episode 16 to illustrate the overlapping sets concept?

Nine example questions are covered in the video to illustrate the overlapping sets concept, including those with two and three overlapping sets.

What is a 'word soup' in the context of GMAT questions?

In the context of GMAT questions, 'word soup' refers to the complex and confusing language used in the questions that can make it difficult for test takers to understand what is being asked.

What is a data sufficiency question in the GMAT quant section?

A data sufficiency question is a type of question that requires test takers to determine whether the given statements provide enough information to answer a specific question, often involving overlapping sets or other quantitative concepts.

What is a shortcut mentioned in the video for handling data efficiency questions in overlapping sets?

The shortcut mentioned for handling data efficiency questions is to invest time in the question stem first and avoid jumping into the answer choices too quickly, which can save time and prevent mistakes.

What is the focus of the latter half of the video if the viewer's goal is to achieve a high score on the GMAT quant section?

The focus of the latter half of the video is to provide comprehensive coverage of overlapping sets with more complex language and variations, including every possible wrinkle and language tweak seen on the GMAT.

What advice is given for students aiming for a high score on the GMAT quant section regarding the study of overlapping sets?

For students aiming for a high score, the advice is to stick with the video through the entire presentation, learn to handle complex language, and understand all the little language tweaks made on the GMAT for overlapping sets.

What is the importance of understanding the language in GMAT quant questions, especially in overlapping sets?

Understanding the language in GMAT quant questions is crucial because the way questions are phrased can significantly affect the approach to solving them. Misinterpreting the language can lead to incorrect assumptions and answers.

Outlines

00:00

📚 Introduction to Overlapping Sets in GMAT Quant Series

Charles from GMAT Ninja introduces Episode 16, focusing on overlapping sets, also known as Venn diagrams, in the GMAT quant series. He mentions that the first 15 videos covered core topics like algebra and geometry, while the last four will delve into minor topics, including overlapping sets, which appear in about 3% of GMAT quant questions. Charles promises to cover nine example questions, a shortcut for solving them, and to address the complexity of the language used in these questions. The video is aimed at beginners as well as those seeking to improve efficiency and understanding of 'word soup' in GMAT questions.

05:01

📈 Avoiding Venn Diagrams for Overlapping Sets

Charles advises against using Venn diagrams for overlapping sets due to potential confusion with labels and placement as the language becomes more complex. Instead, he recommends using a double set matrix, which is a simple way to organize information. The paragraph walks through a basic example involving people eating videniki and drinking nimarov, demonstrating how to use the matrix to find percentages and solve the problem efficiently.

10:01

🤔 The Importance of Reading Questions Carefully

This paragraph emphasizes the importance of reading GMAT questions carefully, especially those involving overlapping sets, to avoid common mistakes. Charles illustrates this with an example about rugby players and tooth retention, showing how a subtle change in the question's denominator can lead to a different answer. He stresses the need to read the question twice and understand what is being asked before attempting to solve it.

15:03

🔢 Solving Three-Way Overlapping Sets Without Venn Diagrams

Charles presents a method for solving three-way overlapping sets without using Venn diagrams, which can become complicated. The approach involves understanding the fundamental issue of overcounting and using a matrix to organize the counts of people visiting different countries. The paragraph includes a detailed example with a matrix setup and a step-by-step guide to finding the number of people visiting exactly two countries.

20:03

🕵️‍♂️ Tips for Tackling Data Sufficiency in Overlapping Sets

The paragraph discusses strategies for answering data sufficiency questions related to overlapping sets. Charles warns against jumping into the answer choices too quickly and suggests investing time in understanding the question first. He also provides a tip for efficiency, recommending that information from each statement be placed in a corner of the matrix to avoid redrawing it multiple times.

25:41

🧩 Navigating Complex Language in Overlapping Sets

Charles acknowledges the complexity of language in GMAT overlapping sets questions and the need to be literal and methodical in interpreting it. The paragraph includes an intricate example involving shipments and salmonella, where the challenge lies in understanding the relationships between different categories of shipments and calculating the percentage of rejected shipments that are not tainted.

30:41

🎯 Minimizing and Maximizing Probabilities in Overlapping Sets

This paragraph introduces a variant of overlapping sets that involves probabilities and the concept of minimization and maximization. Charles explains how to find the least possible probability that both events occur by maximizing the probability of one event not occurring and vice versa. The example provided demonstrates how to think through the problem and arrive at the correct answer.

35:42

🗳️ Advanced Overlapping Sets with Approval Ratings

Charles presents an advanced overlapping sets scenario involving approval ratings for different policies. The paragraph focuses on interpreting the language to understand the difference between 'did not say they approve' and 'disapprove'. It includes a step-by-step breakdown using a double set matrix to find the number of voters who approve of one policy but not the other, highlighting the importance of clear thinking in complex scenarios.

40:42

🏖️ Ranking Vacations: A Complex Overlapping Sets Challenge

The paragraph discusses a complex overlapping sets question involving the ranking of beach, ski, and city vacations. Charles explains how to approach the question by considering the overlap of people ranking vacations ahead of beach holidays. The example illustrates the use of percentages and basic algebra to find the number of people who ranked beach vacations last.

45:42

🍔 Overlapping Sets in Business Context: Fast Food Restaurant Introductions

In the final paragraph, Charles presents a business-related overlapping sets problem involving the introduction of menu items at fast food restaurant locations. The challenge is to determine the maximum and minimum number of locations that could have introduced all three items. The solution involves a thoughtful approach to maximizing and minimizing the overlap and a clear understanding of how the items are allocated across locations.

Keywords

💡Overlapping Sets

Overlapping sets refer to a mathematical concept where two or more sets share common elements. In the context of the video, overlapping sets are used to solve problems involving Venn diagrams, which are a way to visually represent the relationships between sets. The script discusses how to approach questions on the GMAT that involve overlapping sets, including using matrices to organize information.

💡Venn Diagrams

Venn Diagrams are a type of diagram that shows all possible logical relations between different sets. In the script, Venn diagrams are mentioned as a tool for visualizing overlapping sets, although the speaker recommends using a double set matrix for clarity and simplicity when solving GMAT problems.

💡Double Set Matrix

A double set matrix is a method for organizing data related to overlapping sets without the potential confusion of a Venn diagram. The script describes this as a preferred approach for solving GMAT quant questions because it helps to systematically account for all elements and avoid the complexities that arise with increasing numbers of sets.

💡Data Sufficiency

Data sufficiency is a concept in GMAT problem-solving where the examinee must determine if the given information is enough to answer a question definitively. The script mentions data sufficiency in the context of overlapping sets, advising viewers on how to use the information provided in the questions efficiently.

💡Quantitative Reasoning

Quantitative reasoning, often shortened to 'quant', refers to the skills involved in understanding and solving mathematical problems. The video is part of a series focusing on the quant section of the GMAT, and the script provides strategies for tackling specific types of quant questions involving overlapping sets.

💡Word Soup

In the context of the video, 'word soup' refers to the complexity and confusion that can arise from the language used in GMAT questions, particularly those involving overlapping sets. The script emphasizes the importance of carefully interpreting the language in questions to avoid common pitfalls and errors.

💡Efficiency

Efficiency, in this script, relates to the speed and accuracy with which one can solve GMAT quant questions. The video aims to help viewers become more efficient in their approach to overlapping sets problems, offering shortcuts and strategies to streamline the problem-solving process.

💡Language Tweaks

Language tweaks are the subtle changes in wording that can significantly alter the meaning or interpretation of a question. The script warns about these tweaks in GMAT questions, especially in the context of overlapping sets, and advises viewers on how to correctly interpret and respond to them.

💡Probability

Probability is the measure of the likelihood that an event will occur. While not the main focus of the video, probability is mentioned in the context of overlapping sets, particularly when discussing events that may or may not happen and how to calculate the least or most possible overlap.

💡Minimize and Maximize

Minimize and maximize are terms used in the script to describe the process of finding the least or most possible values in a set of conditions. The video includes problems that require the viewer to think about how to minimize or maximize overlaps in sets, which is a common theme in GMAT quant questions.

💡GMAT

The GMAT, or Graduate Management Admission Test, is a standardized exam used for admission to graduate management programs. The script is from a tutorial video aimed at helping students prepare for the quant section of the GMAT, focusing on the specific topic of overlapping sets.

Highlights

Charles from GMAT Ninja introduces Episode 16 on overlapping sets, also known as Venn diagrams, in the GMAT quant series.

Overlapping sets make up about 3% of GMAT quant questions, and the video covers nine example questions with varying difficulty.

A shortcut for solving overlapping sets is introduced, along with strategies for dealing with complex language in questions.

The video is structured to cater to different skill levels, with the first four questions covering basics for beginners and the last five tackling more complex scenarios.

A double set matrix is recommended over Venn diagrams for organizing information efficiently in overlapping sets problems.

An example question demonstrates the use of a double set matrix to solve a straightforward overlapping sets problem.

The importance of reading questions carefully to avoid common traps, especially regarding the denominator in percentage questions, is emphasized.

A method for solving three-way overlapping sets using a simplified matrix algebra approach is presented.

Data sufficiency in overlapping sets is discussed, with a focus on not jumping into answer choices too quickly and using the information given in the question effectively.

A strategy for handling data sufficiency questions by using a corner of the matrix to note information from each statement is introduced.

The video progresses to more complex language scenarios, including a question involving shipments and the probability of rejection based on contamination.

An example of a maximize/minimize problem in overlapping sets is given, involving the least possible probability that two events both occur.

Complex language in GMAT questions is dissected, with an emphasis on understanding the nuances of what is being asked, especially in probability and overlapping sets.

A challenging question involving voter approval of policies is tackled, demonstrating the application of a double set matrix in non-traditional scenarios.

The final questions of the video present extremely difficult language scenarios, requiring a deep understanding of overlapping sets and careful interpretation of the question's language.

The video concludes with a comprehensive review of overlapping sets, highlighting the importance of language interpretation and strategic problem-solving on the GMAT.

Transcripts

hi everybody charles from gmat ninja

here welcome to episode number 16 in

gmat ninja's comprehensive quant series

today we're going to be talking about

overlapping sets also known as venn

diagrams if you haven't watched any

other videos in the series first 15 in

the series harry and branson smart guys

better looking than me covering all of

the really really core stuff on the gmat

algebra arithmetic word problems

geometry that kind of thing

now these last four videos in the series

i'll be taking you home

now all of these are really minor topics

so about three percent of your questions

are going to be overlapping sets on the

gmat quant so not a ton what we're going

to be covering today go take you through

nine example questions some two

overlapping sets some three overlapping

sets show you a nifty little shortcut

for doing those we'll do a couple data

efficiency questions and i'll show you a

little way to make those a little bit

more efficient more than anything the

big focus here is going to be on that

word soup mathematically there's nothing

in overlapping sets that's going to be

super super difficult it's just a

question of penetrating that question

and seeing what they're really asking

for and making your way through language

that can sound pretty wacky so a lot of

what we're going to be doing especially

in the last half make the language tough

on you and giving you some tools for

dealing with it

now who's who is this video ideal for

now obviously if you're totally new to

overlapping sets just get rolling with

the gmat this is going to be really good

for you especially the first four

questions or so if you find that you're

inefficient maybe you know the basics

you know how to set up a double set

matrix or a venn diagram but you still

find that you're slow with questions

we'll help you with a lot of that stuff

today

and again if you're tormented by that

word soup and sometimes you look at the

questions and go durr i don't know what

this is saying

this video is going to be perfect for

you

um so the way this is going to be

structured four fairly easy questions to

warm you up cover the basics uh if your

goal is something like let's say mid 40s

on quant that's going to be enough for

you don't have to watch the last half of

the video it's going to probably be a

little bit more than you really need now

if your goal is super super ambitious

you want to get something like a 50 or

51 quant stick with us through the whole

video first four questions might be easy

phrase we get to those last five

i'm gonna throw pretty much every

wrinkle i can at you pretty much

anything that we can think of that we've

ever seen on the gmat and we're

combining in our own ways and our own

questions but

we're going to get you pretty

comprehensive coverage of overlapping

sets and all the little language tweaks

that they make on the gmat

um and again canvas has this enough only

about three percent of your questions on

quan are going to come from overlapping

sets so maybe you see one or two if you

get really lucky maybe you'll see three

on your actual exam

so don't over study this guys um you

know if your verbal skills are weak you

have limited study time this probably

isn't the thing you want to fall on your

short over but again if you're going for

that super high score if you just want

to cover the basics fantastic this video

is for you

all right with that give you a couple

minutes on our very first example

all right if you need more time on this

feel free to hit the pause button for

the rest of you let's get rolling

so really straightforward warm up

question this is about as as simple and

straightforward as gmat overlapping sets

questions come

so

seventy percent of the population here

is eating fresh energy forty-five

percent drinking nemerov now some people

set this up as a venn diagram um it's

not the end of the world if that's

working for you that's fine but we don't

typically recommend it and here's why

so as soon as we kind of get into this

funnier stuff so we can say well 70

percent here eats verenicki

but then once we kind of get into the 35

percent do one but not the other where

do i put that exactly do i put that here

and now my labels are just confusing can

you keep it straight sure it's it's

totally possible to keep it straight but

it can get a little bit confusing i

think it gets messy as the language gets

more complicated this tends to get you

in a little bit of trouble so my very

strong preference here is not to use the

venn diagram instead we use what's

called a double set matrix nothing fancy

here at all don't think of this as some

magical method or some magic formula

it's just way of organizing information

that's all it is but sometimes when

you're limited to doing these questions

in two minutes each just organizing your

information can make all the difference

in the world so if you haven't seen this

before here's how it works

we've got two kinds of people in the

world or at least in this restaurant

we've got people who eat vegetable

people who do not

and the total number of those people in

this case will have to up to 100 percent

so we know that 70 percent eat videniki

which means that 30 percent us not

and then we have two kinds of people in

the world when it comes to drinking

nimarov

we've got people who drink it

people who do not people who do that's

45 percent

which means that 55 percent don't

and then we know that 35 percent eat

vaneki but don't drink neymar of

so people who eat veneki that's going to

be this column but don't drink nimrod

that's going to be this box right here

35 percent now very very simple logic

from here it is a feeling just like a

little sudoku puzzle or a little

addition table

where well this plus this or the the but

energy eaters who drink nemerov plus the

ones who don't has to have that total of

70 percent

so this must be 35

and we just keep going around so 35

percent plus the 10 here

gives you 45 and this must be 20 percent

and now we've got everything we need

and then some questions asking us what

percent drink numero of but did not eat

but energy so that's right here that's

your 10

and our answer is a so nice gentle warm

up we'll start making the language a

little bit trickier so i'm going to

throw one wrinkle into this next one and

then as the video goes on these get a

little bit tougher give you a couple of

minutes on this next guy

all right as always if you need a couple

more minutes feel free to hit the pause

button

okay this one sounds an awful lot like

the first one nice straightforward

question

so we've got seems like we've got two

kinds of people here rugby players and

non-rugby players i'll put that up top

so people that play rugby people who do

not play rugby and still have their

teeth intact

and then we've got males and females

so we know that 72 percent play a rugby

that's great total has to be 100 by

definition here so we know that 28 don't

play rugby for whatever that's worth

we know that 45 percent of rugby playing

males

so males who play rugby right there and

go do do the subtraction here and we get

27 percent who are rugby playing females

seems like we're done right so the

question's asking you what percent of

rugby players are female

that is this box

and if you picked a

we got you on the language

so very very common tweak you'll see

this

not only in overlapping sets problems

but in general on the gmat but it's one

of their favorite little things to throw

in overlapping sets question

um is just kind of change that

denominator a little bit so we're not

being asked what percent of the total

are rugby playing females we're being

asked what percent of those rugby

players are female so how many rugby

players do we have that 72 percent

of those so 27 of the total are we

playing females

72 percent of the total population plays

rugby so the answer is not 27

it's 27 or over 72 turned into a

fraction or 200 percentage i apologize

so we divide both of those by 9 we get 3

8

which is

37.5 percent

and our answer is actually b

so a little it's almost a cliche in the

in gmat prep to say oh read the question

carefully and one of the things if

you've watched our previous videos

especially branson's arithmetic video

which i highly highly recommend for

anybody struggling with sloppy errors on

the gmat if you miss questions and you

go i don't know why i missed that please

go watch that fourth video in our series

arithmetic with branson

just read the question twice cover your

butt end of the question read it one

more time

not being asked what percent of the

total are rugby playing females i'm

being asked what percent of the rugby

players are female really subtle thing

if you're racing ahead you're under time

pressure really easy to miss that just

take a couple extra seconds always read

the question both the beginning and at

the end

and make sure you're answering the right

thing the answer here is b

all right

couple more kind of warm-up level

questions then we'll start making them

harder so this one's going to be a

three-way

good luck to you

all right as always hit the pause button

if you need a little bit more time

okay so again the nice three-way

overlapping sets question fairly

straightforward version of it these are

gonna get a lot harder later in the

video

temptation here is used venn diagrams

here's the issue

so if we say that there's 50 here that

visit estonia and 45 that visit latvia

and another 28th visit lithuania

and then we're trying to find the number

visit exactly 2 and this is 15 and a

plus b plus c we start throwing

variables in here

again is it possible to solve it using

either some equations or venn diagrams

absolutely you can totally do it it's

possible i find that for most of our

students we've been teaching this stuff

for more than 20 years we typically find

that students who try to do this get

themselves into some trouble if this is

working for you knock yourself out don't

let me stop you i'm going to show you a

different way that we find is a little

bit more bulletproof a little bit more

streamlined a little bit harder to mess

up

so the fundamental issue in a question

like this so overlapping sets

the issue is yeah we're over counting in

some way right so we've got these 50

people who visit estonia 45 who visit

latvia 28 who visit lithuania we add all

that up

and if i'm not mistaken we get 123

visits or if i make it more generic i

can say

countings so if we've got a list of all

the people who visit each of these

countries we have 123 names on the list

problem is we only got 84 people so the

question is all right what happened to

that all that over accounting we did

looks like we've got

39 more countings than we do people

we've got to account for that and that's

basically what these questions are all

about

okay so very very simple way to

kind of pull all this apart it's going

to look like kind of a bit of uh simple

matrix algebra if you've ever done that

so the way this question's set up

everybody's visiting at least one

country

so there's three kinds of people in this

setup there's people who visit one

country two countries or three countries

so we could say that there's the number

of countries per person

and it's got to be either one two or

three

and we've got the number of people in

each category so we know that there's a

total of 84 people we know from the

question that 15 people visit all three

countries

and now we'll take care of these two in

just a second

this is what we're going to be looking

for

and then there's the number of countings

we know there's 123 total countings that

happen here and we know that these 15

people who visit three countries each

they end up on these let's say lists of

visits a total of 45 times now very very

simple thing this is actually the one

i would argue probably the hardest thing

in the entire question if you're doing

it this way and it's not even all that

hard

we're trying to solve for the number of

people who visit exactly two so let's

call this x

the temptation here is just start

slopping variables of the problem put a

y in there don't do that

the logic here is that this plus this

plus this so the number of people

visiting one two and three countries

respectively passed up to 84.

so instead of putting in a new variable

you can just do a little bit of

subtraction here and say well whatever

this is has to be 84 minus

15 minus x

so 84 minus 15 gives us 69 so this has

to be 69 minus x

and you can double check it should be a

nice little tautology here we get 84

equals 84. that's good

and then we're off to the races so this

third column here this is the number of

countings

again countries visited in this case so

these 15 people once again three

countries each 45 countries total

these x people who visit two countries

each must visit

2x countries or account for 2x of these

123 counties

super simple here these guys are only

visiting one country so that's just the

same 69 minus x

and there you go you've got one equation

one variable i really like your chances

here

uh so 69 and minus x plus 2x we're going

to get 69

plus x plus 45 so i believe we get 114

plus x equals 123.

and that's it x must be 9

and our answer here is a nice

straightforward bit of essentially

matrix algebra to super super simplified

and the key is just making sure you keep

your head clear about what are these

things

we've got the number of countings per

person number of people in each of those

categories

and then the number of countings and it

doesn't really matter

sort of exactly which countries they're

going to we don't care about that we

just want to know how many visit exactly

two

and this will clean it up for you pretty

much every time

so this is the last of the

straightforward three-way overlapping

sets questions we're gonna do in this

video uh two of the last questions we're

gonna do are kind of really messed up

versus this with cookie language and you

got to worry about a whole bunch of

wrinkles and you'll see this method

again just apply it on tougher problems

toward the end all right one last fairly

straightforward question a little bit of

data deficiency show you a little

shortcut here and then after that the

video is going to get quite a bit harder

all right as always if you need a little

bit more time feel free to hit the pause

button here

okay first of all is efficiency

questions on overlapping sets um

a couple things here one bit is word

soup second bit is a little thing that

can help you a little bit on data

efficiency when you're doing overlapping

sets

okay so we've got two kinds of people

here people who eat jollof rice

people who do not those guys are missing

out if you don't know what it is google

it see if you can find some wherever it

is you live

there's people who eat suya people who

do not eat suya those guys are also

missing out

and we've got 200 people total

now the temptation here is just to start

barreling into the answer choices and to

kind of say all right that's it okay i

see the numbers down there that's it for

the numbers in the question off i go

huge huge mistake one of the things

you've probably heard us saying some of

the other videos

invest your time in the question on data

sufficiency push the question as far as

you can do everything you possibly can

with it before you jump into the

statements

the most basic mistake we see people

make even if they're fantastic at math

it's jumping into these statements too

quickly huge huge mistake here

if you made that mistake here i can

pretty much guarantee you missed the

question

um one small thing you can do obviously

is just make sure that you've you know

you've drawn your little chart you kind

of know what you're looking for so i

want to know how many people eat suya

but not jollof rice so

suya but not jolof this is the box i'm

looking for fantastic

now embedded in the question and i can

pretty much guarantee that if you missed

the question this is the reason why

there's another number embedded in the

question just really really subtly if i

see everybody in this town either eats

jolof or itsuya or both

i'm saying that nobody eats neither of

those things

so everybody either eats jolof eats suya

eats both

which means nobody's in this box here

nobody's eating neither of those things

so this is a big zero

and now guess what we actually know a

whole bunch of stuff and the question is

already simplified before you can look

at the answer choices if this is what i

want well look this is going to get it

for me too all i need to know is how

many people do not eat jolof and

i've got it right

okay now we can get after the the

question a little bit here

so

statement one

of the 200 residents 140 jollof rice

so

second little thing before i jump into

that

data sufficiency one of the things i

hear from our students all the time is

oh i hate data sufficiency with

overlapping sets because i feel like i

have to draw the chart three times once

for the first answer choice once for the

second answer choice and then if i

haven't finished the question by that

and i need to get decide between c and

i've got to draw it again no you don't

very very simple thing you can do to

avoid it

statement one only just for statement

one anything you get from statement one

just put in a little corner of one of

the boxes draw a pretty big version of

the chart

so here i know that i've got 140 eating

jollof rice

now anything i derive from statement one

i can also put a little corner so 60

here

um 60 0 well this has to be 60 also

and look at that i'm done this is

sufficient i know how many you're eating

suya but not jolof

so i can cross out bce

now once you're done with statement one

just rub that out if you have an eraser

fantastic if you don't

great

and then off you go right you can just

continue to the question from there

without having to redraw the chart so

statement one only to stick in the

little corner of the boxes

statement two of the residents who eat

jola 40 also eats suya it doesn't feel

like this is going to be sufficient but

let's go ahead and push it as far as

it'll go

of the residents who eat jollof rice so

let's call i don't know let's call this

jay there's your total residence who at

jolof 40 of those guys also eat suya so

40 of these guys are eating both lucky

people

0.4 j

i suppose we can keep going here a

little bit and say well this is 200

minus j

we could subtract here as well and get

.6 j but

what's already pretty obvious is we're

just getting variables all over the

place right so

again we can keep doing some goofy stuff

here this is

0.6 j

um and this is 200 minus 0.6 j

bottom line is that there's no world we

can do another little subtraction here

we still have the variable so there's no

way we're getting rid of the variable

statement 2 is not sufficient and that

means that a is our answer okay two big

takeaways here this little bit of

language

pretty common both on the ea and on the

gmat

um where you have how many

they tell you something about people who

do one or the other or both and they

imply in a very subtle way that none of

them are doing neither very very common

thing i said an exam years ago where i

saw it twice on the real thing

um and second thing data efficiency

avoid having to draw too much stuff just

stick statement one little corner

everything else right in there is normal

save you a little bit of time

okay gloves come off now that's four

questions in the books got five more

left now i'm going to get really nasty

with the language all these i think are

really realistic variants on what you

see on the gmat

this next one i we could argue is maybe

the wordiest and the ugliest but

based on things we've seen on the exam

so enjoy

for all right this one's rough so you

need a couple minutes feel free to hit

the pause button keep deciphering it or

if you need more time to curse at the

questions some more that's great too

for the rest of you come join the party

all right over the top a little bit as

far as the difficulty just of the

language but i can point to tons of

questions in the official guide to the

gmat prep testings we've seen on the

actual exam that sound an awful lot like

this

and like a lot of things on the gmat

again the the math itself isn't very

advanced it's just a question of taking

a breath making sure you take the time

to really be

super literal about taking the language

and going word by word and kind of

figuring out what they're going after

here

so kind of the original setup's not so

bad here we got two kinds of shipments

we got the ones that are tainted with

salmonella

the ones that do not have salmonella

and then you've got ones that are

rejected and we've got the ones that are

not rejected

great first couple bits information

given in the question pretty

straightforward one-fifth of the total

are changing with salmonella so 20 i'm

going to put these as percentages i

think those are going to be easier to

work with i also notice all of my answer

choices are in percentages

so 20

tainted with salmonella that means 80

are not tainted

100 total so far i'm feeling pretty good

that's going to change in just a second

eighty percent of the ones that are

tainted are rejected so eighty percent

of that twenty percent we can multiply

those we get sixteen percent of the

total

are rejected and also tainted with

salmonella

put a four percent in here

great

now this part gets fun

right here the total rejected the total

number of rejected shipments so the

total number of rejected shipments here

is going to be one-third the number of

untainted shipments so untainted

shipments that are not rejected

this sounds rough

untainted

not rejected that's this box

so we know that this box total rejected

shipments

is one third as many as the untainted

shipments that are not rejected

so you could do a couple different

things here you can call this x

and then make this one third x

my personal preference if i can avoid

the fractions i like to avoid the

fractions again not the end of the world

but i'd rather say okay i know that this

number is three times that number i'd

rather flip it around so it's the same

exact math

so i'd rather make this x and make this

3x and again take your time here invest

the extra 20 seconds if you need to make

sure you do a sanity check

one third the number of untainted

shipments that are so the total rejected

shipments total rejected

is one-third the number of untainted

that are not rejected yeah x is 1 3x

great so now this isn't so bad we want

to know what's the percentage of

rejected shipments that are not tainted

so we're we're chasing

so rejected

untainted

so we're chasing this box and i'll be

able to tweak to it in a second

all right so maybe this isn't so awful

because this is just

um

we do a couple different things here we

could say that this is

uh x minus 16. that would work

we could also say that that's equal to

80

minus 3x

so okay

um so what i could do here you could do

it either way so i'm going to put in x

minus 16 percent here i'm going to go

right i got an equation

so if i take this i can solve it for x

so

x plus 16 x minus sorry x minus 16

plus 3x

is going to be equal to 80

so add the 16 to both sides x plus 3x

gives me 4x

is 96 percent so x must be 24

now if you got this far congratulations

your temptation might have been to pick

d and drop the mic that is not quite the

right answer

so i'm gonna go ahead and write 24 in

here to make me feel a little bit better

same thing here i know this has to be

eight percent

now and what's the question asking me

for what percent of the rejected

shipments are not tainted so i'm not

being asked for what percent of the

total

are rejected untainted shipments

and yes your head should be spinning

right about now i'm being asked what

percent of the rejected shipments

are untainted this is very much like the

second question we did this last little

part what percent of the rejected

shipments 24 of the shipments are

rejected

eight percent

are rejected shipments that are

untainted so that's a third

so a third of the rejected shipments are

not tinked with salmonella

and that gives me

33 and a third percent

for e

all right everybody having fun

um gotta be honest here this is about as

hard as it comes

i'm gonna throw some more wrinkles at

you the next four questions a lot of

stuff we try to minimize and maximize

stuff that can hurt your brain in a very

different sort of way it doesn't really

get tougher than this though so if your

goal is something like let's say a 45

quan or something in the mid 40s

don't worry about this too much it's

good to challenge yourself with the

language and get better at pulling it

apart this has so many wrinkles in it no

shame at all i'm missing this even if

you're kind of going for a 47 48 49 i

don't necessarily expect you to miss

that or to get this right this could be

something you could miss and be doing

just fine if your goals are the high 40s

again if you're somebody's chasing a 50

or a 51

yeah you need to be able to nail every

bit of the language but for most of you

no shame at all i'm missing this and

i'll say the same thing about pretty

much every other question um in this

video for between on the end of it all

right another little wrinkle good luck

to you

foreign

all right as always pause if you need to

so now we're getting into a little bit

of a different breed of questions sounds

like probability it isn't really i could

write the same exact question without

probabilities write it as percentages

really it's a form of overlapping sets

but now we're getting this business of

minimizing and maximizing things

something you'll see kind of throughout

sort of stats and probability and

overlapping sets questions on the gmat

you'll see more of this in the next

couple of videos as well

in this case we've got two events we've

got x

and as always you could have x occurring

or not occurring

in total we got y we have no y and we've

got the total

so pretty easy on these sides here we

can say we know that uh 70 chance that x

occurs

so notice that i just said that as a

percent you can convert it to if it

makes you feel better knock yourself out

you could say 70 percent

30 100

and it's the exact same thing it doesn't

really matter in this case i'm gonna go

ahead and go with the original numbers

expressed as probabilities which are on

a scale from 0 to 1.

so 0.7 probability that x happens 0.3

probability that it does not total total

has to be 1 here same deal with the y

0.85

probability that it does occur

0.15 probability that it does not

now really nothing technical here it's

just a matter of kind of thinking your

way through and going well what are we

what are we after here if we want to

make we're trying to find the least

possible probability that both occur

we're trying to minimize this

now this is a fixed quantity we know

this is 0.85 so logically if we're

trying to minimize this we got to

maximize something else so we're going

to try to maximize this guy

and equivalently try to maximize this as

well it doesn't really make a difference

how you want to think about it's going

to work the same way

um so what's the biggest this could

possibly be one temptation might be to

say 0.85 well that's not going to work

because

you can't have 0.85 here because this is

only 0.3 that's impossible

so when you think about this

intersection y occurs but x does not

occur

the biggest it can get is whichever the

smallest number is right

so if only

there's only a 0.3 probability that x

does not occur

that's the biggest you can make this

so that's 0.3

that means this has to be 0.55

and i'm feeling pretty darn good about b

now at this point you might be wondering

well what if i decided to work on this

one first no problem it's all going to

work out the same

so same logic here if you decide to

maximize this one first great what's the

biggest this can be what can't be 0.7

because we don't have enough of a

probability that y does not occur

so 0.15 probability that y does not

occur so that's the biggest this can get

0.7 minus 0.15 leads to the exact same

place

if it helps one more way to think about

it doesn't matter which one of these you

do you can say if i'm maximizing this

and this i'm also minimizing this

and obviously the smallest you can make

this is zero

that works too if you want to start with

the zero there it's going to lead to

exactly the same place so tons of ways

to approach this typical gmat right so

typical kind of mid-level question there

might be six ways to solve it and

they're trying to test you can you find

the best way to solve it save yourself

some time find the most efficient of

those ways or at least a relatively

efficient way here uh maybe three four

different ways to do it

whatever one works best for you is

totally totally fine all right we'll

ramp this up another notch

all right lots of words in this one if

you hit the pause button go for it take

your time grapple with it for a little

bit if you need to

for everybody else let's have at it

um and i want to be really clear about

something now we're into some pretty

exotic variations of of overlapping sets

and and again like a lot of these just

about pulling apart the word soup

figuring out how you can kind of cut to

the heart of the question it's tough to

see here i think most of you watching

this either figure it out pretty quickly

and kind of once you sort of saw what

the the joke is in the language

boom you had it pretty fast a lot of you

might still be spinning your wheels

after two three four minutes totally

normal again if you're going for

something in the high 40s or below that

anywhere in the 40s on on gmat quant

you're in perfectly good shape here if

you're taking the executive assessment i

don't think you need this at all to be

honest i mean there's very very rarely

is there a world where you need to get

such a huge score on the executive

assessment

that it's worth your time to really

worry about this so if you're struggling

and you're head spinning reading this no

worries at all you see questions like

this occasionally not super common and

again this is on the hard end just

because of the language and kind of the

do you see your way in or do you not see

your way in

okay

so

if you try to take this original chart

up here with the approved disapproving

neutral it doesn't map nicely onto what

we were doing before where it's

thing a not a

b not b

this isn't exactly the same thing now

you've kind of got this extra dimension

it makes it a mess so you've got to kind

of be a little bit enterprising about

like what are they really going what are

we going after here what do i really

need to know

and can i collapse into this or do i

need to do something else entirely now

again everything's in the language here

so the question is how many voters

approve of a

but did not say they approve of b think

about what that means

did not say they approve of b is not the

same thing as saying they disapprove and

i know i feel like some attorney or

something split in here is over stuff

but not

yeah and gmat does this to every once in

a while right on the harder questions

did not say they approve of b

what does that mean that means that they

either um that they approve of a

and they either

disapproved or were neutral towards b

okay so that's the opportunity it opens

up for me right there so instead of kind

of trying to muck with this i can put in

a little double set matrix how

so this is a proof of a

and this is either disapprove

or neutral

on a and this is total

same thing here approve of a

and this is disapprove

or neutral on a i'm sorry b my bad

and here's your total

um now again it's not to say that hey

it's synchronized swimming you're going

to see a bunch of questions where you

need to do exactly this just depends on

the phrasing right we could flip it

around a little bit you're collapsing

something differently here or maybe this

doesn't even work at all and you got to

do something different that's totally

fine in this case the way it's phrased

what i want i want the number of people

who approve of a

but did not approve of b which means

that they either disapproved or were

neutral

so i need this box right here

all right

now it turns out the answer choices

facilitate that really nicely

statement one turn 75 approve actually

let me get some of this in there first

so approve of a

so we know that 400 approve of a we know

we got a thousand total

we know that 600 either disapprove or

neutral towards a that should add up

same thing here 500 to proof of b

and 500 do not approve of b meaning if

they either disapprove or they're

neutral

okay now out of the answer choice

statement one 275 approve of b

but did not say they approve of a so

proof of b

do not say they approve of a so that's

this one right here again data

sufficiency

statement one only i'm going to shove it

in a little corner

anything else i get from it i'm going to

shove into a little corner and i can go

in either direction i'm going to go this

way 225

great that's 175

and i know i got what i need so this is

sufficient statement one sufficient

can't be bc it's got to be a or d

and again i can smudge out my statement

one

and off i go statement two

325 approve of neither

so meaning that they

said disapprove or neutral towards a and

also disapprove or neutral towards b so

great i got my 325 right here

and i get what i need again 175 here

so my answer has to be d that's

sufficient

all right

having fun last two i think you're

pretty nasty now watch some of you guys

viewing this maybe had no trouble in the

lab or had a lot of trouble in the last

few i'm not going to start on these on

these final two questions i think

they're rough

enjoy

all right hope you guys are having fun

with this one if you little more time

feel free to take it hit the pause

button

if not this is going to be fun um

yeah a lot of different on a question

like this again if you're finding this

really simple right out of the gate

awesome good for you

a lot of people look at this their eyes

start to go crazy uh they go cross-eyed

that's the case for you whatever it

takes to get yourself some intuition a

whole lot of different ways to do this

question i'm going to kind of pick a

couple different ways of going about it

um you can do the entire thing really

with percentages until the very end

that's actually my personal preference

but you know if you're somebody's

looking at this and goes nah i want this

to be a little more visceral maybe it

makes more sense to me if it's not

percentages that's totally fine the

numbers are simple kind of on purpose

here

so we've got 120 people 55

ranked beach holidays number one

so if i'm not mistaken that's 66 people

25 percent rate ski vacations ahead of

beach holidays so that's going to be

30 people and then 30 ranked city trips

ahead of the beach vacation so it's

going to be 36. if you wondered that

knock yourself out kind of feels like a

waste of time to me but again if it

helps us talk about it that's really

great

and we want to know how many ranked

beach vacations last kind of feels like

there's not enough information oh but

there is

so if it helps you can kind of my first

instinct here first i ran into a

question like this on the actual gmat

was to kind of say yeah is there a way

for me to just kind of

feel that information a little bit kind

of put in some sort of order i know that

55 are breaking the beach vacations

first

i'm looking for this thing this is my

question it'd be great if i could just

know how many ranked beach vacations

second they're not telling me that oh

well

too bad sad for me

what i do know

is that

45

total

have to be ranking beach vacations

either second or third okay so i know

that 45 of the population is in one of

these two spots

again if you want to turn it into the

actual numbers you can i think that's

54.

again whatever you prefer i find this to

be a little bit of a waste of time but

if it helps you feel the question feel

like you're on track no big deal

so 45 here now i know that 55 percent

are ranking something or ranking at

least one thing

ahead of the beach holiday

so i've got 55 percent here

that are ranking something ahead of the

beach holiday

45

of the people have to be in these two

categories question is how much overlap

is there and again if you're paying

attention to kind of the underlying

intuition behind really everything in

this video

it's well what's what's overlapping

we're double counting somewhere we're

double counting people here right only

45 of the population does not rank beach

holidays first

but it looks like we've got 55 percent

if we kind of add up these two numbers

so we know that they rank something

ahead of it

so right here you could look at this

question and go

it feels like the answer is going to be

about 10 if that's what you're thinking

you'd be correct it actually is 10

if you wanted to stop there and go 10

great 10 gives me b

10 of the 120 that's 12.

fantastic you win if you're

uncomfortable with that i'll take it one

step further

so the little step further i could take

again if this doesn't resonate with you

no worries at all if this helps you

fantastic if it doesn't no worries so

remember we did that first three-way

overlapping sets question i think it was

a third question in the video

i said well one way to kind of pull

apart this over counting is to kind of

set up a little kind of super basic

piece of matrix algebra sort of thing

where okay we've got the number

of

countings per person

and we've got the number of people

and then we've got the total countings

so here what do we mean by countings

this is where it gets really slippery we

mean things ranked ahead of beach

holidays

so some people ranked one thing ahead of

beach holidays

some people rank two right what we want

to know is how many ranked two things

above the beach holidays how many people

rank both the ski trip and the city trip

ahead of beach holidays this is what we

want to know

this is our variable of interest right

here

um now we know that there are

again 54 people if you want to use the

actual number 45 of your favorite

percentage i'm going to use the rod

number here it's a little bit more

intuitive we know that 54 people

are counted here somewhere 54 people um

had at least one thing ranked

um above beach holidays that's correct

um at least one thing right above beach

holidays

but then if we kind of add up these

countings we get more than that right we

get 66

right here so 55 of the total so there

were 66 occasions when somebody ranked

something about beach holidays but only

54 people who did so

so where's your overlap easy enough to

get to here this has to be 54 minus x

you almost don't need the formality but

if it helps you go for it 54 minus x

again 2x

here's your equation and surprise once

you crunch those numbers

you're going to get 12 again

again

if you're somebody with modest schools

executive assessment or gmat don't worry

about this too too much very very rare

variant on the question i'm mostly

throwing this at you just to say yeah

look these basic tools that we kind of

present the double set matrix

really being deliberate with your

language thinking through over counting

where does the overlap actually occur

intuitively it's those same tools no

matter what so even we get to these

really really kooky really obscure

variants on these questions

same basic tools are going to help you

hard to penetrate this question

personally i think so if you found it

easy awesome you're doing great if your

goals are fairly modest you're looking

for something in the 40s on the gmat

quant

or really any reasonable ea score that

would get you into a good school this

isn't something you should keep you up

at night think of it as a good fun

challenge and that's about it all right

one last question

good luck to you

all right as always if you need a couple

more minutes hit the pause button

otherwise we'll keep rolling

so this is one of those nice problems so

again another one of those kind of

minimize maximize kind of problems a

concept that gmat absolutely loves

you're going to see it kind of scattered

throughout

things like combinations permutations

probability statistics overlapping sets

even just kind of your everyday word

problems so there's kind of an

underlying skill here in the way you

might think your way through this

problem that i think is useful now this

specific variant this exact version of

it very very rare you're going to see

this exactly on your test not very

likely you certainly could not a lot of

these running around but i think it's a

it's a good final challenge question i

kind of think through the process and

part of why i picked it as the last

question of the video is that it kind of

defies really formulaic thinking you

can't re maybe there's a way but i don't

think it's all that useful to shove it

into any of the any of the formulas that

are out there for overlapping sets i

don't think it's that useful to shove it

into a venn diagram or a double set

matrix or anything like that it's really

just a question of like okay can i think

my way through what the overlap needs to

be give myself maybe some way to

visualize it

and that's it it's really just kind of a

pure can you read your way through it

kind of question

at least in my eyes

okay 120 locations of this fast food

restaurant

um we've got ninety to introduce one

item eighty-five that introduced another

72 with a third

my first instinct here again overlapping

sets i know that kind of the joke is

well

we're over counting somehow right we've

got 120 locations but how many items get

introduced i think this is going to be

247.

call those countings if you want

and the deal is well okay how are those

allocated and as i try to think about

minimizing and maximizing the overlap

what ends up happening to them i'm going

to start with

the greatest possible introduce all

three notice in the language of the

question it doesn't say anything at all

about every if it said every restaurant

has to introduce at least one

different question different math behind

it in this case it didn't say that

so i'm going to say all right great as

possible with all three

easy enough if you want to give yourself

a little bit of a visual aid here you

can and say

well let's imagine

let's say a little

kind of bar graphy kind of thing and

let's say this is 120 locations

i know that about 90 of them

introduce x and i can draw a similar

sized one here for

y that's 85 items so a little bit short

of the bar for x

and here's item z it's going to be 72 so

it'll be shorter still and go well look

there's nothing stopping us from having

72 ite they're that all of the

restaurants introduce z

also introduce x and y

so your maximum here

got to be 72 right

so that's great so great as possible

with all three so a is equal to 72. that

part's pretty easy

now the question is what's the least

overlap you can have

or the least number that introduce all

three

so okay so what would have to be the

case there we'd have to try to fill up

as many restaurants as we can

with two of those items and then

whatever's left over has to be the third

item in that location so i'm going to

take kind of a similar approach here and

say

well all right

um

you can kind of take it item by item if

you want to if that's more intuitive

that's fine

so i could look at this and go

90 so if this is 120 locations

um

and i've got these 247 countings here so

okay there's 120 here think of that as

the first item

in all 120 locations

that takes care of 120 of my countings

so second batch locations so 120 of them

are getting their second item that takes

a 240 by counties now so 120 locations

with one 120 locations with the second

one that's 240 what do i have left

just seven items

so i've got seven countings or seven

items left to be introduced so that

means that they're that at the very very

least

i have to have seven locations that are

gonna produce all three of them

and then the rest of 113 locations

introduce exactly two and always double

check of batting it back up 120 plus 120

plus the seven

gives me my 247.

so a is equal to 72

b is equal to 7. i want a minus b that

gives me 65

and my answer here is e

all right once again if you struggled

with this and your goal is you know

fairly modest 40s on the gmat quant

pretty much anything on the executive

assessment don't worry about this too

much if you made some headway on it your

goals or mod is fantastic

congratulations you're probably doing

better than you need to be and that's

wonderful give you a little bit more

leeway and other kinds of questions

all right that's wraps us up here so

that is it we've pretty much covered

everything in overlapping sets thank you

for surviving video number 16

comprehensive gmat ninja quant series

next video number 17 gonna be covering

uh statistics a little bit more of the

minimize maximized kind of questions

you'll see some of these same concepts

disguised very very differently in a

different domain

all right thank you so much for watching

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