GMAT Ninja Quant Ep 13: Overlapping Sets
Summary
TLDRCharles 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
📚 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.
📈 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.
🤔 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.
🔢 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.
🕵️♂️ 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.
🧩 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.
🎯 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.
🗳️ 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.
🏖️ 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.
🍔 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.
Mindmap
Keywords
💡Overlapping Sets
💡Venn Diagrams
💡Double Set Matrix
💡Data Sufficiency
💡Quantitative Reasoning
💡Word Soup
💡Efficiency
💡Language Tweaks
💡Probability
💡Minimize and Maximize
💡GMAT
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
if you haven't yet please hit the
subscribe button and thank you again for
joining us
you
関連動画をさらに表示
How I Scored 750 on the GMAT (Top 3 Best Resources, My Score History, Recommended Study Schedule)
ALL THE FREE GMAT MATERIAL ONLINE | HOW TO GET 670+ on GMAT with FREE Material
Time Speed and Distance 1 | CAT | XAT | IIFT | Arithmetic | Quantitative Aptitude | Udit Saini
Tips For Getting Into Your DREAM MBA School! (From a Wharton and Columbia Admit)
How to Make the PERFECT Revision Timetable with Spaced Repetition
The ONLY WAY to Make YOUR Argument Thesis COMPLEX!
5.0 / 5 (0 votes)