Erika here with PrepScholar GMAT back today with the strategy to beat
overlapping sets problems on the GMAT overlapping sets problems are some of
the hardest problems on the quant section we can identify them pretty
easily there are word problems that focus on
one group that's being evaluated for multiple traits so in this real gmat
problem we're dealing with a group of teachers the two traits were evaluating
each teacher for are his or her gender and whether or not he or she considers
engaging in research and essential goal so this gives us four possible smaller
groups that a teacher can fall into so group number one men who are pro
research group number two men who are anti research group three women who are
pro research and group four women who are anti research we want to find the number
of teachers who are women so this is both female teachers who are Pro
research and female teachers who are anti research the question stem gives us
some information it tells us that there are 1,400 teachers in total and that 42
percent of these teachers both men and women are Pro research then the
statements give us additional information about the number of male and
female teachers who are Pro research so there's a lot going on here how can we
put all of this information together in a meaningful way in order to solve this
problem the key to solving overlapping sets problem is to use a diagram to
organize our information and build equations that express the relationships
between our smaller groups when we're evaluating our larger group for two
traits so like on the problem we just saw and also on most overlapping sets
GMAT problems we're going to use something called a double matrix now a
double matrix is kind of a buzzword you'll see it on all the forums but
basically it's a glorified table and in this table the columns represent the
first trait while the rows represent the second trait so for our problem about
college teachers will have a column for men and a column for women and a row for
pro research and a row for anti research so this gives us our
four possible smaller groups again men who are pro research men who are anti
research women who are pro research and women who are anti research now in every
double matrix we also have an additional column and an additional row for our
totals this means that the first two cells in each row or column will add up
to the total at the end of that row or column so for instance adding men who
are anti research to women who are anti research gives the total number of
teachers who are anti research the same thing works in the row and column of
totals adding the number of teachers who are pro research to the number of
teachers who are anti research gives the total number of teachers so now we can
fill in our information looking at our question stem we can fill in that we
have 1400 teachers in total then we find that 42% of 1400 teachers is 588
teachers so we'll fill in that we have 588 pro research teachers we want to
find the total number of teachers who are women so we'll label that cell with
a W okay well what else can we get from this so if there are 588 Pro research
teachers and 1,400 teachers in total there must be 812 anti research teachers
and if there are W female teachers and 1,400 teachers in total then there must
be 1,400 minus W male teachers so a key takeaway here if we see that we know two
cells in either a row or a column we know that we can solve for the third
cell okay let's go onto statement one thirty-six percent of the men are pro
research and fifty percent of the women are also pro research converting those
percents into decimals this gives us point three six times fourteen hundred
minus W for the number of pro research male teachers and point five W for the
number of pro research female teachers now we could go ahead and start filling
in our anti research cells but we should notice something cool
we have all three cells filled in in our pro
research row so this gives us the equation 0.36 times 1400 minus W plus
0.5 W equals 588 now looking at this we should be able to see that we can
simplify this equation to solve for W which is exactly what we want to find
this would make statement 1 sufficient however if we wanted to we could go
ahead and simplify this down as shown on the screen giving us 600 female teachers
in total so statement one is definitely sufficient now to evaluate statement two
we can just go back to the information we got from the question stem now based
on statement 2 we also know that 288 men are pro research this allows us to solve
for the number of women that are pro research 300 but without the number of
women that are anti research or even the number of men who are anti research we
have no way to solve for W so statement 2 is insufficient and the correct answer
is a now if we have an overlapping sets problem with three traits our best bet
is to set up a Venn diagram where each circle represents one trait then we can
build out equations based on this Venn diagram but be very very careful to
avoid double counting 3 trait problems however are pretty rare and unlikely to
appear on your test so the double matrix is going to be the thing you'll use the
most and that's how you can be overlapping sets problems on the GMAT if
you have any questions or what we talked about today or suggestions for future
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watching and happy GMAT studies