There are 150 students at Seward High School. 66 students

We can create the following equation:

Total students = # who play baseball + # who play basketball + # who play soccer - # who play exactly two - 2(# who play all 3) + # who play neither

150 = 66 + 45 + 42 - 27 - 2(3) + n

150 = 120 + n

n = 30

Answer: C

There's a better way to do the question, as I'll explain below, but if we have 66 baseball players, 45 basketball players, and 42 soccer players, we have 66+45+42 = 153 players in total, but we've counted some of these players twice. We have 3 who play every sport, so we've counted those people three times. We only want to count them once, so we should subtract 2*3 = 6 from our total. We also have 27 who play exactly two sports, so we've also counted those people twice. We only want to count them once, so we should subtract a further 27 from our total. So we really have only 153 - 6 - 27 = 120 unique players who play one or more of the sports, and since there are 150 students in total, 30 play none of the sports.

But you don't need to think through this problem that way. We can draw a 3-circle Venn diagram:

• we know we have 3 players in the middle, where all the circles overlap
• we know we have 27 players somewhere where pairs of circles overlap. We don't know where these players go, but it cannot matter where we put them; if it mattered, i.e. if the answer to the question changed depending where these 27 people are in the Venn diagram, the question would have more than one right answer, and that can never be true of a GMAT PS question. So we can put these 27 anywhere we like, knowing we'll get the right answer no matter what we do. We can put them, say, where baseball and basketball overlap, and then we'll have 0 people where baseball and soccer overlap, and 0 where basketball and soccer overlap
• then it's easy to fill in the rest of the Venn diagram -- we have accounted for 30 of the baseball and basketball players, so 36 play only baseball, and 15 only basketball. We have accounted for only 3 soccer players, so 39 play only soccer.
• now we have an entire Venn diagram filled-in, and adding the numbers in each region, we have 36 + 15 + 39 + 27 + 0 + 0 + 3 = 120 people in the diagram, so 30 must be outside the diagram.

Check out this blog post first: https://anaprep.com/sets-statistics-thr ... ping-sets/

"counted twice" means that the elements in this region belong to two sets.
In my diagram, the elements in the green region d belong to both Set A and Set B.
Similarly, elements in the region e belong to both Set B and Set C.
Elements in the region f belong to both Set A and Set C.

That is why elements in regions d, e and f are counted twice, because they are counted in both sets to which they belong.

great explanation using venn diagram +1

Bunuel can we expect 3 overlapping set question on GMAT and are we supposed to know the formula.

I've seen several GMAT questions on 3 overlapping sets, so you should understand the concept behind such kind of problems. Check this for more: formulae-for-3-overlapping-sets-69014.html#p729340

Hi you try doing question 203 in OG 17 the same way? there the 2*aandband c is not working Bunuel

Please check that question HERE.

Hi Bunuel thanks a lot can question 132 be tackled the same way?

Check HERE.

All other OG questions are HERE.

Bunuel,
I am still unable to understand how 27{exactly 2 sports} is being counted twice when we add Baseball + basketball + soccer ? Even the venn Diagram has 3 yellow parts. So I am confused regarding it. Can you please shed some more light on this one part? I understand the rest of the logic.
Thanks

IanStewart, KarishmaB, chetan2u, MartyTargetTestPrep, If possible. Thanks

Thanks, It makes sense now.