0Lucky0
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.
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.
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ianstewartgmat.com
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wrong 
