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A survey asked 680 runners which marathons they had run in the past year.

The results were:

340: New York marathon

400: Boston marathon

300: Steamboat Springs marathon 

140: New York and Boston

90: New York and Steamboat Springs

240: Boston and Steamboat Springs

50: New York, Boston and Steamboat Springs

 

How many of the runners surveyed didn’t run in any of these three marathons? Note: The statistic of 340 runners who ran in the New York marathon includes everyone who ran in the New York marathon; it does not mean that there were 340 runners who ran only in the New York marathon. (This is the standard assumption in problems like this one.) The same applies to the other statistics, so the task is to deal with the overlap. (This explains, for example, why the numbers in the whole list add up to more than 680.)

 Aug 18, 2020
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Draw a Venn diagram

  Here is my quick sketch  Venn diagram..... add up all of the numbers  then subtract from 680 to find runners who participated in none...

 Aug 18, 2020

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