Puzzle question - check out in detail?

A survey of 300 respondents in TWWI showed that 135 have the habit of biting their nails, 125 have the habit of digging their nose (their own nose and NOT others'), and 115 have the habit of scratching their head. Further, 42 of the employees have the habit of both biting their nails and digging their nose, 48 of them habitually dig their nose and scratch their head and 43 scratch their head and bite their nails. 30 employees have all the three habits!


How many respondents did not have any of the above habits?

Puzzle question - check out in detail?
Employees who don't have nails and nose habit





125 + 135 = 260 - 42 = 218 employess





No nose and head habit





125 + 115 = 240 - 48 = 192 employees





No nail and head habit





135 + 115 = 250 - 43 = 207 employees





Total employees who do not have


(nail %26amp; nose habit) and (nose %26amp; head habit) and (nail %26amp; head habit) =


218 + 192 + 207 = 617 employees


Employees with nail, nose %26amp; head habit = 30 employees





617 - 30 = 587 employees ( do not have all habits)





587 - 375 ( employees who have any of the habit) = 212 employees





300 - 212 = 88 employees who do not have any of the habits
Reply:n = 300 - (135 - 42 - 30 - 43 + 125 - 42 - 30 - 48 + 115 - 43 - 30 - 48 + 42 + 43 + 48 + 30) =





n = 300 - (135 - 42 - 30 - 43 + 125 - 30 - 48 + 115) = 118
Reply:I wanna say 88 but im not sure
Reply:Ah...none of them. Unless you meant 3,000? Then the answer would be 2,462. Maybe I'm just not understanding what the question is saying, but if there are only 300 respondents...125 + 135 + 115...just those three numbers alone add to over 300.
Reply:The answer is 28,





Draw a Venn diagram, and input the data from the end to the beginning. ie enter the 30 first, then the 42,48,43 etc.





All inside the circles add up to 272.


That means 28 are left outside.
Reply:88.....