In the given diagram, the shapes indicate the categories of persons. The numbers given in the different segments represent the number of persons in that category.

How many dancers are either gymnasts or singers but NOT both?

19

many dancers are either gymnasts or singers but NOT both

Step 1 ) Look at the all figures properly but common part of dancers are either gymnasts or singers but NOT both

Step 2) Look at  number represents the dancers are either gymnasts or singers but NOT both

Step 3) By visual observations we conclude that 16 + 3 = 19 is the number which represents the dancers are either gymnasts or singers but NOT both