Consider the following diagram.

How many students like both geography and mathematics but NOT history?

11

Step 1 ) Look at the all figures properly but observe the area outside the part of those student who do not  like history

Step 2) Look at  number given in is as students like both geography and mathematics but NOT history

Step 3) By visual observations we conclude that (7+ 4 = 11)  is the number which represents students like both geography and mathematics but NOT history