In a class of 30 students, exactly 7 have been to Mexico and exactly 11 have been to England. Of these students, 4 have been to both Mexico and England. How many students in this class have not been to Mexico or England?
(A) 23
(B) 16
(C) 20
(D) 12
(E) 18
The first Venn diagram below shows that there are 30 students in the class, 7 students have been to Mexico, 11 students have been to England and 4 students have been to both countries. Of the 7 students that have been to Mexico, 4 have also been to England.

Therefore, $7-4=3$ students have been to Mexico and not England.

Of the 11 students that have been to England, 4 have also been to Mexico. Therefore, $11-4=7$ students have been to England and not Mexico.

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-274.jpg?height=274&width=721&top_left_y=459&top_left_x=756)

Therefore, 3 students have been to Mexico only, 7 students have been to England only, and 4 students have been to both.

In the class of 30 students, this leaves $30-3-7-4=16$ students who have not been to Mexico or England.

ANSWER: (B)