Question

SOMEONE WHO IS GOOD AT GEO MATH PLZ HELPPP!!!
The Venn diagram represents enrollment in various classes at a certain high school. 12 students take math (Math) only. 11 students take English (Eng) only. 16 students take biology (Bio) only. 30 students are enrolled in math and English, but not biology. 15 students are enrolled in all three classes. 200 students attend the school, and 16 students take biology and English, but not math. How many students are enrolled in math and biology, but not English?

A.
12
B.
17
C.
75
D.
100



Please select the best answer from the choices provided


A
B
C
D

Answer 1

Using the symbols in the Venn diagram, we want to find A given that

B = 16

C = 15

D = 30

and given that 25 students don't take any of these courses.

There are 200 students total, so we need to have A plus the total number of students given in the diagram sum to 200. This means

(math only) + (English only) + (biology only) + (math and English, no biology) + (math and biology, no English) + (English and biology, no math) + (all three) + (none of the three) = 200

or

12 + 11 + 16 + 30 + A + 16 + 15 + 25 = 200

Solve for A to get A = 75, making the answer C.