Let the number of people who answer A correctly be A, AB, AC, ABC, B and C. From the meaning of the question, four equations can be listed:

( 1)A+B+C+AB+AC+BC+ABC=25

(2)B+BC=2*(BC+C)

(3)A+ 1=AB+AC+ABC

(4)A=B+C

Replace all the first equations with equations expressed by B and C, then merge and eliminate them, and so on, and finally the equation is simply obtained:

4B+C=24

Here is the key. Please have a look. After analysis, there are seven possibilities, namely

B=0 C=24

B= 1 C=20

B=2 C= 16

B=3 C= 12

B=4 C=8

B=5 C=4

B=6 C=0

Let me show you how to exclude the first result, and so on for the next six results.

When B=0 C=24, we can know from the fourth equation that A=B+C, then A=24. If we substitute it into the first equation, the left side is greater than the right side by 25, so we exclude it. ...

Only the last B=6 C=0 is left, which can only be the case.

For the sake of my hard work, reward me with some wealth. Thank you!