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Mathematical Problems: Inclusion and Exclusion
There are 25 people right in the first question and 10 in both questions, which means that among the 25 people right in the first question, there are 15 people wrong in the second question and 18 people wrong in the second question, leaving 3 people wrong in the first question.

105=3×5×7, so the coprime with 105 cannot contain factors of 3, 5 and 7.

Use 3: (105-36) ÷ 3+1= 24.

Use 5: (105-35) ÷ 5+1=15.

Use 7: (105-35) 7+1=11.

Use 3.5: (105-45) ÷15+1= 5.

Use 3.7: (105-42) ÷ 21+1= 4.

Use 5.7: (105-35) ÷ 35+1= 3.

And 3.5.7: 1

24+ 15+ 1 1-5-4-3+ 1=39

7 1-39=32

The solutions to these problems are all the same. You can draw a diagram with three circles partially overlapping, with a total of A+B+C, minus AB coincidence minus AC coincidence minus BC coincidence, plus all overlapping parts of ABC.

25+26+24-16-15-14+5 = 35 people.

250=2×5×5×5

The simplest true fraction is that the molecule does not have two factors, 2 and 5.

Use 2: 125 and 5: 50.

Use 2.5: 250÷ 10=25

125+50-25= 150

250- 150= 100

Just draw a picture to understand.

A+B+C is required.

75+83+65 = 223 = D+E+F+2(A+B+C)+3x 50

a+B+C+D+E+F+50 = 100- 10 = 90

A+B+C=33

Sorry, I read the wrong question just now. The fifth question is the total number of two plus three, that is, A+B+C+50=83.