Intelligence test

Paľo, Jano, Karol, and Rišo were doing an intelligence test. Palo correctly answered half of the questions plus 7 questions, Jano to a third plus 18 questions, Karol to a quarter plus 21 questions and Risho to a fifth plus 25 questions.
After the test, Karol said, “I feel I was doing quite well. I was quite pleased to find that there were fewer questions in the test than the practice test I did at home. I almost did not finish because he had up to 100 questions. "

How many questions were in the test?
What was the name of the boy who had the most correct answers? How many correct answers did he have?

Result

n =  60
x = (Correct answer is: J) Wrong answer
y =  38

Solution:

P=n/2+7 J=n/3+18 K=n/4+21 R=n/5+25  2=23=34=225=5LCM(2,3,4,5)=2235=60  n0=LCM(2,3,4,5)=60  25<n<100  n=n0=60  P=n/2+7=60/2+7=37 J=n/3+18=60/3+18=38 K=n/4+21=60/4+21=36 R=n/5+25=60/5+25=37P = n/2 +7 \ \\ J = n/3+18 \ \\ K = n/4+21 \ \\ R = n/5 + 25 \ \\ \ \\ 2 = 2 \\ 3 = 3 \\ 4 = 2^2 \\ 5 = 5 \\ LCM(2, 3, 4, 5) = 2^2 \cdot 3 \cdot 5 = 60\\ \ \\ \ \\ n_{ 0 } = LCM(2,3,4,5) = 60 \ \\ \ \\ 25<n<100 \ \\ \ \\ n = n_{ 0 } = 60 \ \\ \ \\ P = n/2 + 7 = 60/2 + 7 = 37 \ \\ J = n/3 + 18 = 60/3 + 18 = 38 \ \\ K = n/4 + 21 = 60/4 + 21 = 36 \ \\ R = n/5 + 25 = 60/5 + 25 = 37
x=J=38x = J = 38
y=J=38y = J = 38



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