Intelligence test

Paľo, Jano, Karol, and Rišo were doing an intelligence test. Palo correctly answered half of the questions plus seven 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 in 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?

Correct answer:

n =  60
x = J
y =  38

Step-by-step explanation:

P = n/2 +7 J = n/3+18 K = n/4+21 R = n/5 + 25  2 ...  prime number 3 ...  prime number 4=22 5 ...  prime number LCM(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=37

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