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:

$$\begin{gathered} P=n/2+7 \\ J=n/3+18 \\ K=n/4+21 \\ R=n/5+25 \\ 2...\text{ prime number} \\ 3...\text{ prime number} \\ 4=2^2 \\ 5...\text{ prime number} \\ LCM(2,3,4,5)=2^2\cdot 3\cdot 5=60 \\ {n}_0=LCM(2,3,4,5)=60 \\ 25<n<100 \\ n=n_0=60 \\ P=n/2+7=60/2+7=37 \\ J=n/3+18=60/3+18=38 \\ K=n/4+21=60/4+21=36 \\ R=n/5+25=60/5+25=37 \end{gathered}$$

$x=J$

$y=J=38$

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