# 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)
y =  38

#### Solution:

$P = 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
$x = J = 38$
$y = J = 38$

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