Answer:
The fourth year he took 8 exams
Explanation:
We must do it by trial and error:
We must start from the first year:
A = 1 exam
If the first year he took 1 exam, the last year he did 3, but this answer is not possible because the rule that the more the years pass, the more exams he does, is not fulfilled.
A = 2 exams
In this case, if it is true that each year increases, but it does not meet the total rule, since:
Year 1 = 2
Year 2 = 3
Year 3 = 4
Year 4 = 5
Year 5 = 6
2 + 3 + 4 + 5 + 6 = 20
A = 3 exams
Therefore the fifth year would be 9, therefore it would be:
Year 1 = 3
Year 2 = 4
Year 3 = 5
Year 4 = 6
Year 5 = 9
3 + 4 + 5 + 6 + 9 = 27
This means that we are missing 4 units to reach 31, therefore we must add 4 units between years 2, 3 and 4, but always bearing in mind that each year should increase with respect to the previous one.
If we add 2 exams to year 4, 1 exams to year 3 and 1 exam to year 2, we would have the following results:
Year 1 = 3
Year 2 = 5
Year 3 = 6
Year 4 = 8
Year 5 = 9
3 + 5 + 6 + 8 + 9 = 31
Which means that in the fourth year he took 8 exams