Alex took 31 exams for 5 years studying at the MaPhAs University. Each year, he took more exams than the previous year. During his 5th year, he took three times as many exams as in the 1st year. How many exams did Alex take during his 4th year at the university?

The fourth year he took 8 exams

Step-by-step 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