Logic puzzle that the solution doesn't need solve all the problem

 3) UFBA - 35 foreign students came to Brazil. 16 visited Manaus, 16 visited São Paulo and 11 visited Salvador. Of these students, 5 visited Manaus and Salvador and, of these 5, 3 also visited São Paulo. The number of students who visited Manaus or São Paulo was:

*a) 29

b) 24

c) 11

d) 8

e) 5

Original

3) UFBA - 35 estudantes estrangeiros vieram ao Brasil. 16 visitaram Manaus; 16, S. Paulo e 11, Salvador.Desses estudantes, 5 visitaram Manaus e Salvador e , desses 5, 3 visitaram também São Paulo. O númerode estudantes que visitaram Manaus ou São Paulo foi:

*a) 29
b) 24
c) 11
d) 8
e) 5

First the Universe of the problem is gaved;

after collect the informations;

after construct the system of the groups or sets;

and the first operation with the info of the intersection of the 3 groups and the intersection of two of the 3.

The solution of the intersections are place in the system of groups;

now using letters for the unknow values but of a intelligent way, this make so much easier the solution, if you don't do that way probably will gonna fall in the dificult of the problem, the solution isn't solve but find one information that you can find with 2 unknow values;

right  to the 2nd part of the solution, with what is find find the z that is the people that visit only SP, the SP is in the bottom because in the problem is the last to be solved only in the 2nd part of the problem, so is in the bottom because will be the last to be solved, you see already in the beggining that SP will be solved and and the Manaus and Salvador would be only operated and previously to find the SP that is unique.

Know to the climax of the problem that is with the Universe you came to one conclusion the problem isn't to solve and you gonna read what is asked to know what is the information that is asked that is one that can be finded without the solution of the problem and is asked the Union of SP and Manaus so you see that I didn't knew what is "a" or "x" they will be used like I find an sum, because is that what is asked "x+a(that is 11)" + "z(that I find that is 13)" + 5 = 29

Of course is good know and not only apply, a is the intersection of SP with Man. less the 3 that will be sum, and 2 is the intersection of the Man. but is used because is part of Man. so no problem of be part of Salv. its count because is Manaus also.

Rute Bezerra de Menezes Gondim