Logic puzzle with well-explanned solution

2) 52 people discuss their preference for two products A and B, among others, and it is concluded that the number of people who liked B was:

I - Four times the number of people who liked A and B;

II - Twice the number of people who liked A;

III - Half the number of people who liked neither A nor B. Under these conditions, the number of people who disliked both products is equal to:

*a)48

b)35

c)36

d)47

e)37

Translated with DeepL.com (free version)

Original:

2) 52 pessoas discutem a preferência por dois produtos A e B, entre outros e conclui-se que o número de pessoas que gostavam de B era:

I - O quádruplo do número de pessoas que gostavam de A e B;

II - O dobro do número de pessoas que gostavam de A;
III - A metade do número de pessoas que não gostavam de A nem de B.Nestas condições, o número de pessoas que não gostavam dos dois produtos é igual a:

*a)48
b)35
c)36
d)47
e)37

1) collecting the info

1st the universe of the problem

2) Making the sets

3) the Method to simplify the resolution isn't just use letters to the unkown values but reference each unknow value and before named the next solve and dismiss the letter of the unknow to we have always only one letter for all the unknow values.

So in the previous frame we have x and y unknow values and know we gonna have only one letter one value will be y and the other 3y.

The next we gonna compare using another value for the next sentence and once solved we gonna replace the z by the value y.

After we gonna solve of the same way the next setence giving an letter k to compare and coming to the conclusion that k is 8y.

Know we have all the values with one letter with relative comparision,that we know that the universe is 42, so the only unknow letter is 4 but we want all less the intersection of the two groups that is 42 less the center that being y that is 4 the answer is would be 38.

Rute Bezerra de Menezes Gondim

Rute Bezerra de Menezes Gondim