Bunuel wrote:
Of 200 surveyed students, 20% of those who read book \(A\) also read book \(B\) and 25% of those who read book \(B\) also read book \(A\). If each student read at least one of the books, what is the difference between the number of students who read only book \(A\) and the number of students who read only book \(B\)?
A. 20
B. 25
C. 30
D. 35
E. 40
My technique may not be the most accurate but this was logical to me in understanding while I was going through the complex solutions above
20% of A is 25% of B.
Think this way, out of the 200 students there are those who read A and those who read B and those who read both,
Lets name them Group X who read book A and Group Y who read book B. Since there are only 2 books we are talking about.
In both the groups there are students who also like to read the other groups book apart from their own group.
WHEN I SAY A & B I AM REFERRING TO THE BOOKS A & B
Group X
80% only A,
20% A+BGroup Y
75% only B,
25% A+BThe number that is highlighted should be same for both groups.
Lets take :
X=100
80% of X is 80 ; 20% is 20 which is also 25% of Y so,
25% of Y is 20 ; 75% is 60 which makes 80
So total is 180 but we want 200
X=120
80% of X is 96 ; 20% is 24 which makes Y=80 because total should be 200
25% of Y is 20 ; This does not match because look at the highlighted part above,
it has to be the same number of studentsX=125
80% of X is 100 ; 20% is 25 ( now ask 25 is 25% of what?) 100 right
75% of Y is 75 ; 25% is 25 (its a match)
Therefore 100 who read only A -75 who read only B =25
P.S. This is just meant for understanding since it takes a lot of time while doing it in actual.