Of 300 surveyed students, 20% of those who read book A also read book B and 50% of those who read ...
Of 300 surveyed students, 20% of those who read book A also read book B and 50% 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?
Answer/Solution
150
Steps/Work
Say the number of students who read book A is A and the number of students who read book B is B.
Given that 20% of those who read book A also read book B and 50% of those who read book B also read book A, so the number of students who read both books is 0.2A=0.5B --> A=2.5B.
Since each student read at least one of the books then {total}={A}+{B}-{Both} --> 300=2.5B+B-0.5B --> B=100, A=2.5B=250 and {Both}=0.5B=50.
The number of students who read only book A is {A}-{Both}=250-50=200;
The number of students who read only book B is {B}-{Both}=100-50=50;
The difference is 200-50=150.
Answer: E.
Given that 20% of those who read book A also read book B and 50% of those who read book B also read book A, so the number of students who read both books is 0.2A=0.5B --> A=2.5B.
Since each student read at least one of the books then {total}={A}+{B}-{Both} --> 300=2.5B+B-0.5B --> B=100, A=2.5B=250 and {Both}=0.5B=50.
The number of students who read only book A is {A}-{Both}=250-50=200;
The number of students who read only book B is {B}-{Both}=100-50=50;
The difference is 200-50=150.
Answer: E.