How many have at least one brother and one sister

Question

35 students in a class.  18 have at least one brother.  16 have at least 1 sister.  7 have no brothers or sisters.  How many have both a brother and a sister.  How do you set this up to solve for answer.  Need both how to set up and answer.  Thanks,

Answer 1

Hi Lenny,

 

What this question is asking is how much overlap there is between the group with a brother and the group with a sister.

 

Out of the 35 students, 7 have no sibling, so you can ignore them.

35-7 = 28

 

Out of the remaining 28 students, 18 have a brother.

28-18 = 10 students do NOT have a brother (but must have a sister, since we already removed the students with no siblings at all.)

 

This means that out of the 16 students that have a sister, 10 of them do not have a brother. Therefore 16-10=6 of them must have both a brother and a sister.