Problem Solving

In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?


a.13
b.10
c.9
d.8
e.7

qa is b

Simba,


For three sets the formula is

Total = Group1+Group2+Group3+Neither - (grp 1 &2)- (grp2 &3)-grp (3&1) - 2(grp 1 and 2 and3)

{68 = 25+25+34+0 - (grp 1 &2)- (grp2 &3)-grp (3&1) - 2(3)}

We are asked to find (grp 1 &2) + (grp2 &3) + grp(3&1)



Taking (grp 1 &2)- (grp2 &3)-grp (3&1) to left hand side


(grp 1 &2)+ (grp2 &3)+grp (3&1)

= Group1+Group2+Group3+Neither-- 2(grp 1 and 2 and3)-Total
= 25 + 25 + 34 - 0 - 2(3) - 68
=10

B)

Hope this helps! Let me know if u still hv questions.