Bunuel wrote:
Every man in a certain class either belongs to group A, belongs to group B, or belongs to both groups. 20% of group A consists of men and 65% of group B consists of men. What percentage of the two groups together is made up of men?
(1) Group A contains 50 people.
(2) Group B contains 100 people.
Kudos for a correct solution.
i drew a double matrix chart..
A-> not A
B
Not B
we know that 0.2A = men
we know that 0.65B = men
now..statement 1 tells that A=50. so 10 are men. nothing about the group B or how many men are in both groups.
statement 2 - tells that B=100, or that 65 from group B are men, but nothing about A or how many men are in both groups.
1+2:
since we dont know how many men are in both groups, we can have 2 or even more cases, but I took the extremities:
all 10 men from A are in B as well - total number of men = 65
all 10 men from A are not in B - total number of men = 75.
but!!!
even if we knew how many men are in total, we DO NOT KNOW how many people are in total.
thus, we can have 116 total people, or we can have 117 total people, or 118, or 119.
so as we can see, even together, we cannot answer the question.