Hi! Could you please help me solve this by minimizing and maximizing the solutions?
Set A has 50 members and Set B has 53 members. At least 2 of the members in Set A are not in Set B. Which of the following could be the number of members in Set B that are not in Set A?
A. 3
B. 5
C. 13
D. 25
E. 50
F. 53
Extreme 1 – Minimal case (maximum overlap):
Only 2 members of A are not in B → So, 48 members are shared between A and B.
Therefore, the intersection |A ∩ B| = 48.
Set B has 53 members, so:
The number of members in Set B that are not in Set A = 53 −∣𝐴∩𝐵∣
= 53 − 48
= 5
So 5 is possible.
Extreme 2 – No overlap (minimal intersection):
All members of A are not in B → A and B are disjoint.
Then, |A ∩ B| = 0, so:
The number of members in Set B that are not in Set A = 53 − 0
= 53
So 53 is possible too.
Among the answer choices, the values that fall in this range are:
B, C, D, E, F