Bunuel wrote:
Each of 20 parents chose one of five days from Monday through Friday to attend parent-teacher conferences. If more parents chose Monday than Tuesday, did at least one of the parents choose Friday?
(1) None of the five days was chosen by more than 5 parents.
(2) More parents chose Monday than Wednesday.
Target question: Did at least one parent choose Friday? Given: ]There are 20 parents. More parents chose Monday than Tuesday Statement 1: None of the five days was chosen by more than 5 parents. I'll show that statement 1 implies that is it impossible that ZERO parents chose Friday.
In order to MINIMIZE the number of parents who chose Friday, let's MAXIMIZE the other days the parents could have chosen.
So, let's say 5 parents chose Monday, 5 parents chose Wednesday, and 5 parents chose Thursday. Since more parents chose Monday than Tuesday, the maximum number of parents who chose Tuesday is 4.
5 + 5 + 5 + 4 = 19.
So, even though we have MAXIMIZED the number of parents who chose Monday, Tuesday, Wednesday and Thursday, we still have 1 parent remaining. So, this parent MUST have selected Friday.
Since we have shown it is impossible that ZERO parents chose Friday, we can conclude that
AT LEAST one parent chose Friday Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: More parents chose Monday than Wednesday There are several scenarios that satisfy statement 2. Here are two:
Case a: 12 chose Monday, 7 chose Wednesday and 1 chose Friday. In this case,
AT LEAST one parent chose FridayCase b: 12 chose Monday and 8 chose Wednesday. In this case,
ZERO parents chose FridaySince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: