Viddar wrote:A certain student sold exactly 40% of all the tickets sold for a raffle, and exactly 10% of all ticket-holders won prizes in the raffle. If all ticket-holders purchased only one ticket, and if each ticket could win a maximum of one prize, how many tickets did the student sell?
(1) The student sold 3 winning tickets.
(2) There were 25 available prizes to be won in the raffle.
The answer is B. But the problem I'm having is what if 20 people won prizes then we have 200 tickets total. We have no statement that tells us that all prizes were won. Shouldn't the answer be Neither because of this?
Note: Always use spoiler function to hide the correct answer so that others can attempt the question.
To answer your question: For this question to be valid, we need to assume that all of the prizes were raffled off. In other words, the contest organizers didn't advertize 25 prizes and then give away only 20 of them. So, to avoid any confusion, it might be useful to add some language about this.
For the solution below, I will assume that all of the prizes were raffled off.
Target question:
How many tickets did the student sell?
We know that the student sold 40% of all tickets, so if we can determine the total number of tickets sold, then we can answer the
target question.
Statement 1: The student sold 3 winning tickets.
Even though the student sold 40% of all tickets, there is no guarantee that 40% of the winners will have purchased their winning ticket from the student. It's possible that
none of the winners purchased their winning ticket from the student, and it's possible that
all of the winners purchased their winning ticket from the student.
So, knowing that the student sold 3 winning tickets does not help us answer the
target question with certainty.
INSUFFICIENT
Statement 2: There were 25 available prizes to be won in the raffle.
We're told:
exactly 10% of all ticket-holders won prizes in the raffle.
If 25 prizes were won by 10% of all ticket-holders, there must have been 250 tickets sold in total.
Since the student sold 40% of all tickets, we know that the student sold 40% of the 250 tickets.
In other words,
the student sold 100 tickets.
SUFFICIENT
Answer =
B
Cheers,
Brent
