rahuldev31 wrote:
Of the 20 people who each purchased 2 tickets to a concert, some used both tickets, some used only 1 ticket, and some
used neither ticket. What percent of the tickets that were purchased by the 20 people were used by those people?
(1) Of the 20 people, 10 used only 1 ticket.
(2) Of the 20 people, 4 used neither ticket.
We can create the following formula:
Total people = # who only used only 1 ticket + # who used both tickets + # who used neither ticket
20 = # who only used only 1 ticket + # who used both tickets + # who used neither ticket
Since each of the 20 people bought 2 tickets, a total of 40 tickets were bought. Of course, not all tickets were used since some used only 1 ticket and some used neither ticket. We need to determine what percentage of the tickets that were purchased by the 20 people were used by those people.
Statement One Alone:Of the 20 people, 10 used only 1 ticket.
We see that the # who only used only 1 ticket is 10. However, since we know nothing about the number of people who used neither ticket, we still cannot answer the question. Statement one alone is not sufficient.
Statement Two Alone:Of the 20 people, 4 used neither ticket.
We see that the # who used neither ticket is 4. However, since we don’t know the number of people who used only 1 ticket, we still cannot answer the question. Statement two alone is not sufficient.
Statements One and Two Together:Using the information from statements one and two, we see that:
20 = 10 + # who used both tickets +4
Thus, 20 - 14 = 6 people used both tickets.
Since a total of 40 tickets were purchased and only (6 x 2) + (10 x 1) = 22 were used, the percentage of tickets purchased by the 20 people that were used is 22/40 x 100 = 11/20 x 100 = 55 percent.
Answer: C
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