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Of the 20 people who each purchased 2 tickets to a concert [#permalink]
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13 Feb 2017, 07:36
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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. Can this be solved using Overlapping sets instead of double matrix?
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Re: Of the 20 people who each purchased 2 tickets to a concert [#permalink]
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13 Feb 2017, 07:50
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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.
Can this be solved using Overlapping sets instead of double matrix? 20 people who each purchased 2 tickets, so there are total 40 tickets. Of 20 people, some used both tickets, some used only 1 ticket, and some used 0 ticket. (1) 10 people used only 1 ticket, but we can't know how many people who used both and how many people who used neither. Insufficient. (2) 4 people used neither, so 16 remainings used both or only 1. We still don't know how many people who used only 1 and how many people who used both. Insufficient. Combine (1) and (2) we have 4 used neither, 10 used only 1 so remaining 6 used both. Since that, we can deduce the number of used ticket. Sufficient.
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Re: Of the 20 people who each purchased 2 tickets to a concert [#permalink]
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13 Feb 2017, 08:12
nguyendinhtuong wrote: 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.
Can this be solved using Overlapping sets instead of double matrix? 20 people who each purchased 2 tickets, so there are total 40 tickets. Of 20 people, some used both tickets, some used only 1 ticket, and some used 0 ticket. (1) 10 people used only 1 ticket, but we can't know how many people who used both and how many people who used neither. Insufficient. (2) 4 people used neither, so 16 remainings used both or only 1. We still don't know how many people who used only 1 and how many people who used both. Insufficient. Combine (1) and (2) we have 4 used neither, 10 used only 1 so remaining 6 used both. Since that, we can deduce the number of used ticket. Sufficient. Thank you. The only confusing part is " What percent of the tickets that were purchased by the 20 people were used by those people?" So I interpret (1 ticket used + Both) /Total. Since option (2) gives us number of neither used, remaining must have been used. But obviously I'm misinterpreting something cuz C is the right answer



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Re: Of the 20 people who each purchased 2 tickets to a concert [#permalink]
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13 Feb 2017, 08:14
Bunuel, whats your take on this?



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Re: Of the 20 people who each purchased 2 tickets to a concert [#permalink]
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13 Feb 2017, 08:31
rahuldev31 wrote: Bunuel, whats your take on this? 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?Say: x people used both tickets; y people used one ticket; z people used 0 tickets. x + y + z = 20. What percent of the tickets that were purchased by the 20 people were used by those people: (2x + y)/40 = ? (1) Of the 20 people, 10 used only 1 ticket > y = 10. Not sufficient. (2) Of the 20 people, 4 used neither ticket > z = 4. Not sufficient. (1)+(2) y = 10 and z = 4 > x = 6 > (2x + y)/40 = 22/40 = 0.55. Sufficient. Answer: C.
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Re: Of the 20 people who each purchased 2 tickets to a concert [#permalink]
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13 Feb 2017, 10:07
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.
Can this be solved using Overlapping sets instead of double matrix? S1: 10 used 1 ticket but we don't know how many tickets each of the other 10 used.....INSUFFICIENT S2: 4 used neither ticket but we don't know how many tickets each of the other 16 used.....INSUFFICIENT S1+S2: 10 buy 1 = `10*1 =10 4 buy 0 =0*4=0 therefore, 6 buy 2 = 6*2 =12.....SUFFICIENT...SO C



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Re: Of the 20 people who each purchased 2 tickets to a concert [#permalink]
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13 Feb 2017, 18:42
rahuldev31 wrote: Thank you. The only confusing part is " What percent of the tickets that were purchased by the 20 people were used by those people?"
So I interpret (1 ticket used + Both) /Total. Since option (2) gives us number of neither used, remaining must have been used. But obviously I'm misinterpreting something cuz C is the right answer The question is like this: 20 people purchased total 40 tickets. What percent of these 40 tickets that were used by those 20 people. In (2), we know the number of people who used neither, then yes we know the total number of people who used only 1 or both. However, the question is asking the percent of tickets, not the percent of people. Hence, we need to know the specific number of people who used only 1 ticket and the specific number who used both. Hope this helps.
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Re: Of the 20 people who each purchased 2 tickets to a concert [#permalink]
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14 Feb 2017, 01:32
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.
Can this be solved using Overlapping sets instead of double matrix? misread the question and thought that not all purchased 2 ticket rather some have purchased ...so landed to E its C...



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Re: Of the 20 people who each purchased 2 tickets to a concert [#permalink]
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14 Feb 2017, 16:02
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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Re: Of the 20 people who each purchased 2 tickets to a concert [#permalink]
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14 Feb 2017, 19:06
rahuldev31 wrote: nguyendinhtuong wrote: 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.
Can this be solved using Overlapping sets instead of double matrix? 20 people who each purchased 2 tickets, so there are total 40 tickets. Of 20 people, some used both tickets, some used only 1 ticket, and some used 0 ticket. (1) 10 people used only 1 ticket, but we can't know how many people who used both and how many people who used neither. Insufficient. (2) 4 people used neither, so 16 remainings used both or only 1. We still don't know how many people who used only 1 and how many people who used both. Insufficient. Combine (1) and (2) we have 4 used neither, 10 used only 1 so remaining 6 used both. Since that, we can deduce the number of used ticket. Sufficient. Thank you. The only confusing part is " What percent of the tickets that were purchased by the 20 people were used by those people?" So I interpret (1 ticket used + Both) /Total. Since option (2) gives us number of neither used, remaining must have been used. But obviously I'm misinterpreting something cuz C is the right answer Hi Rahul, For finding percentage you require the count of tickets utilised and not the count of people. Option 2 gives us the count of people who have utilised the tickets. Out of 16, the breakup of number of people who utilized 2 tickets and the number of people who utilised 1 ticket is not provided.The total number of tickets used depends on this. Only after getting this value can we calculate the percantage of used tickets using formula(Total used tickets/40).




Re: Of the 20 people who each purchased 2 tickets to a concert
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