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11 Aug 2021, 04:00
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
46% (02:55) correct
54%
(02:25)
wrong
based on 162
sessions
History
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A children’s theater sells tickets to a show. Tickets for children cost $10 and tickets for adults cost $35. If ticket revenues from the last performance were $390, and everyone at the performance had a ticket, how many people were at the performance?
(1) The number of children was more than 3 times the number of adults.
(2) The maximum capacity of the theater is 32 seats.
(1) The number of children was more than 3 times the number of adults.
(2) The maximum capacity of the theater is 32 seats.
14 Aug 2021, 17:12
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Bunuel
Set the number of children as C and the number of adults as A. Then we have \(10C + 35A = 390\). We need only one more linear independent equation for sufficiency.
Statement 1:
C > 3A. One such solution is (C, A) = (39, 0). We can exchange 7 C with 2 A so another possible solution would be (C, A) = (32, 2) or (25, 4). Note the next possible solution in line is (18, 6), which does not satisfy C > 3A. Insufficient.
Statement 2:
Insufficient.
Combined:
We can eliminate (C, A) = (39, 0) and (32, 2). The only viable solution left is (C, A) = (25, 4). Sufficient.
Ans :C
14 Jul 2024, 23:12
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I got it wrong because I assumed
1. "everyone at the performance had a ticket" as housefull. No, it just means no one was ticketless.
2. Children were more than 3 times and not 3 times of the adult.
1. "everyone at the performance had a ticket" as housefull. No, it just means no one was ticketless.
2. Children were more than 3 times and not 3 times of the adult.
