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When tickets to a popular concert went on sale, a group of f [#permalink]

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04 Jun 2014, 05:26

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When tickets to a popular concert went on sale, a group of five friends collectively purchased a total of 30 tickets. If no two friends purchased the same number of tickets, did any one friend purchase at least nine tickets?

(1) Among the five friends, the median number of tickets purchased exceeded the mean number of tickets purchased.

(2) One of the five friends purchased exactly three tickets.

When tickets to a popular concert went on sale, a group of five friends collectively purchased a total of 30 tickets. If no two friends purchased the same number of tickets, did any one friend purchase at least nine tickets?

Let the number of tickets purchased be a, b, c, d, and e, where \(a<b<c<d<e\) and \(a+b+c+d+e=30\). The question asks whether \(e\geq{9}\).

(1) Among the five friends, the median number of tickets purchased exceeded the mean number of tickets purchased. The mean number of tickets is 30/5=6 and the median number of tickets is the middle term, c. Hence we are told that \(c>6\). This implies that the least value of c is 7, the least value of d is 8 and the least value of e is 9: \(e\geq{9}\). Sufficient.

(2) One of the five friends purchased exactly three tickets. If \(a=3\) and \(e<9\), then the maximum possible sum is 3+5+6+7+8=29<30. So, this case is not possible. If b or c is 3 and \(e<9\), the maximum is even less than that. Therefore e must be more than or equal to 9. Sufficient.

Re: When tickets to a popular concert went on sale, a group of f [#permalink]

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11 Aug 2017, 23:16

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