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A museum sold 30 tickets on Saturday. Some of the tickets [#permalink]

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11 Jun 2012, 08:14

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A museum sold 30 tickets on Saturday. Some of the tickets sold were $10 general exhibit tickets and the rest were $70 special exhibit tickets. How many general exhibit tickets did the museum sell on Saturday?

(1) The museum’s total revenue from ticket sales on Saturday was greater than $1,570 and less than $1670. (2) The museum sold more than 20, but fewer than 25, special exhibit ticket on Saturday.

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Re: A museum sold 30 tickets on Saturday [#permalink]

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11 Jun 2012, 08:37

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Hi,

let there be x tickets sold at $10, so, the tickets sold at $70 would be (30-x). and total revenue would be: $10(x)+$70(30-x)

Using (1) 1570 < 10(x)+70(30-x) < 1670 or 1570 < 10x + 2100 - 70x < 1670 or 1570-2100 < -60x < 1670-2100 or -530 < -60x < -430 (multiply by -1) or 430 < 60x < 530 or 7.16 < x < 8.33, since x is integer and only one value exist between 7.1 & 8.3, i.e., 8 thus, x=8. Sufficient.

Using (2), 20 < special exhibit ticket < 25 or 20 < 30-x < 25 or -10 < -x < 5 or 5 < x <10, thus, x = 6, 7, 8, 9 Clearly, not sufficient.

A museum sold 30 tickets on Saturday. Some of the tickets sold were $10 general exhibit tickets and the rest were $70 special exhibit tickets. How many general exhibit tickets did the museum sell on Saturday?

Say the museum sold \(G\) general exhibit tickets and \(30-G\) special exhibit tickets, then the museum's total revenue wold be \(10G+70(30-G)=2100-60G\).

(1) The museum’s total revenue from ticket sales on Saturday was greater than $1,570 and less than $1670 --> \(1570<2100-60G<1670\) --> \(-530<-60G<-430\) --> reduce by -10 and flip the sign: \(43<6G<53\) --> since \(G\) must be an integer then \(G=8\). Sufficient.

(2) The museum sold more than 20, but fewer than 25, special exhibit ticket on Saturday --> \(20<S<25\) --> \(S\) could be be 21, 22, 23 or 24, so \(G\) could be 9, 8, 7, or 6 respectively. Not sufficient.

Re: A museum sold 30 tickets on Saturday. Some of the tickets [#permalink]

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12 Jun 2015, 03:39

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Re: A museum sold 30 tickets on Saturday. Some of the tickets [#permalink]

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05 Oct 2017, 09:37

Bunuel wrote:

A museum sold 30 tickets on Saturday. Some of the tickets sold were $10 general exhibit tickets and the rest were $70 special exhibit tickets. How many general exhibit tickets did the museum sell on Saturday?

Say the museum sold \(G\) general exhibit tickets and \(30-G\) special exhibit tickets, then the museum's total revenue wold be \(10G+70(30-G)=2100-60G\).

(1) The museum’s total revenue from ticket sales on Saturday was greater than $1,570 and less than $1670 --> \(1570<2100-60G<1670\) --> \(-530<-60G<-430\) --> reduce by -10 and flip the sign: \(43<6G<53\) --> since \(G\) must be an integer then \(G=8\). Sufficient.

(2) The museum sold more than 20, but fewer than 25, special exhibit ticket on Saturday --> \(20<S<25\) --> \(S\) could be be 21, 22, 23 or 24, so \(G\) could be 9, 8, 7, or 6 respectively. Not sufficient.

Answer: A.

Hope it's clear.

But if we check only special ticket 22 with 8 general ticket fall into range as given in question...then how B is wrong

A museum sold 30 tickets on Saturday. Some of the tickets sold were $10 general exhibit tickets and the rest were $70 special exhibit tickets. How many general exhibit tickets did the museum sell on Saturday?

Say the museum sold \(G\) general exhibit tickets and \(30-G\) special exhibit tickets, then the museum's total revenue wold be \(10G+70(30-G)=2100-60G\).

(1) The museum’s total revenue from ticket sales on Saturday was greater than $1,570 and less than $1670 --> \(1570<2100-60G<1670\) --> \(-530<-60G<-430\) --> reduce by -10 and flip the sign: \(43<6G<53\) --> since \(G\) must be an integer then \(G=8\). Sufficient.

(2) The museum sold more than 20, but fewer than 25, special exhibit ticket on Saturday --> \(20<S<25\) --> \(S\) could be be 21, 22, 23 or 24, so \(G\) could be 9, 8, 7, or 6 respectively. Not sufficient.

Answer: A.

Hope it's clear.

But if we check only special ticket 22 with 8 general ticket fall into range as given in question...then how B is wrong

Are you sing info from (1) to evaluate (2)?
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