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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. [Searched, but unable to find the old post if there is any]
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Re: A museum sold 30 tickets on Saturday [#permalink]
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11 Jun 2012, 08:37
Hi,
let there be x tickets sold at $10, so, the tickets sold at $70 would be (30x). and total revenue would be: $10(x)+$70(30x)
Using (1) 1570 < 10(x)+70(30x) < 1670 or 1570 < 10x + 2100  70x < 1670 or 15702100 < 60x < 16702100 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 < 30x < 25 or 10 < x < 5 or 5 < x <10, thus, x = 6, 7, 8, 9 Clearly, not sufficient.
Thus, Answer is (A).
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Re: A museum sold 30 tickets on Saturday [#permalink]
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11 Jun 2012, 09:03
i did following: General=G Special=S G+S =30 70*S+ 30*G= Revenue
Statement 1: 1570<Revenue<1670
70*S+70*G=2100 70*S+ 30*G= 1660 [Within the range]
40G=440 G=11
70*S+70*G=2100 70*S+ 30*G= 1620 [Within the range]
40G= 480 G=12
I am having multiple integer value for General tickets G[11, 12]. What am i doing wrong?



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Re: A museum sold 30 tickets on Saturday. Some of the tickets [#permalink]
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11 Jun 2012, 09:04
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 \(30G\) special exhibit tickets, then the museum's total revenue wold be \(10G+70(30G)=210060G\). (1) The museum’s total revenue from ticket sales on Saturday was greater than $1,570 and less than $1670 > \(1570<210060G<1670\) > \(530<60G<430\) > 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.
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Re: A museum sold 30 tickets on Saturday [#permalink]
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11 Jun 2012, 09:14



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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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13 Mar 2016, 09:16
Excellent Question.. Does anyone have a list of such questions? Word problems based on inequality..
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Re: A museum sold 30 tickets on Saturday. Some of the tickets [#permalink]
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03 Mar 2017, 12:50
Posting official solution of this problem.
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Re: A museum sold 30 tickets on Saturday. Some of the tickets
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