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A museum sold 30 tickets on Saturday. Some of the tickets

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

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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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New post 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.

Thus, Answer is (A).

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

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New post 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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New post 11 Jun 2012, 09:04
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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?

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

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New post 11 Jun 2012, 09:14
BDSunDevil wrote:
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?


Revenue=70S+10G not 70S+30G.
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Re: A museum sold 30 tickets on Saturday. Some of the tickets [#permalink]

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

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New post 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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New post 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 [#permalink]

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New post 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

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

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New post 05 Oct 2017, 09:41
thunderbird350 wrote:
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


Are you sing info from (1) to evaluate (2)?
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: A museum sold 30 tickets on Saturday. Some of the tickets   [#permalink] 05 Oct 2017, 09:41
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