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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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New post 11 Jun 2012, 07:14
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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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New post 11 Jun 2012, 07:37
1
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, 08:03
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, 08:04
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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, 08:14
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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New post 13 Mar 2016, 08:16
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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, 11:50
Posting official solution of this problem.
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A museum sold 30 tickets on Saturday  [#permalink]

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New post 10 Sep 2018, 09:57
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 $1,670.
(2) The museum sold more than 20, but fewer than 25, special exhibit tickets on Saturday.
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A museum sold 30 tickets on Saturday  [#permalink]

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New post 10 Sep 2018, 11:56
alphak3nny001 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?

(1) The museum's total revenue from ticket sales on Saturday was greater than $1,570 and less than $1,670.
(2) The museum sold more than 20, but fewer than 25, special exhibit tickets on Saturday.

\(\left. \begin{gathered}
\$ 10/\,{\text{each}}\,\,G\,\,\, \hfill \\
\$ 70/\,{\text{each}}\,\,S \hfill \\
\end{gathered} \right\}\,\,\,\,\,G + S = 30\,\,\,\left( * \right)\,\,\,\,\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\,\,\,\,? = G\)

\(\left( 1 \right)\,\,\,1570 < 10G + 70S < 1670\)

\(10G + 70S\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,10G + 70\left( {30 - G} \right) = 60\left( {35 - G} \right)\,\,\, \Rightarrow \,\,\,{\text{multiple}}\,\,{\text{of}}\,\,60\)

\(\frac{1570}{60} = \frac{1200 + 360 + 10}{60} = 26\frac{1}{6}\)
\(\frac{1670}{60} = \frac{1200 + 420 + 50}{60} = 27\frac{5}{6}\)

\(\Rightarrow \,\,\,\,60\left( {35 - G} \right) = 27 \cdot 60\,\,\,\,\,\,\, \Rightarrow \,\,\,\,G\,\,{\text{unique}}\)

\(\left( 2 \right)\,\,\,20 < S < 25\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,20 < 30 - G < 25\,\,\,\,\, \Leftrightarrow \,\,\,5 < G < 10\,\,\,\)

\(\left\{ \begin{gathered}
G = 6\,\,\,\,\,\left( {S = 24} \right)\,\,\,\,\,\,{\text{viable}} \hfill \\
G = 7\,\,\,\,\,\left( {S = 23} \right)\,\,\,\,\,\,{\text{viable}} \hfill \\
\end{gathered} \right.\,\)


This solution follows the notations and rationale taught in the GMATH method.

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

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New post 10 Sep 2018, 20:42
alphak3nny001 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?

(1) The museum's total revenue from ticket sales on Saturday was greater than $1,570 and less than $1,670.
(2) The museum sold more than 20, but fewer than 25, special exhibit tickets on Saturday.


Merging topics. Please search before posting.
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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

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A museum sold 30 tickets on Saturday. Some of the tickets   [#permalink] 10 Sep 2018, 20:42
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A museum sold 30 tickets on Saturday. Some of the tickets

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