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Tickets to a play cost $10 for children and $25 for adults. If 90

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Tickets to a play cost $10 for children and $25 for adults. If 90  [#permalink]

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New post 30 Apr 2015, 09:08
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  75% (hard)

Question Stats:

59% (02:09) correct 41% (02:17) wrong based on 147 sessions

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Tickets to a play cost $10 for children and $25 for adults. If 90 tickets were sold, were more adult tickets sold than children's tickets?

(1) The average revenue per ticket was $18

(2) The revenue from ticket sales exceeded $1600
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Re: Tickets to a play cost $10 for children and $25 for adults. If 90  [#permalink]

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New post 01 May 2015, 15:21
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Hi Gmatdecoder,

This DS question is based on a shortcut that exists in "System math"; knowing the shortcut allows you to avoid some of the "math" involved in this prompt....

We're told a number of facts about tickets for a play:
1) Children's tickets cost $10 each and Adult's tickets cost $25 each
2) A total of 90 tickets were sold

We're asked if MORE Adult's tickets were sold than Children's tickets. This is a YES/NO question.

To start, we can create an equation using the above information:

C = number of children's tickets
A = number of adult's tickets

C+A = 90

If we're given enough information to create a second UNIQUE equation, then we'll have a "System" of equations, we'll be able to solve for C and A and we'll be able to answer the question.

Fact 1: The average revenue per ticket was $18

With the given information and this new Fact, we can create the following equation....

(10C + 25A)/90 = $18
10C + 25A = 1620

Combined with the original equation (C+A = 90), we now have a "System" and can solve for C and A (and thus answer the question).
Fact 1 is SUFFICIENT

Fact 2: The revenue from ticket sales exceeded $1600

This Fact requires a little more work AND you have to think about what the original question ASKS for.....

IF....we had 45 Children's tickets and 45 Adult tickets, the revenue would be....

45($10) + $45(25) = 450 + 1125 = $1575

Since this Fact tells us that the revenue EXCEEDED $1600, there must be MORE than 45 Adult tickets. As such, however many actual Adult tickets there are, there MUST be more than 45, so there must be FEWER than 45 Children's tickets. This means that the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer:

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Re: Tickets to a play cost $10 for children and $25 for adults. If 90  [#permalink]

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New post 30 Apr 2015, 09:21
Answer straight D.

Let the number of children's tickets be x and no of adults ticket be y.

From the question.

X+Y=90;

10x+18Y / x+y =18 ( you can say which one is bigger X or Y)


10X + 25=1600; X+Y=90. (you can tell the answer)


Hence both are sufficient to answer the question.


Gmatdecoder wrote:
Tickets to a play cost $10 for children and $25 for adults. If 90 tickets were sold, were more adult tickets sold than children's tickets?

1) The average revenue per ticket was $18

2) The revenue from ticket sales exceeded $1600
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Re: Tickets to a play cost $10 for children and $25 for adults. If 90  [#permalink]

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New post 04 May 2015, 06:25
Hi Rich,

For statement 2, I solved it this way
Using the same parameters as yours above

10C + 25A> 1600 -------eqn1

and C+A = 90, therefore we can say C=90-A

substituing this into the equation 1, we have
10 (90-A) +25A > 1600
900 - 10A +25A > 1600 -------> 15A> 700 ------> A>46.
And this answers the target question...A > C
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Re: Tickets to a play cost $10 for children and $25 for adults. If 90  [#permalink]

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New post 04 May 2015, 14:38
Hi Tmoni26,

Yes, that method absolutely works too. In DS questions, It's important to do whatever work is necessary to PROVE that you're correctly answering the question that is ASKED. You'd be amazed how often Test Takers just stop working and assume that a Fact is sufficient or insufficient based on an 'instinctual response' without realizing that they might be wrong. As long as you continue to do the necessary work, you'll find that there are often a variety of ways to get to the correct answer.

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Re: Tickets to a play cost $10 for children and $25 for adults. If 90  [#permalink]

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New post 24 Apr 2016, 17:03
this is a weighted average problem

so the dollar values for tickets are $10 dollars for children and $25 dollars for adults, the questions is if there were more adult tickets sold.

stmt1 says that the average revenue per ticket is $18 dollars, that means that the (18-10 = 8 , 25 -18 = 7) the number of adult tickets is closer to the average value of tickets ($18) so the answer is yes there are more number of adult tickets sold. Suff!

stmt2 says that the revenue exceeds $1,750. Use extremes meaning $10 * 100 = $1,000 and $25 * 100 = $2,500. Again you can see that $2,500 - $1,750 = $750 is closer to the Adults than $2,500 - $1,000 = $1,500 to the children. Also see that the mean is $1,750, meaning that is the number of Adult tickets is 50 and Children is 50, then 50 * $25 + 50 *10 = $1,750. This means that if the gross revenue from selling these tickets is more than $1,750, there must more Adult tickets sold out. Suff!

Answer is D.
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Re: Tickets to a play cost $10 for children and $25 for adults. If 90  [#permalink]

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Re: Tickets to a play cost $10 for children and $25 for adults. If 90   [#permalink] 31 Aug 2017, 22:25
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