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

Question

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

EMPOWERgmatRichC · Accepted Answer

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:  D

GMAT assassins aren't born, they're made,
Rich

shriramvelamuri · Answer

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.

Tmoni26 · Answer

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

EMPOWERgmatRichC · Answer

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.

GMAT assassins aren't born, they're made,
Rich

lalania1 · Answer

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.

Archit3110 · Answer

let children ticket = x and adult be y
so 
x+y=90

target is y>x
#1The average revenue per ticket was $18
10x+25y/90 = 18
10x+25y = 1620
x+y=90
sufficient find y
#2

The revenue from ticket sales exceeded $1600
10x+25y>1600
x+y=90
if we have 45*10+45*25 = 450+ 1125 ; 1575 which is <1600 i.e more of adult tickets would had been sold
sufficient
OPTION D

Fdambro294 · Answer

Since we are given two data points ($price per ticket for each group) and two different groups of people ———> the concept of weighted averages comes to mind where:

Weighted Average = (Total SUM of all Revenue) / (Total Number of tickets sold)

Let A = # of adult tickets sold

Let C = # of children tickets sold

Where A + C = 90

Question: is A > C?

If we had an equal amount of children as adults, then the Overall Average Ticket Price per attendee would = Arithmetic Mean of the Ticket Prices per attendee

Arithmetic Mean = $10(1/2) + $25(1/2) = $17.50

-if the overall Weighted Average of Ticket price per attendee > $17.50 ———-> this means there must have been more Higher priced Adult tickets sold and: A > C

-if the overall Weighted Average of Ticket price per attendee < $17.50 ————> this means there must have been more LOWER Priced Children tickets sold and: A < C

Question stem becomes:

Is the Average Revenue per ticket holder > $17.50?

S1: directly answers our question YES

There must be more A tickets > C tickets sold

Sufficient alone

S2: we are told that the overall total revenue from all ticket sales must be greater than > $1600

Given that we know 90 people attended, we therefore know the following about the Weighted Average:

Average ticket revenue per attendee > ($1600) / (90)

Average ticket Revenue per attendee > $17.77777

We can answer the Re-Phrased question stem with a definite YES

D
EACH Statement alone is sufficient

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Rutvik01 · Answer

Can it be done using weighted averages?

sayan640 · Answer

Of course...

First statement
gives ,

10-------------18----------25

Hence , adult and children tickets are in the ratio of = 7:8

Adult tickets sold = 48 and childrens' tickets sold = 42

Hence answer is YES ..Statement 1 is sufficient.

Statement 2 says ,
10x + 25y > 1600 ....x= no. of children and y = no of adult
15x < 650
x< 43.33

since x+ y = 90
y=90 -43 > 47

Hence again answer is YES..Adult tickets were sold more.

D is the answer.
KarishmaB MartyMurray

Rutvik01

Can it be done using weighted averages?

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

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