Question

Tickets to a play cost 10$forchildrenand$ $25$ for adults. If $90$ tickets were sold, were more adult tickets sold than children's tickets?
(1) The average revenue per ticket was 18$.
(2) The revenue from ticket sales exceeded 1,750$

• A. Data in statement I alone is sufficient.
• B. Data in statement II alone is sufficient.
• C. Data in both statements together is sufficient.
• D. Data in both statements together is not sufficient.
• E. Either of the Statements I or II is sufficient

Answer 1

The correct option is E Either of the Statements I or II is sufficient

First things first: how would you recognize that this question is about weighted averages? The two different prices for tickets are like two different data points, and the number of tickets sold will act as the weight.

You can use weighted averages to work through the statements. Statement (1) may seem familiar by now: 18$iscloserto$ $25$ than to 10$. That means that there must have been more adult tickets sold than children's tickets. Statement 1 is sufficient. Cross off answers (B), (C), and (E) on your grid.

Statement (2) says that the total revenue from ticket sales exceeded 1,750$. Where did that number come from?

To figure that out, look at the information in the question stem again. Notice that the question actually told you that $90$ tickets were sold. Consider two extreme scenarios:

$90$ children's tickets sold $=90\times$10 = $900$ revenue

$90$ adult tickets sold $=90\times$25 = (100 \times $25)-(10\times$25) =$2,500-$250 = $2,250$ revenue

If there were an equal number of adult and children's tickets sold, the revenue would be an average of 900$and$ $2,250$, or 1,575$.Tha{t}^{\prime }stheconnectiontoweightedaverages.Iftherevenueisgreaterthan$ $1,750$, it is closer to 2,500$thanto$ $1,000$, which means more adult tickets must have been sold.Statement (2) is also sufficient. The correct answer is (E).