Gmat_mission wrote:For a recent play performance, the ticket prices were $25 per adult and $15 per child. A total of 500 tickets were sold for the performance. How many of the tickets sold were for adults?
(1) Revenue from ticket sales for this performance totaled $10,500.
(2) The average (arithmetic mean) price per ticket sold was $21.
[spoiler]OA=D[/spoiler]
Source: Official Guide
Target question: How many of the tickets sold were for adults?
Given: A total of 500 tickets were sold for the performance
Let C = # of child tickets sold
Let A = # of adult tickets sold
So,
C + A = 500
Statement 1: Revenue from ticket sales for this performance totaled $10,500
In other words,
25A + 15C = 10,500
When we add our given equation,
C + A = 500, we can see that we have a system of 2 different linear equations with 2 variables.
Since we COULD solve this system for A, we COULD answer the
target question with certainty.
So statement 1 is SUFFICIENT
Statement 2: The average (arithmetic mean) price per ticket sold was $21.
We'll use this fact:
average of n numbers = (sum of the n numbers)/n
Rearrange to get
sum of the n numbers = (average of n numbers)(n)
If 500 tickets were sold and the average ticket price was $21, then the sum of all tickets sold = (21)(500) = $10,500
IMPORTANT: Statement 2 is just another way of telling us that the total revenue from ticket sales was $10,500 (this is
exactly what statement 1 told us)
Since statement 1 was SUFFICIENT, statement 2 must also be SUFFICIENT
Answer: D
Cheers,
Brent
