AAPL wrote:Manhattan Prep

A children's theater sells tickets to a show. Tickets for children cost $10 and tickets for adults cost $35. If ticket revenues from the last performance were $390, and everyone at the performance had a ticket, how many people were at the performance?

1) The number of children was more than 3 times the number of adults.
2) The maximum capacity of the theater is 32 seats.
OA C

Given: Tickets for children cost $10 and tickets for adults cost $35. Ticket revenues from the last performance were $390
Let A = # of adults in attendance
Let C = # of children in attendance
So, we can write: 35A + 10C = 390
Since A and C must be POSITIVE INTEGERS, there are not many possible solutions to the above equation. So, let's list all possible solutions:
a) A = 0 and C = 39
b) A = 2 and C = 32
c) A = 4 and C = 25
d) A = 6 and C = 18
e) A = 8 and C = 11
f) A = 10 and C = 4

Target question: How many people were at the performance?
This is a good candidate for rephrasing the target question.
REPHRASED target question: What is the value of A + C?
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Statement 1: The number of children was more than 3 times the number of adults.
So, we can write: C > 3A
When we examine the 6 possible solutions, we see that only solutions b and c satisfy statement 1.
Solution b: If A = 2 and C = 32, then the answer to the REPHRASED target question is A + C = 2 + 32 = 34
Solution c: If A = 4 and C = 25, then the answer to the REPHRASED target question is A + C = 4 + 25 = 29
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The maximum capacity of the theater is 32 seats.
In other words, A + C ≤32
When we examine the 6 possible solutions, we see that solutions c, d, e and f satisfy statement 2.
Solution c: If A = 4 and C = 25, then the answer to the REPHRASED target question is A + C = 4 + 25 = 29
Solution d: If A = 6 and C = 18, then the answer to the REPHRASED target question is A + C = 6 + 18 = 24
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that solutions b and c are possible
Statement 2 tells us that solutions c, d, e and f are possible
Since only solution c satisfies BOTH statements, it MUST be the case that A = 4 and C = 25, in which case, the answer to the REPHRASED target question is A + C = 4 + 25 = 29
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent