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

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:

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