Official Guide Explanation:
Data Sufficiency #14

Background

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Solution and Metadata

Question: 14
Page: 154
Difficulty: 4 (Moderately Easy)
Category 1: Word Problems > Other >
Category 2: Arithmetic > Descriptive Statistics > Average
Category 3: Algebra > Linear Equations-Two Unk >

Explanation: This is a common Data Sufficiency question structure. There are two types of tickets, a total number of tickets, and a price for each sort of ticket. Say the number of adult tickets sold is a, the number of child tickets sold is c, and the total cost of the tickets is x. Thus:

25a + 15c = x

a + c = 500

That isn't enough to solve, but if we find the value of one of those three variables, we will reduce the question to two variables and two linear equations, which is sufficient to solve.

Statement (1) is sufficient. It gives us x, so the two equations only have a and c. We can solve a system of two linear equations with two variables.

Statement (2) is also sufficient. It doesn't directly tells us any of the variables, but if the average ticket price is $21, we can calculate the total revenue from ticket sales. We know that 500 tickets were sold, so x = 500(21). No need to solve for that (though it is easy, since it needs to be the same number as that given in (1)); it's enough to recognize that we can solve the problem. Choice (D) is correct.

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