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## Official Guide Explanation:

Data Sufficiency #14

**Background**

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

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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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