# SAT Math Multiple Choice Question 868: Answer and Explanation

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**Question: 868**

**13.** Five numbers are given by the expressions *x*, 2*x* - 3, 2*x* + 1, 3*x* - 4, and 3*x* + 1. If the average (arithmetic mean) of these numbers is 10, what is the mode ofthe numbers?

- A. 10
- B. 11
- C. 12
- D. There is not enough information to determine the value of the mode.

**Correct Answer:** B

**Explanation:**

**B**

**Difficulty:** Hard

**Category:** Problem Solving and Data Analysis / Statistics and Probability

**Strategic Advice:** Try not to overthink a question like this-instead, use what you know about finding an average and see where that takes you.

**Getting to the Answer:** The average of a set of values is the sum of the values divided by the number of values. Use this definition along with the average given in the question (10) to solve for *x*:

Now, substitute 5 for *x* in each of the expressions: 5, 2(5) - 3, 2(5) + 1, 3(5) - 4, and 3(5) + 1 give the numbers 5, 7, 11, 11, and 17. The *mode* of a data set is the number that occurs most often, which in this case is 11. This means (B) is correct.