SAT Math Multiple Choice Question 458: Answer and Explanation

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Question: 458

8.

Manufacturing companies typically have a number of fixed costs (such as rent, machinery, insurance, etc.), which do not depend on output, and variable costs (such as wages, utilities, materials, etc.), which vary with output, usually at a constant rate. The graph shows a company's costs for manufacturing a particular product over the course of two years. Which of the following could explain the difference between the 2013 and 2014 costs?

  • A. The company reduced its fixed costs by 50%.
  • B. The company reduced its variable costs by 50%.
  • C. The company reduced the number of units produced by 50%.
  • D. The company reduced its fixed costs, variable costs, and the number of units produced by 50%.

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Heart of Algebra / Linear Equations

Strategic Advice: This question is very conceptual. You need to understand what each part of the graph represents. The y-intercept represents the fixed costs, while the slope (the per-unit cost) represents the variable costs.

Getting to the Answer: Compare the two lines. The second line (2014) has a lower y-intercept than the first (2013), which means the company reduced its fixed costs. You don't need to worry about the 50% because all the answer choices involve this same amount. You can eliminate B and C because they don't mention fixed costs. To determine whether the variable costs changed, look at the slopes. The lines are parallel, so the slope did not change, which means the variable costs did not change. Therefore, the company only reduced its fixed costs, and (A) is correct.

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