SAT Math Multiple Choice Question 294: Answer and Explanation

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Question: 294

9. An egg farmer packs his eggs in standard 12-hole cartons and then packs the cartons in large shipping boxes. The number of boxes needed, b, to transport c cartons of eggs can be found using the function If the carton-packing machine can pack a maximum of 4,000 cartons per day, and it does not pack partial boxes, what is the range of the function in this context?

  • A. All integers from 0 to 100
  • B. All integers from 0 to 4,000
  • C. All integers greater than or equal to 40
  • D. All integers greater than or equal to 100

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Passport to Advanced Math / Functions

Strategic Advice: The range of a function is the set of possible values of y, or output values.

Getting to the Answer: Think about the scenario-if c represents the maximum number of crates (which is 4,000), then the range can certainly never be greater than this, so eliminate C and D. Now you need to think about the meaning of range-range refers to y-values, not x-values, so substitute 4,000 for c (which represents x in this scenario) to find that the y-values must fall between 0 and 100. The range consists only of integers because the question states that the machine does not pack partial boxes.

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