SAT Math Multiple Choice Question 460: Answer and Explanation

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Question: 460

10. Premature babies are typically born underweight and are cared for in a neonatal intensive care unit (NICU). At a certain NICU, the mean weight of all the male babies is 4 pounds, and the mean weight of all the female babies is 3.6 pounds. Which of the following must be true about the mean weight w of the combined group of male and female babies at this NICU?

  • A. w = 3.8
  • B. w > 3.8
  • C. w < 3.8
  • D. 3.6 < w < 4

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Problem Solving and Data Analysis / Statistics and Probability

Strategic Advice: To calculate the combined mean weight, you would need to know how many male babies and how many female babies there are in their respective groups, which is not provided in the question.

Getting to the Answer: Because the mean weights are different and you do not know how many male or how many female babies there are in the NICU, you need to reason logically to arrive at the correct answer. The mean weight of the female babies is lower than that of the male babies, so the combined mean cannot be greater than or equal to that of the male babies. Similarly, the mean weight of the male babies is greater than that of the female babies, so the combined mean cannot be less than or equal to the mean weight of the female babies. In other words, the combined mean weight must fall somewhere between the two means, making (D) correct.

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