SAT Math Multiple Choice Question 519: Answer and Explanation
9. According to the American Association of University Women, the mean age of men who have a college degree at their first marriage is 29.9 years. The mean age of women with a college degree at their first marriage is 28.4 years. Which of the following must be true about the combined mean age m of all people with college degrees at their first marriage?
- A. m = 29.15
- B. m > 29.15
- C. m < 29.15
- D. 28.4 < m < 29.9
Correct Answer: D
Category: Problem Solving and Data Analysis / Statistics and Probability
Strategic Advice: In order to calculate the combined mean age, you would need to know how many men and how many women there are in their respective groups, which is not provided in the question.
Getting to the Answer: Because the mean ages are different and you do not know how many men or women have college degrees and get married, you need to reason logically to arrive at the correct answer. The mean age of the women is lower than that of the men, so the combined mean cannot be greater than or equal to that of the men. Similarly, the mean age of the men is greater than that of the women, so the combined mean cannot be less than or equal to the mean age of the women. In other words, the combined mean age must fall somewhere between the two means, making (D) correct.