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  3. Compare Quantity A and Quantity B, using additional information centered above t

Compare Quantity A and Quantity B, using additional information centered above t

游客2025-02-24  9
问题 Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices:
(A)Quantity A is greater.
(B)Quantity B is greater.
(C)The two quantities are equal.
(D)The relationship cannot be determined from the information given.
A symbol that appears more than once in a question has the same meaning throughout the question. [br] S is a set of 8 numbers, of which 4 are negative and 4 are positive.
选项
答案 D
解析 In the question, the only information you are given about the 8 numbers in set S is that 4 are negative and 4 are positive. Sets with 4 negative and 4 positive numbers can vary greatly, so it is likely that the relationship between Quantity A, the average of the numbers in S, and Quantity B, the median of the numbers in S, cannot be determined from the information given. To explore this by trial and error, consider some different sets with 4 negative and 4 positive numbers. Here are some examples.
Example 1: {-4, -3, -2, -1,1,2, 3,4}. In this case, the average of the numbers in the set is 0, and the median is also 0, so Quantity A is equal to Quantity B.
Example 2: {-100, -3, -2, -1,1, 2, 3,4}. In this case, the median of the numbers is 0, but the average of the numbers is less than 0, so Quantity B is greater than Quantity A.
Example 3: {-4, -3, -2, -1,1,2, 3,100}. In this case, the median of the numbers is 0, but the average of the numbers is greater than 0, so Quantity A is greater than Quantity B.
From the three examples, you can see that the correct answer is Choice D.
This explanation uses the following strategies.
Strategy 10: Trial and Error
Strategy 13: Determine Whether a Conclusion Follows from the Information Given
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