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  3. For each of Questions 1 to 9, compare Quantity A and Quantity B, using additiona

For each of Questions 1 to 9, compare Quantity A and Quantity B, using additiona

游客2025-02-24  20
问题 For each of Questions 1 to 9, compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices and fill in the corresponding oval to the right of the question.
(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]
选项
答案 D
解析 Two approaches that you could use to solve this problem are:
    1: Translate from algebra to a number line.
    2: Plug in values for the variables.
    Approach 1: The following figure represents the information given in the problem on a number line.

    On the number line, 1 - y is the distance between 1 and y, and y — x is the distance between y and x. If y is exactly halfway between x and 1, then 1 -y is equal to y -x; and if y is not halfway between x and 1, then 1 -y is not equal to y - x. But y can be any number between x and 1, so the correct answer is Choice D.
    Approach 2: Since this problem involves subtraction, it is a good idea to choose values for x and y that are close to each other as well as values that are far apart. For example, if x = 0.4 and y = 0.5, then 1 -y = 0.5 and y - x = 0.1; and if x = 0.1 and y = 0.9, then 1 - y = 0.1 and y - x = 0.8. This shows that the relationship cannot be determined, and the correct answer is Choice D.
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