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  3. Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given,

Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given,

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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.
选项
答案B
解析 Set up the initial comparison:

However, the problem asks for a comparison between Quantity A and Quantity B, not a comparison between 1 and y. To go from the comparison between 1 and y to a comparison between Quantities A and B, start with the last comparison, 1 < y, and carefully consider each simplification step in reverse order to determine what each comparison implies about the preceding comparison, all the way back to the comparison between Quantities A and B if possible. Since step 3 was "divide both sides by 2," multiplying both, sides of the comparison 1 < y by 2 implies the preceding comparison 2 < 2y, thus reversing step 3. Each simplification step can be reversed as follows:
    Reverse step 3: multiply both sides by 2.
    Reverse step 2: add 3y to both sides.
    Reverse step 1: divide both sides by 5.
When each step is reversed, the relationship remains less than(<), so Quantity A is less than Quantity B.
Thus the correct answer is Choice B, Quantity B is greater.
This explanation uses the following strategy.
Strategy 5: Simplify an Arithmetic or Algebraic Representation
While some simplification steps like subtracting 3 from both sides or dividing both sides by 10 are always reversible, it is important to note that some steps, like squaring both sides, may not be reversible.
Also, note that when you simplify an inequality, the steps of multiplying or dividing both sides by a negative number change the direction of the inequality; for example, if x < y, then —x > -y. So the relationship in the final, simplified inequality may be the opposite of the relationship between Quantities A and B. This is another reason to consider the impact of each step carefully.
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