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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2024-01-12  31
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 One way to compare the two quantities is to plug in a few values of n. If you plug in n = 36, you find that both the remainder when n is divided by 12 and the remainder when n is divided by 18 are equal to 0, so Quantity A is equal to Quantity B. However, if you plug in n = 18, you find that the remainder when n is divided by 12 is 6 and the remainder when n is divided by 18 is 0, so Quantity B is greater than Quantity A. Therefore, the correct answer is Choice D.
    Another way to compare the two quantities is to find all of the possible values of Quantity A and Quantity B. The positive integers that are divisible by 6 are 6, 12, 18, 24, 30, 36, etc. When dividing each of these integers by 12, you get a remainder of either 0 or 6, so Quantity A is either 0 or 6. When dividing each of these integers by 18, you get a remainder of either 0 or 6 or 12, so Quantity B is either 0 or 6 or 12. Note that when the value of Quantity B is 12, the value of Quantity A, 0 or 6, is less than the value of Quantity B; but when the value of Quantity B is 0, the value of Quantity A is greater than or equal to the value of Quantity B. Thus, the correct answer is Choice D.
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