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Three is the largest number that can divide evenly into both 27 and the positive integer x, while 10 is the largest number that can divide evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 2,100? A 30 B70 C 210 D 300 E 700 正确答案是c，求NN解释下这道题的题目意思和解题过程
下面是Kaplan对这道题的解释，但我没看懂
Analyze the Question: We are told that 3 is the greatest common factor of 27 and x, and that 10 is the greatest common factor of 100 and x. Since 3 and 10 have no factors in common, x must be some multiple of 3 × 10 = 30. Identify the Task: We must find the largest number that will divide evenly into x and 2,100. Approach Strategically: Begin by considering the possible values of x. If x were an even multiple of 30, such as 60, x and 100 would share a common factor of 20. Since the problem says that 10 is the greatest common factor of x and 100, x must be an odd multiple of 30. That allows us to eliminate choices (B), (D), and (E). Since we are looking for the largest possible number that divides evenly into x and 2,100, let’s check (C): The greatest common factor of 27 and 210 is 3 because 27 = 3 × 3 × 3 and 210 = 2 × 3 × 5 × 7 (both have at most a single 3 in common). By the same token, the greatest common factor of 100 and 210 is 10 because 100 = 2 × 2 × 5 × 5 and 210 = 2 × 3 × 5 × 7 (both have at most the 2 × 5 in common). The correct answer is Choice (C). Confirm Your Answer: All the answer choices divide evenly into 2,100. Even if we counted all the multiples of 30, we could eliminate choices (B) and (E) because 7 does not divide into all multiples of 30. The greatest common factor of 100 and 300 is 100, which is too large, eliminating choice (D). The greater of the 2 remaining choices is 210, divisible by both 3 and 10. We can be confident that the correct answer is Choice (C).
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发表于 2020-10-10 15:49:34
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