2. 外语
  3. When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n ?

When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n ?

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问题 When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n ?
选项 A、11
B、9
C、7
D、6
E、4
答案B
解析 The given information tells you that n can be expressed in the form n = 45k +18, where k can be any nonnegative integer. Consider how the divisors of 45 and 18 may be related to the divisors of n. Every common divisor of 45 and 18 is also a divisor of any sum of multiples of 45 and 18, like 45k +18. So any common divisor of 45 and 18 is also a divisor of n. Of the answer choices given, only 9 is a common divisor of 45 and 18. Thus the correct answer is Choice B.
This explanation uses the following strategies.
Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation
Strategy 8: Search for a Mathematical Relationship
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