2. 外语
  3. If j and k are even integers and j < k, which of the following equals the number of even integers that are greater than j and le

If j and k are even integers and j < k, which of the following equals the number of even integers that are greater than j and le

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问题 If j and k are even integers and j < k, which of the following equals the number of even integers that are greater than j and less than k ?
选项 A、
B、
C、
D、k-j
E、k-j-1
答案A
解析 Since j and k are even integers, it follows that k=j + 2n for some integer n. Consider the sequence of even integers from; to k.
j, j +(2)(1), j +(2)(2), j +(2)(3),..., j +(2)(n - 1), j + 2n
Note that there are n — 1 integers in the sequence between j and k, and these are the even integers greater than j and less than k. Therefore the answer is n - 1, but the answer must be given in terms of j and k. Since k=j + 2n, you have n =and so

Thus the correct answer is Choice A.
This explanation uses the following strategies.
Strategy 5: Simplify an Arithmetic or Algebraic Representation
Strategy 8: Search for a Mathematical Relationship
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