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Is the average of n consecutive integers equal to 1? (1) n is even.
(2) If S is the sum of the n consecutive integers, then 0 < S < n.
Solution:
4. (D): Statement (1) states that there is an even number of consecutive integers. This statement tells you nothing about the actual values of the integers, but the average of an even number of consecutive integers will never be an integer. Therefore, the average of the n consecutive integers cannot equal 1. SU F F I C I E N T .
Statement (2) tells you that the sum of the n consecutive integers is positive, but smaller than n. Perhaps the most straightforward way to interpret this statement is to express it in terms of the average of the
n numbers, rather than the sum. Average = Sum + Number, so you can reinterpret the statement by dividing the compound inequality by n:This tells you that the average integer in set S is larger than 0 but less than 1. Therefore, the average number in the set does NOT equal 1. SUFFICIENT. The correct answer is (D).
注意上面这句话
As a footnote, this situation can happen ONLY when there is an even number of integers, and when the “middle numbers” in the set are 0 and 1. For example, the set of consecutive integers {0, 1}has a median number of 0.5. Similarly, the set of consecutive integers {-3, - 2, - 1, 0, 1, 2, 3, 4} has a median number of0.5. |
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