The sum of n different positive integers is less than 100. What is the greatest possible value of n?

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问题 The sum of n different positive integers is less than 100. What is the greatest possible value of n?

选项 A、10
B、11
C、12
D、13
E、14

答案D

解析 n个不同正整数的和小于100，问n的最大值(the greatest possible value)是多少?
解：本题的正确答案是(D)。要求n的最大值，就要使每个加数都尽可能的小。而题中已限制加数为不同的正整数，所以要使加数的个数最多，只能从最小正整数开始，依次从小到大取值，即1+2+3……<100。任取n=13，则1加至13的和为91，小于100而不可能再加上14，否则将不能满足小于100的条件。

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The sum of n different positive integers is less than 100. What is the greatest possible value of n?

GRE QUANTITATIVE

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