How many odd multiples of 7 are there between 100 and 1,000?
这是题目给的解释
The first multiple of 7 that’s greater than 100 is 7 x 15 = 105 (found by trial and error, or by dividing 100 by 7 to first find the multiple of 7 just under 100). Now, to find the largest multiple of 7 under 1,000, we can divide 1,000 by 7, which yields a quotient of 142 and a remainder of 6. However, 7 x 142 = 994 is even. The largest odd multiple of 7 under 1,000 is 994 – 7 = 987. To find the number of terms in the sequence 105, 119, …, 987, we subtract the smallest term from the largest, divide by the step size, and finally add 1 to the result. Note that the step size is 14, not 7, because we are only considering odd multiples of 7:
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The correct answer is 64.
我是这么算的,从100到200有14个7的倍数,200-300,300-400,。900-1000依次也是各14个,其中一半奇数一半偶数,所以7*9=63个,不明白另一个少在哪里