AMC 8 1997 Problem 5
AMC8 1997 年第 5 题
整除与因数★★☆☆☆
There are many two-digit multiples of 7, but only two of the multiples have a digit sum of 10. The sum of these two multiples of 7 is
7 的两位数倍数有很多，但其中只有两个倍数的各位数字之和为 10。这两个 7 的倍数之和是
- A.119
- B.126
- C.140
- D.175
- E.189
正确答案 · Correct Answer
A
解析 · Solution
Solution 1
Writing out all the two digit multiples of 7, you get 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, and 91. Again you find 28 and 91 have a digital sum of 10, giving answer.
You may notice that adding 7 either increases the digital sum by 7, or decreases it by 2, depending on whether there is carrying or not.
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