AMC 8 1994 Problem 6
AMC8 1994 年第 6 题
余数与同余★★☆☆☆
The unit's digit (one's digit) of the product of any six consecutive positive whole numbers is
任意六个连续正整数的乘积的个位数字是
- A.0
- B.2
- C.4
- D.6
- E.8
正确答案 · Correct Answer
A
解析 · Solution
Solution 1
Within six consecutive integers, there must be a number with a factor of 5 and an even integer with a factor of 2. Multiplied together, these would produce a number that is a multiple of 10 and has a units digit of .
We can easily compute the product of the first 6 positive integers: Therefore the units digit must be .
The question asked for ANY six consecutive whole number. Some include multiples of 10, so the unit digit must be .
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