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考题21-22 2014 AMC 8

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AMC 8数学竞赛专为8年级及以下的初中学生设计,但近年来的数据显示,越来越多小学4-6年级的考生加入到AMC 8级别的考试行列中,而当这些学生能在成绩中取得“A”类标签,则是对孩子数学天赋的优势证明,不管是对美高申请还是今后在数学领域的发展都极其有利!那么接下来跟随小编来看一下AMC 8数学竞赛试题及答案吧:

Problem 21The?-digit numbers??and??are each multiples of?. Which of the following could be the value of??

SolutionThe sum of a number′s digits??is congruent to the number?.??must be congruent to 0, since it is divisible by 3. Therefore,??is also congruent to 0.?, so?. As we know,?, so?, and therefore?. We can substitute 2 for?, so?, and therefore?. This means that C can be 1, 4, or 7, but the only one of those that is an answer choice is?.

Problem 22A?-digit number is such that the product of the digits plus the sum of the digits is equal to the number. What is the units digit of the number?

SolutionWe can think of the number as?, where a and b are digits. Since the number is equal to the product of the digits () plus the sum of the digits (), we can say that?. We can simplify this to?, and factor to?. Dividing by?, we have that?. Therefore, the units digit,?, is

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