AMC数学竞赛8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的官方真题以及官方解答吧：

Problem 11

Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is 

Solution

We can write the two digit number in the form of ; reverse of  is . The sum of those numbers is:We can use brute force to find order pairs  such that . Since  and  are both digits, both  and  have to be integers less than . Thus our ordered pairs are  or  ordered pairs.

Problem 12

Jefferson Middle School has the same number of boys and girls. Three-fourths of the girls and two-thirds of the boys went on a field trip. What fraction of the students were girls?

Solution 1

Set the number of children to a number that is divisible by two, four, and three. In this question, the number of children in the school is not a specific number because there are no actual numbers in the question, only ratios.This way, we can calculate the answer without dealing with decimals.  is a number that works. There will be  girls and  boys. So, there will be  =  girls on the trip and  =  boys on the trip. The total number of children on the trip is , so the fraction of girls on the trip is  or 

Solution 2

Let there be  boys and  girls in the school. We see , which mean  kids went on the trip and  kids are girls. So, the answer is , which is 

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