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请教三道PREP数学题

1. What is the greatest prime factor of 4^17-2^28?  不知道为什么答案是7.

2. In a class of 30 students. 2 students didnot borrowed any books from the library. 12 students each borrowed 1 book. 10 students each borrowed 2 books and the rest of the student each borrowed at least 3 books.  If the average (arithmetic mean) numbers of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed?  怎么算出来答案13?

3. Acertain car averages 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driven on the highway.  According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is drivin 10 miles in the city and 50 miles on the highway?  怎么算出来答案36?

谢谢解答!

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1, 2^34-2^28=2^28*(2^6-1)=2^28*7*3^2==>最大质数是7

2,最少借3本的人共有6个,另其中5个人只借3本,则剩下那个人必定是借最多的,x+3*5+12+10*2=2*30==>x=13

3,2种路的平均油耗为,1/25和1/40, 故分别走10m和50m时总油耗为10*1/25+50*1/40=33/20,全程的平均油耗=60/(33/20)=36

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谢谢!!!!!

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