费费的数学难题,求助

zephyr1977

median of A is 80 of B is 78
average score of A is 82 of B is 74
问AB两班的考试分数average〉median否？
（1）A 37 people B 40 people
（2）A+B 77people
想知道1的推导过程


n=ABCD（A-D都是大于1的质数），问n出了1外还有几个因子
15个

谢谢!

licheng

1.u can easily calculate the mean by (1) , that is 77.8, then we should know that there are 77 people in all, the median must be the 39th person in the array if sorted. we also know that there are 18 people that have marks > 80(because median of A is 80), and 20 person have marks > 78(because median of B is 78) and those people can't be same people. therefore, there are totally 39 people > 78. therefore the median must be greater than the avg.

2. there is a formula determining the number of factors(not prime factors)
after you write n = A^a*B^b*C^c*D^d*....
while A,B,C,D are all prime numbers,
the number of factors are (a+1)(b+1)(c+1)...
including 1 and itself.
therefore, ur question is solved by :
(1+1)(1+1)(1+1)(1+1) - 1 = 15

zephyr1977

i got it at last. tons of thanks!