还是数学机经题~想问一下老师这个题不用反证法可以解吗??或者反证法合理吗??谢谢~~
DS:问h是不是prime number
条件1:h的factor都大于根号h
条件2:h的factor都大于h/2
反证法:
假设h = a*b 且a, b >1, h不是质数。
条件1: a,b>根号h,then H > 根号h*根号h = h, 推出矛盾,所以h不能写成两个大于1的数相乘,所以h是质数;
条件2: 同理 H>2/h*2/h=h^2/4 推出h<4, then h = 2 or 3, 是质数, 与假设矛盾。所以h是质数。
选D
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提问:
GMAT数学(博智教材)第62页:If X is equal to the sum of the even integers from 40 to 60, inclusive, and y is the number of even integers from 40 to 60, inclusive, what is the value of x+y?
X=40+42+44......60=550
Y=(60-40)/2+1=11, 答案应该是561,为什么书后面的答案显示是560?
DS:5个数中 median 小于 average ;另外7个数也median 小于 average,然后这12个数没有重复的,12个数放在一个数集里面,问是不是median 小于average?
条件1:7个的average 小于 5个的average
条件2:7个的median 小于 5个的 median
题目:of the 200 students at college T majoring in one or more of the sciences, 130 are majoring in chemistry and 150 majoring in biology. If at least 30 of the students are not majoring in either chemistry or biology, then the number students majoring in both biology and chemistry could be any number from
a) 20 to 50
b) 40 to 70
c) 50 to 130
d) 110 to 130
e) 110 to 150
问题:这道题能理解到是用集合的知识点,但是无论怎么做都无法突破,得到最后结果。还请老师讲解。谢谢