本月几道Math JJ重要难题讨论

1.
              DS:一个数是不是靠近10^(-3)more than10^(-2)?

1.靠近10^(-4)more than10^(-1);  2.靠近10^(-3)more than 10^(-1)

我选的A   条件2可能有出入,记不太清了~可能是靠近10^(-4)more than 10^(-2),

Another similar one: DS, x离10^-3近还是离10^-2近？（1）X is colser to 10^-4 than to 10^-1   (2) X is closer is 10^-3 than to 10^-1

答案：E   

I am still not sure what the answer is? Some NN can answer it?

2. DS：r,s,t是正数，问1/r+1/s+1/t>2?
1)r+s+t>1/2
2）r+s+t<1
答案：B，
        条件1，无法单独判断,条件2得到r<1,s<1,t<1,即1/r>1,1/s>1,1/t>1,1/r+1/s+1/t>2

Another similar one: DS. 是否s/1+t/1+r/1>2?
  (1) s+t+r<2

Another one: x,y,z are positive, 1/x+1/y+1/z>2?  1)x+y+z>1/2   2)x+y+z<1
答案：B，思路：1）用几个数代一下，很快排除。2）中，由于3个1/3加起来是1，xyz都取1/3时，1/X+1/Y+1/Z=3>2，而1/x+1/y+1/Z肯定>3。

Not sure about this one either. Can someone get it without plugging in any numbers?

3. 已知一个三角形内接于一个半径为r的圆，不知三角的面积，请估计这个三角的周长？
            
答案：0~3sqrt(3)r(我猜测是这个范围，但是不知道怎么计算

Don't know how to calculate.

1.
     DS:一个数是不是靠近10^(-3)more than10^(-2)?

1.靠近10^(-4)more than10^(-1);  2.靠近10^(-3)more than 10^(-1)

find the average number for each one. for initial question, average=0.0055, for 1. average=0.05005;for 2, average=0.0505. Hence to satisfy initial question, the number satisfy 1 or 2 need to be less than 0.0055. However, 0.0055 < 0.05005 < 0.0505, no one is sufficient to initial question.

2. The simplest way to find the answer is just by using trial and error method. No need to prove it mathematically.
  

3. When 3 points of triangle approach to each other, the perimeter->0; when the triangle is equilateral triangle, the perimeter is max and each side is sqrt(3)r.

hi,Pipo, my friend, thanks a lot!! I am taking the exam in two days! thanks for your help.