1月27日起数学机经讨论帖【1-92题】(31日美西10：41pm )

wangxiaoqing

23.   可否求出mn?
I. 4^n=2^m
II. 2^n=3^m

这两个怎么做？

I: 2n=m

n=1,m=2

or

n=3,m=6,

get different results

so 1 is not good

I: m= n* (Ln2/Ln3)

n=1, m= Ln2/Ln3

or

n=2, m= 2*(Ln2/Ln3)

get different results, so not good

I+II: 2^n=(2/3)^m

n* Ln2 = m * Ln(2/3)

n= m*(1-Ln3/Ln2)

m=1, n= 1-Ln3/Ln2

m=2, n= 2*(1-Ln3/Ln2)

can get different results

so Answer is E

            

wangxiaoqing

19题：

我记得考题问的是
“圆内嵌小正方形，外嵌大正方形，问周长至少10？
i
                小正边长大于2
                   
ii  大正边长大于4
选B

如果此题问的是圆的周长

解：i . 圆的半径>1.414, 圆的周长2x 3.14x1.4<10

   ii. 圆的半径>2, 圆的周长2x3.14x 2>10

i: 圆的周长至少2x 3.14x1.414， 可以回答问题
ii: 圆的半径>2, 圆的周长2x3.14x 2, 可以回答问题

so Answer is D

wangxiaoqing

49. 一个大圆里面切了一个小圆，说小圆的outside diameter is equal to inside radius of the large circular. And the cross-section area of the large  circular is 49pai, what is the cross-section area of the small circular?

解：这个cross-section area就是圆面积
        

        大圆面积 49pià大圆半径7à小圆半径7/2à小圆面积49pi/4

哪位NN帮忙解答一下這題，什么是outside diameter,什么是inside radius啊？读不懂哦~

pie*(r+r)^2=pie*(2r)^2=49*pie

so if radius is r, then the area is 1/4*49*pie= 12.25*pie

33. (PS) 60% of employee has CPA, 40% of employee  has CPA and male; and 80% of employee are Male, Ask what is percentage for fmale has CPA?

解：

should be 20%

wangxiaoqing

19题：

我记得考题问的是
“圆内嵌小正方形，外嵌大正方形，问周长至少10？
i
            小正边长大于2
               
ii  大正边长大于4
选B

如果此题问的是圆的周长

解：i . 圆的半径>1.414, 圆的周长2x 3.14x1.4<10

   ii. 圆的半径>2, 圆的周长2x3.14x 2>10

i: 圆的周长>2x 3.14x1.414
could be >=10, or >=8, or >=200, so not sure
ii: 圆的半径>2, 圆的周长>2x3.14x 2,
so for sure >10

so Answer is B
so Answer is D

wangxiaoqing

19题：

我记得考题问的是
“圆内嵌小正方形，外嵌大正方形，问周长至少10？
i
            小正边长大于2
               
ii  大正边长大于4
选B

如果此题问的是圆的周长

解：i . 圆的半径>1.414, 圆的周长2x 3.14x1.4<10

   ii. 圆的半径>2, 圆的周长2x3.14x 2>10

i: 圆的周长>2x 3.14x1.414
could be >=10, or >=8, or >=200, so not sure
ii: 圆的半径>2, 圆的周长>2x3.14x 2,
so for sure >10

so Answer is B

fatpeng

还请高人指点第60题

wangxiaoqing

66. 可否求出mn?

i. 4^n=2^m

ii. 2^n=3^m

解：ià 2n=m

        iiàn=m=0

答案：B

ii: not right

nLn2= mLn3

n=0, m=0
n=1, m= Ln2/Ln3

so Answer is E

wangxiaoqing

33. (PS) 60% of employee has CPA, 40% employee  has CPA and are male; and 80% of employee are Male, Ask what is percentage for fmale has CPA?

解：20%

59. 一条线段上有4个距离相等的点a b c d, 问可否求出a+c阿或者b+c之类的

i. a+b=-8

ii.a+d=0

解：a,b,c,d都在数轴上，且等距离à线段a,d被b,c两点等分

        ià
            不能够确定

        iià0点a,d两点的正中央àb+c=0

        i+ii à
            设a,b之间的距离为x，那么a=-3x/2, b=-x/2,c=x/2,d=3x/2àx=4àa+c=-4

答案：C

should be E
how do you know the value of x? Is it given? What if x=5 or 6 or other values, then a+c get different results

fatpeng

Hi Wangxiaoqing,

59: Since a=-3x/2,b=-x/2 and a+b=-8

a+b=-2x=-8

x=4

fatpeng

for 66, yes, you are right.

If n,m are integers then B