[求助]GWD数学！求教高手~~

If 3^6x = 8100, what is the value of (3^x-1)^3?
(注：3^6x 是 3的6x次方；(3^x-1)^3 是 3的x-1次方然后再3次方)

A. 90
B. 30
C. 10
D. 10/3
E. 10/9

[3^(x-1)]^3 = 3^(3x-3) = 3^(3x) / (27) = [3^(6x)]^(1/2)/(27)=[8100^(1/2)]/27=90/27=10/3

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Six Cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is numbered 5?

A. 1/6
B. 1/5
C.1/3
D. 2/5
E. 2/3

4, 4 is also a possibility

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数据充分题（选项省略）

What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?

(1) The average height of the students in class X is 120 centimeters.
(2) The average height of the students in class X and class Y combined is 126 centimeters.

for expression, let m = average height in class X, let x= number of students in class X

let n = average height in class Y, let y = number of students in class Y

we want to know : m/n

(1) m = 120 (insufficient)

(2) (mx + ny)/(x+y)=126 (insufficient)

combine (1)+(2) = (120x+ny)/(x+y)=126 (not sufficient)

the answer is (E)

数据充分题 （选项省略）

A total of $60,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 fot that year was $4,080, what is the value of x?

(1) x = 3y/4
(2) The ration of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.

Suppose amount P earned interest at rate of x%, (60000 - P) earned interest at rate of y%

P*x/100 + (60000-P)*y/100 = 4080 => P*x + (60000-P)*y = 408000

(1) x = 3y/4

P * 3y/4 + (60000-P)*y = 408000

we have 2 unknowns (P and y) but only one equation, there is no way to solve it => insufficient

(2) P/(60000-P) = 3/2

P = 36000, 60000-P = 24000

36000*x + 24000*y = 408000 (insufficient)

combine (1) and (2), 36000*x + 24000*y = 36000*3y/4 + 24000*y = 408000, we can solve for y from this equation, then we can solve for x from x = 3y/4.

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If a and b are positive integers such that a - b and a/b are both even integers, which of the following must be an odd integer?

A. a/2
B. b/2
C. (a+b)/2
D. (a+2)/2
E. (b+2)/2

这题我很不解。a-b是偶数，说明a和b都是偶数。(it is not ture, counterexample: 5-3=2)

同样，a/b是偶数，说明a和b都是偶数。 (also not true, counterexample: 6/3=2)

第一题

3^6x=（3^3x）^2 =8100 所以3^3x=90

 第一题

3^6x =8100   所以 3^3x =90

(3^x-1)^3=3^（3x-3）=3^3x /（3^3） =90/27=10/3

但是 a/b是偶数 说明a是偶数 再由a-b是偶数 知b也是偶数啊 感觉 D E都成立啊

请nn解答~

第二题

有放回的取两次卡片，那么两数和是8的组合有5个，3和5，5和3，2和6，6和2，4和4

其中有5的有两种，所以概率是2/5

a/b even 得出 a 偶数

a-b even 得出 b 偶数

可以确定 a/2 一定为偶数 

由条件一可以看出 a除以一个偶数b还得偶数，

最小的偶数是2，那么a除以2一定为偶数

于是(a+2)/2= a/2 +1  一定为奇数