再问几道GWD数学！

aruora

The function f is defined for each positive three-digit integer n by f(n) = 2^x 3^y 5^z, where x, y and z are the hundreds, tens and units digits of n, respectively. If m and v are three-digit positive integers such that f(m) = 9*f(v), then m - v =?
（注：2^x 3^y 5^z是2的x次方，3的y次方 和 5的z次方 三者相乘的积）

A. 8
B. 9
C. 18
D. 20
E. 80

正确答案是D。

首先我想弄清这道题讲的什么意思。是不是说，对于任何一个正整数n，都可以用它的百位、十位和个位作为2, 3, 5的指数 相乘的积？
这道题该怎么算啊~

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The parallelogram shown has four sides of equal length. What is the ratio of the length of the shorter diagonal to the length of the longer diagonal?

图拜托各位画一下吧~ 图中显示平行四边形有一个内角是60°。

A. 1/2
B. 1/根号2
C. 1/2倍根号2
D. 1/根号3
E. 1/2倍根号3

正确答案是D

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数据充分题 （选项省略）

If k is a positive integer, what is the remainder when 2^k is divided by 10?
（2^k 是指 2的k次方）

(1) k is divisible by 10
(2) k is divisible by 4

我选的是D，也就是每一个条件都是充分的，正确答案是B，就是只有第二个条件是充分的。

说实话，对于这种题每次都是找数字试，有没有哪位大侠能给我说一下比较标准的做法？不胜感激！

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 To be eligible for retirement benefits at the Omega Corporation, the sum of an employee's age, in years, and the number of years of employment must be at least 70. If x, where x < 70, is a certain employee's age when hired and y is the minimum number of years of employment required for the employee to be eligible for retirement benefits, which of the following equations represents the relationship between x and y?

A. xy = 70
B. x + y = 70
C. 2x + y = 70
D. x + 2y = 70
E. 2x + 2y = 70

我选的是B 正确答案是D。。
对于此题 我巨没头脑。。。

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If 10^50 - 74 is written as an integer in base 10 notation, what is the sum of the digits in that integer?

A. 424
B. 433
C. 440
D.449
E. 467

正确答案是 C


什么叫做 written as an integer in base 10 notation？
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There are 8 books on a shelf, of which 2 are paperbacks and 6 are hardbacks. Howmany possible selections of 4 books from this shelf include at least one paperback?

我算出来的事D 55；答案是C 50.
我的式子：C(2 1)C(6 3) + C (2 2)C(6 2)
也就是至少有1本paperback另外3本hardback 加上 两本paperback 另外2本hardback

为什么不对呢？

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A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster.
If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?

A. 0
B. 1/9
C. 2/9
D.1/3
E.1

正确答案是C 2/9 请问式子怎么列 为什么？

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Chris mixed 3 pounds of rasins with 4 pounds of nuts. If a pound of nuts costs 3 times as much as a pound of raisins, then the total cost of the raisins was what fraction of the total cost of the mixture?

A. 3/7

B.1/3
C. 1/4
D. 1/5
E. 1/7

正确答案是 D 怎么算呢？

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yingS

已知f(n)=2^x 3^y 5^z  

x y z  分别为n的百位十位和个位

f(m)=9f(v)=3^2f(v) 

也就是说m比v的十位数大2  m-v=20

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平行四边形四条边相等

一个内角60度  另外一个120度 画个图就可以看出来

最短的对角线等于边长 （60度+2条边相等为等边三角形） 

长的对角线为根号3倍的边长（2边相等 夹角120度 对边等于2倍边长乘以sin60度）

ans is 1:根号3

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2^k  尾数循环为 2 4 8 6

k能被4整除 那么尾数一定为6  除以10余数为6

条件一 k能被10整除，尾数不确定 例如k=10的时候 尾数为4，k=20的时候尾数为6  不充分

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x为被雇佣时候的年龄  工作了y年之后  他的年龄为x+y 然后再加上他工作的时间y等于70

结果 x+2y=70

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10^50-74= 10^48*100-74

100-74=26

前面48位全部为9  那么位数之和为 48*9+2+6=440

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原事件的对立事件为  没有一本书是paperbacks C(6 4)

用总数减去即可 C(8 4)-C(6 4)=55

你用的方法也没错  应该是答案错了吧？

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说个简单点的思路  3辆车骑3次  一共3^3共27种可能

下面看三次分别骑三辆车

第一次骑  有3辆车可以选

第二次骑  有2辆车可以选

第三次骑  只有1辆车可以选

一共3*2*1=6   答案就是2/9

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设raisin 价格 x/pound

raisin总价格 3*x

混合后总价格 3*x + 4*3*x= 15x

ans is  1:5