BruceNornia

11.

Is the integer n odd?

(1)   n is divisible by 3

(2)   2n is divisible by twice as many positive integers as n

 

条件(1) n能被3整除，明显不能判断n是不是奇数，NOT SUFFICIENT

条件(2) 将n分解质因数计为：n = a1^n1 * a2^n2 * ... * am^nm 这里a1 ... am均为质数 而n1 ... nm分别表示其质因数的指数

那么n的正整数因子个数为：(n1+1) * (n2+1) * ... * (nm+1)

当n为奇数时，a1 ... am均为奇数

从而2n的质因数分解为 2n = 2 * a1^n1 * a2^n2 * ... * am^nm 其正整数因子个数为：(1+1) * (n1+1) * (n2+1) * ... * (nm+1) 为n的正整数因子个数的2倍

当n为偶数时，可知a1 ... am 中存在一个2，取a1 = 2 即 n = 2^n1 * a2^n2 * ... * am^nm

从而2n的质因数分解为 2n = 2^(n1+1) * a2^n2 * ... * am^nm 其正整数因子个数为： (n1+2) * (n2+1) * ... * (nm+1) 为n的正整数因子个数的(n1+2)/(n1+1)倍 由于n1 != 0 所以不可能为2倍

则在条件(2)的约束下 只有奇数n能满足，从而n为奇数可以判断，SUFFICIENT

 

The correct answer is B

Statement (2) ALONE is sufficient

BruceNornia

Working alone at its own constant rate, a machie seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machine, each working at its own constant rate and for the same period of time, together sealed a certain of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

 -          25%
 -          (33*1/3)%
 -          50%
 -          (66*2/3)%
 -          75%

 

题目是不是写错了 66%吧

一个是另外一个工作效率的两倍 一起干活 两倍那个肯定干了2/3阿

不知道楼主敲的（66*2/3）%是什么意思 44%？

BruceNornia

建议楼主去下一个prep破解看看 或者看看CXD的数学

BruceNornia

QUOTE:

以下是引用小萧笑在2009-6-10 6:39:00的发言：
(1) 2~100 的even numbers = 2550.   2550+1= 2551  -> prime number

(2)200 * 6 =1200 ounce.

1200 / 4 = 300 (sets for concentrate unit)

300/12 = 25 (cans)

(3)350 = 7 * 50 = 77 + 63 + 210

77 (佔1), 63 (佔9), 210 (佔30) => n=40

(4) 你帶 2, 5 進去做  就知道 只有乘法會ㄧ致

(5) 0.1 + 0.3+0.3   是每一天結束才算過期  所以周4沒有罰錢

 

 

第一题写错了吧... 题目说的是乘积 你算的是和阿