问prep1中的2道数学题目

victoria820

1. Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income.  Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is I ?
A. 50 + I/200
B. 50+ 3I/100
C. 50+ I/40
D. 100+ I/50
E. 100 + 3I/100
Answer: C
题目什么意思

2. If n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what is the value of r ?
(1) n is not divisible by 2.
(2) n is not divisible by 3.
Answer:C

victoria820

谢谢 ，明白了.

sunny9653

第二题的话。选C
n不能被2整除，那说明n是奇数。那么n-1和n+1都是偶数。
n不能被3整除，那说明n-1和n+1肯定有一个是3的倍数。

(n - 1)(n + 1)这个式子能被24整除。
因为24=2*2*2*3
3这个因子已经有了。
然后由于n-1和n+1都是偶数 那么设n-1=2k   n+1=2k+2=2（K+1）
那么(n - 1)(n + 1)=4k(k+1)
然后k和k+1肯定有一个是偶数。所以(n - 1)(n + 1)就是8的倍数。
那么3*8=24
就是24的倍数。所以余数为0

xiangzhengj

第二题想了半天还没什么结果，考试的时候就用上那无敌代入法做吧

victoria820

谢谢，通过你的解释现在第一题明白了～

xiangzhengj

第一道题就是让你写出那个复杂的公式然后进行简化。
关键是理解这部分add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income.
翻译后就是：年收入的2%+（100块钱 + 年收入的1%）/ 2。请按颜色对应起来。

因为年收入为I，所以就是2%I + (100 + 1%I) / 2 = I / 50 + 50 + I / 200 = 50 + I / 40。

congcircle

同问