请教NN们几个数学题，多谢

如题。多谢各位先。

1. DS: In the xy-plane, does the line with equation y=3x+2 contain the point (r,s)?

(1) (3r+2-s)(4r+9-s)=0

(2) (4r-6-s)(3r+2-s)=0

  Answer is (C). But why not (D)?

2. DS: If 1000 is deposite in a bank account and remains in the account along with any accumulated interest, the dollar amount of interest, L, earned by the deposit in the first n years is given by the formula L=1000[(1+r/100)^n-1], where r percent is the annual interest rate paid by the bank. Is the annual interest rate paid by the bank greater than 8percent?

(1) the deposite earns a total of $210 in interest in the first 2 years.

(2) (1+r/100)^2 > 1.15

     Answer is (A). But why not (D)?

3. A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

A. 10700                   B. 10800               C. 10900          D. 11000               E. 11100

    Answer is (D)

如题。多谢各位先。

1. DS: In the xy-plane, does the line with equation y=3x+2 contain the point (r,s)?

(1) (3r+2-s)(4r+9-s)=0

(2) (4r-6-s)(3r+2-s)=0

  Answer is (C). But why not (D)?

(1) 中当且仅当3r+2-s=0时，(r,s)所有的点集才会落在y=3x+2上；当4r+9-s=0时，因为与y=3x+2只有一个交点，不能确定(r,s)是否是这个点，即不能确定y=3x+2是否包含这个点(r,s)；

同理判断(2)。

因此这两个条件单独成立时都不能判断。但是当(1)(2)同时成立时，能确认(r,s)都落在3r+2-s=0这条直线上，即与y=3x+2重合。

所以选C: both together are sufficient.

2. DS: If 1000 is deposite in a bank account and remains in the account along with any accumulated interest, the dollar amount of interest, L, earned by the deposit in the first n years is given by the formula L=1000[(1+r/100)^n-1], where r percent is the annual interest rate paid by the bank. Is the annual interest rate paid by the bank greater than 8percent?

(1) the deposite earns a total of $210 in interest in the first 2 years.

(2) (1+r/100)^2 > 1.15

     Answer is (A). But why not (D)?

(1) 推出1000[(1+r/100)^2-1]=210  => r=10 >8

(2) 反推当r>=8时， (1+8/100)^2>=1.1604>1.15  因此 不能保证所有满足(2)的r大于8

所以选A

3. A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

A. 10700                   B. 10800               C. 10900          D. 11000               E. 11100

    Answer is (D)

把这11个districts从小到大排队：A1<A2<...<A11.

要保证最大的district population不能超过最小的district population的10%，即(A11)<=1.1*(A1) 可见当A2=A3=....=A11=1.1*(A1)的时候，A1的值最小

A1+A2+..+A11= A1 +10*1,1*(A1)=12 * (A1)=132,000 => A1=11000

所以选D

终于明白了，解释得好清楚啊，太感谢了