[求助]GMATPrep Math 几道题

(1) 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, I don't know why. Please help.

(2) For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is:

A: Between 2 to 10

B: Between 10 to 20.

C: Between 20 to 30

D: Between 30 to 40

E: Great than 40.

The answer is (E), I don't know how to solve.

(3) If p is production of interger from 1 to 30, inclusive, what is the greatest integer k for which 3^K   is a factor of p?

A: 10, B:12, C:14, D: 16 E: 18

Anser is C. I don't know how.

谢谢帮忙！

第二题费费上课讲过。因为相邻的自然数互质，所以100！与（100！+1）互质，所以100！+1不含有100！的质因子。

100！=（2*4*6*。。。*100)*(3*5*7*。。。*99)=2*（2*3*4*...*50）*(3*5*7*...*99)

由最右端第一个括号可以看出，100！的质因子是包含有50以内的所有质数的，也就是100！+1没有这些数字作为质因子。feifei当时还说，这道题答案完全可以改为：E greater than 50.

第三题 我笨 就把30内所有3的倍数列出来了，很快的。

3 6 12 15 21 24 30共7个，每个含一个3作为因子

9 18 27是各含2 2 3个3的因子。

所以7+2+2+3=14~~~

第一题解释有点麻烦，两个式子相乘=0 意味着 其中一个式子=0，则两个条件都有可能不满足原题中的式子。当他们联立的时候，只有一个解，就是令3r+2-s=0。

另外可以通过在xy-坐标轴上画直线看交点的方法做题。不用仔细画，斜率一样就表明有交点。

ps：我明天下午考试，现在在积攒rp,谁有空帮我看看这个难题，感激：http://forum.chasedream.com/dispbbs.asp?boardid=22&id=202074

谢谢大家，明白了。