4道百思不得其解的数学，希望指教，已经含正确答案

mramarni

先谢谢各位啦，请提供下具体的思路，我问了几个人都没有什么思路。

Did one of the 3 members of a certain team sell at least 2 raffle tickets yesterday?

(1)  The 3 members sold a total of 6 raffle tickets yesterday.

(2)      No 2 of the members sold the same number of raffle tickets yesterday.

E

 

If Bob produces 36 or fewer items in a week, he is paid x dollars per item.  If Bob produces more than 36 items in a week, he is paid x dollars per item for the first 36 items and 1.5 times that amount for each additional item.  How many items did Bob produce last week?

(1) Last week Bob was paid a total of $480 for the items that he produced that week.

(2) This week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week.

E

 

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

C

 

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

A: between 2 and 10

B: between 10 and 20

C: between 20 and 30

D: between 30 and 40

E: greater than 40

E

mramarni

都是PREP原题，尤其是最后一题。。。见到是傻眼了。。。

emdisc

1题可能主要是读题理解有误,题1问的是3人中的某个是否sell at least 2,条件都无关.

题2答案应该是C,设上周产Y

则36X+1.5X(Y-36)=480

36X+1.5X(Y+2-36)=510

得X=10 Y=44

题3 (1)  (3r + 2 - s)(4r + 9 - s) = 0

(2)  (4r - 6 - s)(3r + 2 - s) = 0

由于4r + 9 - s=0和4r - 6 - s=0不可同时成立,则3r + 2 - s=0必成立, 即S=3R+2

proudking

第一道题，我百思觉得Prep错了，第一个条件，3个人卖了6个东西，至少有某一个人卖了2个，难道不是吗？

第二道题，假设上星期做了Y个，要分三种情况计算，Y小于34，y在34-36之间（也就是上个星期的数字小于36，而这个星期的数字大于36），还有y大于36.综合两个条件，可以得出两个解，x=32，y=15，或者x=44，y=10。没有唯一解，所以是E

第三题，综合两个条件，可知(3r + 2 - s)=0，则，s=3r + 2，在直线上。

第四题，不会。

emdisc

题4, H(100)+1=2*4*6*......*78*80*...*98*100+1 此数不可能有小与50的因子

emdisc

第二题四楼的对, 我考虑不周

maomm

我怎么查到第一题的答案是D呀,而且确实是两个条件都分别充分呀.

Haling

some thoughts on the 4th one,

H(100)+1=2*4*6*8...*100+1
=2^50*50!+1
50! includes every primes below 50, think of 2^50 as a coefficient,
任何p的整倍数加1都不可能被p整除，处分加上他本身...

hope this helps...

redhead

说说第一题 .

注意题目说的是one of the members这里的one可以是任何一个.

两个条件可以算出平均每人卖了2张, 以及每个人卖的数量不一样. 这说明并不是每一个人都卖了2张以上.

这个one可能是那个卖得少的人, 也可能是卖得多的人, 所以不确定.选E

je_sais_pas

8楼高手！