请教几道数学题~

1. the function f is defined for all positive integars n by the following rule: f(n) is the number of positive integars each of which is less than n and has no positive factor in common with n other than 1. if p is any prime number then f(p)=
a. p-1   b. p-2   c.(p+1)/2   d.(p-1)/2   e. 2                                                 答案是a

f(p)求的是比p小的且与p无公因子（1除外）的正整数的个数，p为质数，比p小的都没公因子，所以等于p-1

2.DS题：if ab不等于0 and points(-a,b) and (-b,a) are in the same quadrant of the xy-plane, is point (-x,y) in this same quadrant?
    (1) xy>0
    (2) ax>0
答案是C 但我觉得是A    因为由于（-a,b）（-b,a）在同一象限就可以得出a、b同号，那么对于（-x，y）来说不是只要同号就可以了么？为什么还需要第二个条件呃。。。？

问是否在（-a,b）所在象限，所以要在保证xy同号的同时确认和a同号，所以c

3.DS题 a certain group of car dealeships agreed to donate x dollars to a Red Cross chapter for each car sold during 30-day period. what was the total amount that was expected to be donated?
   (1) a total of 500 cars were expected to be sold
   (2) 60 more cars were sold than expected, so that the total amount actuallu donated was $28,000
答案C     请问为什么只用第一个条件解不出？ 不应该是500x吗。。。？还是说这个x是未知数是让求出来的而不是只用式子表示出来就OK

是需要解出具体数字的......

4.DS   whenever Martin has a restaurant bill with an amount between $10 and $99, he calculates the dollar amount of the ship as 2 times the tens digit of the amount of his bill. if the amount of Martin's most recent restaurant bill was between $10 and $99, was the tip calculated by Martin on this bill greater 15percent of the amount of the bill?
   (1) the amount of the bill was between $15 and $50
   (2) the tip calculated by Martin was $8
答案B   这一题题目就没看懂。。。。。。

第一个“ship”应该是“tip”吧...小M在饭店吃饭，只要账单在10-99刀之间，就付价钱的十位数字的二倍做小费，问某次的tip是不是大于15%。应该自己可以解了...

5.DS  is the integar  n odd?
   (1) n is divisible by 3
   (2) 2n is divisible by twice as many positive integars as n
答案B   第一个条件没问题，我想问第二个条件是什么意思 我理解的意思是2n/2n 那不就=1么。。。？

第二个条件比较绕，其实就是说2n可以被x个数字整除，n可以被y个数字整除，这里x=2y。为什么选B我解释不清楚，等NN来解答吧。

6. DS  of the 200 members of a certain association, each member who speaks German also speaks English, and 70 of the members speak only Spanish. if no member speaks all three languages, how many of the members speak two of the three languages?
   (1) 60 of the members speak only engllish
   (2) 20 of the members do not speak any of the three languages
答案c

题干中可以看出总人数，只说德语的是0，说德语和西班牙语的是0，说三种语言的是0，只说西班牙语的70.
条件1：只说英语的60
条件2：三种都不说的20

求说两种语言的，用总人数-只说一种的-说三种的-不说的........

7. a certain business produced x rakes each month from Noverber through February and shipped x/2 rakes at the beginning of each month from month from March through October. the business paid no storage costs for the rakes from Noverber through February, but it paid storage costs of $0.10 per rake each month from March through October for the rakes that had not been shipped. in terms of x,what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months from November through October?
  a    0.40x
  b   1.20x
  c    1.40x
  d   1.60x
  e   3.20x
答案c      可是这题我怎么觉得是0.1*6*（x/2）=0.3x    估计我看题有偏差。。。望高人解答

四个月造，八个月运，第一个月运的x/2不需要仓储成本，最后一个月的月初运走也不要算在内，然后就是一个等比数列求和，算就可以了...

8. machine A produces pencils at a rate of 9.000 pencils per hour, and machine B produces pencils at a constant rate of 7,000 pencils per hour. if the two machines together must produce 100,000 pencils and if each machine can operate for at least 8 hours, what is the least amount of time, in hours, that machine B must operate?
答案是4    请问怎么算的。。。

应该是at most 8 hours，（10，000-9，000×8）/7，000 = 4

题目很多。。。快要考试了，做了prep觉得数学不简单啊，我都没做完。。。有点着急。。。在这里先谢谢各位高人的解答~！

个人意见仅供参考，LZ加油