PREP 里几道数学， 各位帮帮忙 好吗？

sydneyang

Sorry to ask so many at a time. Really hope someone could help, as I tried and couldn't

figure out WHY!!!  Thanks in advance.

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

a)       (3r+2-s)(4r+9-s)=0

b)       (4r+6-s)(3r+2-s)=0

Key:C

       I thought D

 

2)  A constuction company was paid a total of 500,000 for a job. The only costs are labor and materials. Was the company's profit greater than 150,000?

         a)  Company's total cost was 3 times it's cost for materials.

         b)  The company profit was greater than its cost labor.

                   Key:C

        I thought E

 

3)  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 3/2 times that amount for each additional item. How many items did Bob produce last week?

         a)  Last week, Bob was paid a total of $480.

         b)  This week Bob produced 2 items more than last week and was paid a total of $510.

              Key: E

              I thought C

 

4)  If n and t are positive integers, what is the greatest prime factor of the product nt ?

         a)  The greatest common factor of n and t is 5.

         b)  The least common factor of n and t is 105.

             Key: B

             I thought D

guozili

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

a)       (3r+2-s)(4r+9-s)=0

b)       (4r+6-s)(3r+2-s)=0

Key:C

       I thought D

由a）3r+2-s=0或4r+9-s=0都满足a，4r+9-s=0产生的(r,s)不满足y=3x＋2

b）同理，

所以a)b)联立可得3r+2-s=0，满足

所以选C

guozili

2)  A constuction company was paid a total of 500,000 for a job. The only costs are labor and materials. Was the company's profit greater than 150,000?

         a)  Company's total cost was 3 times it's cost for materials.

         b)  The company profit was greater than its cost labor.

500000应该是收入

要profit=500000-(costL+costM)>150000,      应有(costL+costM)<350000

a)不能得出profit>150000

b)假设profit=100000,costL可以小于100000

a/b联立，推出profit=500000-(costL+costM)>costL=2/3(costL+costM)可得300000>(CL+CM)

从而得到profit=500000-(costL+costM)>200000>150,000

[此贴子已经被作者于2007-10-18 0:58:58编辑过]

sydneyang

Thanks for your help. But I still don't get it. I am math dummie.

Could you further explain why "4r+9-s=0产生的(r,s)不满足y=3x＋2".

I guess i don't see the relationship of the statements given to the problem itself.

Many thanks...if you could explain...

guozili

3)  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 3/2 times that amount for each additional item. How many items did Bob produce last week?

         a)  Last week, Bob was paid a total of $480.

         b)  This week Bob produced 2 items more than last week and was paid a total of $510.

              Key: E

              I thought C

由条件 假设bob做了n个item

则bob的收入Income

当n<36  Income=xn

当n>36  Income=36x+(n-36)*(3/2x)

a)b)条件均无法判断n<36还是>36所以是E

guozili

Could you further explain why "4r+9-s=0产生的(r,s)不满足y=3x＋2".

应该这样说，4y+9-x=0是一条直线，y=3x＋2也是一条直线，他们会有交点，会有解，但是不是4y+9-x=0上所有的点都能落在y=3x＋2上，也就是说4y+9-x=0不一定满足y=3x＋2.，也就不能推出（r,s）一定在y=3x＋2上

guozili

4)  If n and t are positive integers, what is the greatest prime factor of the product nt ?

         a)  The greatest common factor of n and t is 5.

         b)  The least common factor of n and t is 105.

             Key: B

             I thought D

选B么？选E吧

a)考虑 n=5 t=5*17 or5*19 or 5*一个比较大的质数，都不能得到最大的prime factor of n*t

b)这种情况可能出现么？既然105都是n和t的factor，那3,5,7就更应该是n和t的factor了啊？

sydneyang

Hee....Sorry.

It should read: "The least common multiple of n and t is 105.

Btw, i got the other problems, thank YOU.

sydneyang

nn,

FINALLY, I GOT THEM ALL! YEAH...

THANK YOU, THANK YOU, and Thank You.