请教陈向东数学后面模拟题~

这几道题百思不得其解,希望高人可以解答一下^^

problem solving
1.if n is a positive interger and n^2 is divisible by 72, then the largest positive integer that must divide n is
a.6 b.12 c.24 d.36 e.48

2.a square countertop has a square tile inlay in the center, leaving an untiled strip of uniform width around the tile. if the ratio of the tiled area is 25 to 39, which of the following could be the width, in inches, of the strip?
(1).1 (2).3 (3).4
a.(1)only b.(2)only c.(1) and (2) only d. (1) and (3) only e. (1), (2), (3)

data sufficient
1. a home owner must pick between paint A, which costs $6.00 per liter, and paint B, which costs $4.50 per liter. Paint B takes one-third longer to apply than paint A. If the home owner must pay the cost of labor at the rate of $36 per hour, which of the two paints will be cheaper to apply?
(1) the ratio of the area covered by one liter of paint A to the area covered by paint B is 4:3
(2) paint A will require 40 liters of paint and 100 hours of labor

2. in a certain law firm there are five senior partners and all senior partners receive bonuses greater than those of the junior partner. Does senior partner Johnson receive the largest bonus of the lawyers at the firm?
(1) Johnson receives a bonus greater than twice the average bonus for all the senior partners.
(2) all partners receive some bonus, and Mr. Johnson receives five times the average given to all the partners.

1.72=6*6*2，n^2可以被72整除，那么n就应该=6*2*m，m为整数

可以整除n的就有2，6，12，12m。因为m的值未知，因此我们只能肯定能够整除n的最大整数一定是12

2、把图画出来

设contertop的边长为b,tile的边长为a，就有a^2/b^2-a^2=25/39，解得a/b=5/8

设strip的宽为x,得b=a+2x，因此x=3a/10=3b/16 题目没有说明a或b得范围 所以三个数都可以

ds2、（1）只能知道J得到了所有senior的2/5，没有关于junior的信息，因此不能得出结论

     （2）知道J得到了senior+junior所有人的1/2，又知道每个人都有bonuses，所以可以判断J是最多的

选B

讹``我想问问为什么72=6*6*2，n^2可以被72整除，n就应该=6*2*m? 我数论不好```每次都要想很久```

还有想问问高人``知道J得到了senior+junior所有人的1/2是怎么推出来的啊``我就卡这了```

Mr. Johnson receives five times the average given to all the partners.

J=5[(senior+junior)/10]然后约分出来的

还有那个...不是什么高人...只是做过这些题，互相帮助吧！