PREP破解版-数学难题求解！（真是难题啊）

zz20090607

90.       

On Jane's credit card account, the average daily balance for a 30-day billing cycle is the average (arithmetic mean) of the daily balances at the end of each of the 30 days.  At the beginning of a certain 30-day billing cycle, Jane's credit card account had a balance of $600.  Jane made a payment of $300 on the account during the billing cycle.  If no other amounts were added to or subtracted from the account during the billing cycle, what was the average daily balance on Jane's account for the billing cycle?

 

(1)  Jane's payment was credited on the 21st day of the billing cycle.

 

(2)  The average daily balance through the 25th day of the billing cycle was $540.

ANSWER: D

不解（2）为什么sufficient，条件只给了第25天的余额，表明当天花了60元，但payment 300中剩余的240元并不知道是哪天花的.那怎么算the average daily balance for a 30-day billing cycle is the average (arithmetic mean) of the daily balances at the end of each of the 30 days?

149.      15609-!-item-!-187;#058&010412

A certain library assesses fines for overdue books as follows.  On the first day that a book is overdue, the total fine is $0.10.  For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount.  What is the total fine for a book on the fourth day it is overdue?

 

(A) $0.60

(B) $0.70

(C) $0.80

(D) $0.90

(E) $1.00

ANSWER: B

本人解法：total fine 分2种算法,结果取小值：（1）Total = 0.1+ 0.3 X（X 为the number of additinal days)

                                                                (2)  Total= 0.1+0.2+0.4+0.8+.....

本题算第4天的，取小，应为：TotaL=0.1 +0.3*3 =1

                        

烦牛人也翻译下次题

 

7：

For every  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 and 10

(B) between 10 and 20

(C) between 20 and 30

(D) between 30 and 40

(E) greater than 40

ANSWER:E

27.       

38, 69, 22, 73, 31, 47, 13, 82

Which of the following numbers is greater than three-fourths of the numbers but less than one-fourth of the numbers in the list above?

 

(A) 56

(B) 68

(C) 69

(D) 71

(E) 73

ANSWER

烦牛人翻译下此题

33.       

If x^4 + y^4 = 100, then the greatest possible value of x is between

 

(A) 0 and 3

(B) 3 and 6

(C) 6 and 9

(D) 9 and 12

(E) 12 and 15

ANSWER:B

zz20090607

是太简单了，大家屑于帮忙吗？

麻烦好心人帮帮忙，解1道是1道

LLsheep

90题：第25天余额540不是说当天花了60，是到1-25天的平均余额。并且题目说了，除了花300之外没有任何变动。

设600的天数X，300的天数Y

（2）推出（600X+300Y）/25=540且X+Y=25，得出X等于20，即从21天开始余额由600变为300。算30天平均条件充分。

LLsheep

149题：

whichever results in the lesser amount. 意思是选两种算法在当天计算少的那个来罚款

不是按你所想的两种方法各自独立的得出结果

                DAY               1         2                   3                                4

Method1(+0.3)         0.1        0.4              0.2+0.3 =0.5          0.4+0.3=0.7(取低，为答案) 

Method2 (double)    0.1        0.2(取低)    0.2*2=0.4(取低)     0.4*2=0.8

我想是楼主没有理解题意。

[此贴子已经被作者于2009/9/7 12:02:38编辑过]

hcy_sy

27.

38, 69, 22, 73, 31, 47, 13, 82

Which of the following numbers is greater than three-fourths of the numbers but less than one-fourth of the numbers in the list above?

以下哪个数比list中的3/4个数大，1/4个数小

先按大小顺序排列一下 13 22 31 38 47 69 73 82 一共8个数

比3/4大说明比8个数中的6个大 此数>69

比1/4小说明比8个数中的2个小 此数<73

所以选71

不知lz明白否？

LLsheep

以下是引用hcy_sy在2009/9/7 11:47:00的发言：

27.

38, 69, 22, 73, 31, 47, 13, 82

Which of the following numbers is greater than three-fourths of the numbers but less than one-fourth of the numbers in the list above?

以下哪个数比list中的3/4个数大，1/4个数小

先按大小顺序排列一下 13 22 31 38 47 69 73 82 一共8个数

比3/4大说明比8个数中的6个大 此数>69

比1/4小说明比8个数中的2个小 此数<73

所以选71

不知lz明白否？

同意。楼主也是没正确理解题意。

Dancy123

90.这个题目我的理解是300元是一次支出的。

   B是说的意思是前25天的平均是540，说明这300元已经支出了，那么假设有X天是600元，Y天是300元  则方程式：600X+300Y=540*25，X+Y=25，解出方程式就可以得出了

149.首先，那个double的算法不是一次递加只是将前一天的double，而且这个题目说的是每天都看最小的支出：

也就是说第一天是0.1，

第二天是double是0.2比＋0.3=0.4要便宜，所以double，得出第二天需要付的钱是0.2，

同理，第三天double需要是0.4，比＋0.3=0.5便宜，

到了第四天，double是0.8，但是加0.3是0.7，所以每次都用可以付最少的钱的话，最后就是付0.7

33.当Y=0时，X最大，所以X=3.16......，所以选B

剩下的那两道我也很迷糊，弄不清楚，不好意思啦！

hcy_sy

33.       

If x^4 + y^4 = 100, then the greatest possible value of x is between

X^4,Y^4都大于0,问X可能的最大值between...

当Y=0的时候X最大，此时X^4=100，X为正负3点几，因为问最大的可能值 所以选B between3 and 6

zz20090607

楼主非常感谢大家帮忙！

看来主要是题意不解

heroelite

7.

h(100) = 2*4*6*8*...*100
变形，即2^50*(1*2*3*...*50).

所以可以使从1-50 的倍数，公因子从1-50都有

所以h(100)+1 的质factor 必定大于50

选E

[此贴子已经被作者于2009/9/7 17:25:49编辑过]