[求助]如何解答这几道数学题？请高手帮忙。

xiulingwang

    

 

    

请大牛们指点迷津！
        我在OG11中遇到了这几道题，不知道如何解答。

    

1.A rainstorm increased the mount of water
stored J reservoirs from 124 billion gallons to 138 billion gallons. If the
storm increased the mount of water in the reservoirs to 82 percent of total
capacity, approximately how many billion gallons of water were the reservoirs
short of total capacity prior to the storm?

    

A 9

    

B14

    

C25

    

D 30

    

E 44

    

 

    

2． Right triangle PQR is to be constructed in the xy-plane so that the
right angle is at P and PR is parallel to the X-axis. The x- and y-coordinates
of P,Q, and R are to be integers that satisfy the inequalities -4<=x<=5 and 6<=y<=16.How many
different triangles with these properties could be constructed?

    

A 110

    

B 1100

    

C 9900

    

D 1000

    

E 12100

    

 

    

下面是两道date
sufficiency 类型题：

    

 

    

3. Does the integer k have a factor p such
that 1<p<k?

    

(1)k >4!

    

(2)13! + 2<= K <=
13! +13

    

4. 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 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 21^st day of the billing cycle.

    

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

freedomzhx

以下是引用xiulingwang在2008-1-15 1:33:00的发言：

1.A rainstorm increased the mount of water
stored J reservoirs from 124 billion gallons to 138 billion gallons. If the
storm increased the mount of water in the reservoirs to 82 percent of total
capacity, approximately how many billion gallons of water were the reservoirs
short of total capacity prior to the storm?

138/0.82-124约等于44
  

2． Right triangle PQR is to be constructed in the xy-plane so that the
right angle is at P and PR is parallel to the X-axis. The x- and y-coordinates
of P,Q, and R are to be integers that satisfy the inequalities -4<=x<=5 and 6<=y<=16.How many
different triangles with these properties could be constructed?

 相当于在一个10乘以11的矩形边界中，枚举所有的直角三角形个数。思路为：在这样一个矩形边界中存在C(10,2)*C(11,2)=45*55个小的矩形，每一个小的矩形中都可以有4个直角三角形（以其中三个矩形定点为端点）

结果为：4*45*55=9900
 

3. Does the integer k have a factor p such
that 1<p<k?

(1)k >4!

 4!=24,大于24的质数还有很多，例如29。所以如果k=29，则不存在p

(2)13! + 2<= K <=
13! +13

 满足上述条件的k总可以写成 (n+1)*m，其中m=2,3,....,13，n*m=13!，因此存在这样的p

第四题没太理解，请哪位NN回答一下，谢谢！

[此贴子已经被作者于2008-1-15 14:39:00编辑过]

xiulingwang

freedomzhx,Thank you so much!