og12~161

chanyeen

161. Beginning in January of last year Carl made deposits of $120 into his account on the 15th of each month for several consecutive months and then made withdrawals of $50 from the account on the 15th of each of the remaining months last year. There were no other transactions in the account last year. If the closing balance of Carl's account for May of last year was $2600, what was the range of the monthly closing balances of Carl's account last year?

(1) Last year the closing balance of Carl's account for April was less than $2625
(2) Last year the closing balance of Carl's account for June was less than $2675
这题选c。看了og的解释，还是不明白，大侠们，能帮帮我吗？这题应该如何解决呢？谢谢

caicainiao

客气客气呀

chanyeen

回复 5# caicainiao


    太感谢了

myice

回复 5# caicainiao


    good

caicainiao

回复 4# chanyeen


    本来里面就有钱呀

设X代表为X月开始取钱月,则X-1月为存款月

(1) Last year the closing balance of Carl's account for April was less than $2625

4月<2625,如果5月是取款月，则5月<2575,而5月为2600.所以5月不是取款月，X>5

(2) Last year the closing balance of Carl's account for June was less than $2675

6月<2675,如果6月是存款月，则6月=2600+120=2720。所以6月不是存款月，X<=6

所以X=6 。

因为X>120/50,所以最后一月账户值比年初要低，所以为最小值，而最大值为X-1月即5月账户值，极差=50*7=350

chanyeen

回复 3# MAXworld


    but 即使他每月存钱不取钱，从一月份开始到5月份，每月存120,5各月才600阿，怎么可以产生两千多来呢

MAXworld

回复 1# chanyeen


   
这题的关键在于找出转折点，既哪个月开始取钱，根据（2）我可以知道6月已经在取钱，但不能肯定5月的情况，如果我发现5是存钱的，那我就知道6月是转折点，从而找出各月的balance.

MAXworld

首先题中说closing balance of May 是2600，closing balance of April 少于2625，那说明5月肯定是存钱了，因为如果是取钱，4月底少于2625，5月如果取乐50，那5月底的balance就少于2600了。同时，题中说六月底的balance少于2675,那说明六月肯定是取钱了，不然的话六月底的balance应该是2720（不符合题意）。所以综上所述c是对的。