本月数学机经请教

lkmxy1988212

<v2> 另一道是说一个人有一个账户，他只可以进行存500，取三百或者取四百三种方式的交易，是不是交易超过了10次？

（1）三种交易方式至少有一种

（2）最后账户有1600元
这个题怎么做啊？

xxgoodluck

500a-300b-400c=balance

1. because this condition does not restrict on balance, so it is not sufficient. for instance, a=b=c=1 is ok, a+b+c<10, but a=b=c=4 is also ok, and a+b+c>10

2. 500a-300b-400c=1600. a=4, b=0, c=1, a+b+c<10, but a=10, b=10, c=1, a+b+c>10, so this one alone is not sufficient.

1+2, the minimum of a , b, c, is a=7, b=1,c=4, a+b+c>10. so the answer should be C.

PS. I had this one when I took it. C was the anwser I put. And I think it was right.

sdcar2010

500, 1000, 1500, 2000
-400, -800, -1200, -1600, -2000
-300, -600, -900, -1200, -1500, -1800, -2100.

Condition 1. At least once. 500 - 400 - 300 = -200.  Only three transactions. Hence, there is no way you can answer if this month the account holder had at least 10 transactions. Not sufficient.

Condition 2. Sixteen hundred more this month.  Well, if the account holder made 4 deposits of 500 each, and take out cash once 400, 4 * 500 - 400 = 1600, he/she would have 1600 more.  He does not need to use more than 10 transactions. Not sufficient.

Combine both conditions. At least once. 500 - 400 - 300 = -200.  To get 1600 more this month, three different transaction gives -200, so we need to get 1800 more.  Then the question is can you use 6 or fewer steps to get a 1800 by a combination of the three transactions. 500 x 5 - 300 - 400 = 1800.  At least 7 steps.  So combining both conditions is sufficient.

xxgoodluck

-500, -1000, -1500, -2000
400, 800, 1200, 1600, 2000
300, 600, 900, 1200, 1500, 1800, 2100.

Condition 1. At least once. -500 + 400 + 300 = 200.  Three times. There is no way you can answer if this month the account holder had at least 10 transactions. Not sufficient.

Condition 2. Sixteen hundred more this month.  Well, if the account holder made 4 deposits of 400 each, he/she would have 1600 more.  Not sufficient.

Combine both conditions. At least once. -500 + 400 + 300 = 200.  Sixteen hundred more this month.  Three transaction gives 200 more. 1600 - 200 = 1400.  Then the question is can you use 6 or fewer steps to get a 1400 by a combination of the three transactions. 400 x 4 + 300 - 500 = 1400.  Only 6 steps.  So combining both conditions is not sufficient, either.

-- by 会员 sdcar2010 (2010/11/12 11:07:25)

The problem says "deposit" 500, or "withdraw" 300 or 400. not the opposite~~

lkmxy1988212

有能用中文给解释一下的吗？