请教Game 2003-A-14, A-19

dragon07

2003 - A-14

A bakery makes exactly three kinds of cookies-oastmean, peanut butter, and sugar. Exactly three batches of each kind of cookie are make each week (Monday to Friday) and each batch is made, from start to finish, on a single day. The following conditions apply:

No two batches of the same kind of cookie are make on the same day.

At least one batch of cookies is made on Monday.

The second batch of oatmeal cookies is made on the same day as the first batch of peanut butter cookies.

The second batch of sugar cookies is made on Thursday

14 Question:

How many of the days, Monday through Friday, are such that at most two batches of cookies could be made on that day.?

(A) one

(B) Two

(C) three

(D) four

(E) five

Answer: (A);  why? I think (C) is right.

2003-A-19

For the school paper, 5 students - J, K, L,M, and O - each review one or more of exactly 3 plays: S, T, and U, but do not review any other plays. The following must apply:

K and L each review fewer of the plays than M.

Neither L nor M reviews any play J reviews.

K and O both review T

Exactly two of the students review exactly the same play or plays as each other.

Question:

which one of the following could be an acuurate and complete list of the students who review only S?

(A). L

(B). O

(C). J, L

(D). K, O

(E). L, M

My answer is (C), but the right answer is (A), why?

况天佑

２００３年１２月的题吧

楼主的Ａ－１９　第二组题确实选Ａ答案

原因是这样

条件是

１．Ｋ＜Ｍ　Ｌ＜Ｍ

２．ＬＪ（否）＆ＭＪ（否）

３．Ｋ＝Ｏ＝Ｔ

４．至少两个学生完全一样

从条件１和２可以得知：Ｋ、Ｊ、Ｌ肯定只有１个play，Ｍ肯定只有两个plays

（简单原因是既然K有1个了，那么M肯定是2个或者3个，然而M是3个的话，肯定就和J有一样的，所以M只能是2个，那么自然J、L就只有1个了，K也只能有1个了）

问题是哪个学生只有S，那么首先排除K、M、O，只剩J和L

然而他们俩根据条件2又不能一样

因此只能其中之一有

那么看选项，只有（A）答案符合

dragon07

谢谢, 我以为该题是问有多少人可以只选S, 则J.L都可,就如以前的题一样, 但这次却不一样了.

况天佑

嗯，第一题还真可以探讨探讨，我也觉得答案很麻烦

dphxmg

If we exhaust what is implied by the conditions, we can have the following two scenarios:

Scenario 1:    

     >=1                     

      1   2   3   4   5                                                                

o             o2                                                   

p     x       p1  p2  p3                                

s                    s2  s3 

o1=1/2,o3=4/5,

s1=1/2/3

x means void. It is the same in the next Scenario 2.

Or Scenario 2:

       >=1

       1     2    3    4    5             

o      o1  o2                                

p      x     p1                                   

s                        s2   s3   

o3=3/4/5,

p2=3/4, p3=4/5

s1=1/2/3

               

The question implies that threre must be one or more days when it is impossible that 3 or more than three batches are baked. Thus our task is to first find such day or days when three or more batches can be baked and exlude it or them.   

In scenario 1, it is possble to bake 3 batches on wed,thu, or friday.

In scenaro 2, it is possible to bake 3 batches on tue,wen,thu, or friday.

Thus, monday is the only day when at most 2 batches can be baked.

So the key is  A.                                           

[此贴子已经被作者于2007-4-6 2:20:31编辑过]

bsmzel

由于O2P1，故MON不可能有O1，故MON不可能有3炉

若O2P1在TUE，则TUE，WED，THU，FRI都有可能出现一天3炉的情况，自己画图就能明白，很容易的(这图我没法画出来在论坛上-_-""）

[此贴子已经被作者于2007-4-6 2:12:34编辑过]

dragon07

谢谢! 看来, 理解提问是关键. 敌情很严重.

况天佑

呵呵，对啊，第一题我也没有好好理解了