A couple of Maths Qs for As ?

gigi

1. By the use of a certain code to distinguish 12 participants, this code can be one letter or two letters in alphabetical order. How many at least the numbers of the letters should be used? ********** Is the answer 5? A B C D E 4 letters: 3+2+1+4=10 AB BC CD DE 5 letters: 4+3+2+1+5= 15 AC BD CE AD BE AE 2. A gentleman possesses 5 suits and 7 ties, in which only one suit can match exactly the specific tie, and others can be matched in will ( randomly ). How many combinations does the man can match his tie and suit? ************ C(4,1)* C(6,1) +1= 25 ???? Why the answer in Feifei’s handouts is 29? How to solve this out? 3. A parallelogram with the length of two sides 6 and 7, which one of the followings can be the area of the parallelogram? A) 21 B) 42 C) 84 ********** How to figure out? 4. From 1-100 inclusive, what is the possibility of N*(N+1) that can be divided by 4? What is the possibility of N*(N+1) that can be divided by 3? ************ I calculated by writing the first several numbers and found out that for 4 numbers, there are two that can be divided by 4 and 2 out of 3 that can be divided by 3. Therefore the answer should be ½ and 2/3. Is that right? And is there any easy way to think out of the Q? 5. There are 8 books, 6 of them are paper books and 2 of them are hardcover books, what is the combination of at least one hardcover book? ************ C(2,1) * C ( 6, 3) Why C ( 6, 3) ? Took for 4 times? Not sure! Thx! 6. DS: 45% the apartments with <=3 people living in each one. What’s the median? (1) 80% of the apartments have <=5 (2) 35% of the apartments have >=5 ************* Is the answer B? Why or Why not? Tons of Thx! [em18][em18]

tongxun

5、题目不完整，因为没说取几本。
  取2本，则C6，1 * C2，1 +`C2，2`
  取4本，则C2，1 * C6，3 +C2，2 * C6，2
6、B
  条件1）：中数有可能是4、5
  条件2）：在中间的数字=中数是4。
因为人是整数。

gigi

THX once more!

2. You meant that only the tie had specific requirement for matching? That explains.

3. the Ans in Feifei is 1&2.

tongxun

1、这题主要是对in alphabetical order的理解。我认为是 5。
   但也有人认为in alphabetical order 是：AB、BA都行。这个我不同意。
2、问题出在你对英文的阅读上。
  and others can be matched 这里的and others 是指suits ，而不是ties。
所以，C4，1 *C7，1 +1=29
3、平行四边形的面积=底 * 高。
  画图，做一高。若底=7，则该高小于6，因为直角边小于斜边。
  面积小于42。
因此，选A