JoshwuS

1. for all positive integers m,
m（包了一个方框）=3m， if m is odd;
m(包了一个方框）=1/2m, if m is even
which is equivalent to 带方框的9*带方框的7？

First, I believe, the nubmer 7 should be number 6.

Secondly, I believe the answers are all in blocks!  Think about the ramifications!

JoshwuS

2.if n is a positive integer and the product of all the integers from 1 to n,  is a multiple of 990, what is the least possible value of n?

n! = n*(n-1)*. . . *2*1= m*990 = m*11*9*5*2

So n! contains the factors of 11, 9, 5, and 2.  Then n is at least as big as 11!

JoshwuS

3. of the 60 animals on a certain farm, 2/3 are either pigs or cows. how many of the animals are cows?
1) the farm has more than twice as many cows as it has pigs.
2) the farm has more than 12 pigs.

So among the 60 animals are 40 pigs and cows.

1) number of cows > 2*[numbers of pigs]. Two many possibilities.  39 cows and 1 pig; 38 cows and 2 pigs; etc. Insufficient.
2) number of pigs > 12.  Again two many possibilities. 39 pigs and 1 cows; 38 pigs and 2 cows, etc. Insufficient.

1) and 2).  Based on 2) At least 13 pigs. Then according to 1), at least 27 cows.  But wait. 13+ 27 = 40.  That's it.  That's the only possibility.  Sufficient.