6、If x and y are integers and xy<>0, what is the remainder when x is divided by y?
(1) when x is divided by 2y, the remainder is 4;
(2) when x+y is divided by y, the remainder is 4;
【答案】B
【思路】(1)X=2Y*K+4 举反例：当Y=4，X=4时，X/Y的余数为0。当Y=3，X=10时,X/Y的余数为1. (2)X+Y=Y*K+4 则X=(K-1)Y+4, 所以X/Y的余数为4
7、One set of numbers consists of consecutive integers and the least number is 3. How many numbers are there in the set?
(1) The average of all the numbers in the set is 6;
(2) The number of integers is one more than the range of the set.
【答案】A
【思路】设最大的数为X, 则共有(X-3+1)个数字, (1)利用求和公式, (3+X)(X-3+1)/(X-3+1)=6, 则X=9, 所以这个集合共有7个数字. (2) The number of integers为(X-3+1), one more than the range of the set为(X-3+1), 两边一样的，无法求出X.
8、10*10的table里每个格里只能放-100， 0， 100这3个数中的一个，问sum of the table entries>0?
(1)每一行只有一个是正数;
(2)每一列只有一个是正数;
【答案】E
【思路】无论是(1)或(2), 还是(1)+(2),都无法确定整个表格的和,因为在每个格中都放0,或100或-100或每一行只有一个是正数100,其他还是可以随便放,可都放0或-100,结果就不同,前者和大于0,后者和小于0.同样地条件一和二都无法确定和的正负情况.
9、If n=p/q，and both of p and q are non-zero integers, is n an integer?
(1) n^2 is an integer;
(2) n^3 is an integer;
【答案】D
【思路】主要考虑到这样的数字,如:通过条件一N可能为根号2, 可是根号2是无限不循环小数,是无法用分数表示的.只有循环小数和分数都是有理数,可以互相转化.
10、|a-b|>|a+b|?
(1) ab<0;
(2) a>b;
【答案】A
【思路】(1)知A与B是异号,可得|a-b|>|a+b|