GMAT數(shù)學(xué)備考資料：費費數(shù)學(xué)寶典詳解版(八).

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 舉反例：當(dāng)Y=4，X=4時，X/Y的余數(shù)為0。當(dāng)Y=3，X=10時,X/Y的余數(shù)為1. (2)X+Y=Y*K+4 則X=(K-1)Y+4, 所以X/Y的余數(shù)為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】設(shè)最大的數(shù)為X, 則共有(X-3+1)個數(shù)字, (1)利用求和公式, (3+X)(X-3+1)/(X-3+1)=6, 則X=9, 所以這個集合共有7個數(shù)字. (2) The number of integers為(X-3+1), one more than the range of the set為(X-3+1), 兩邊一樣的，無法求出X.

8、10*10的table里每個格里只能放-100， 0， 100這3個數(shù)中的一個，問sum of the table entries>0?

（1）每一行只有一個是正數(shù)；

（2）每一列只有一個是正數(shù)；

【答案】E

【思路】無論是(1)或(2), 還是(1)+(2),都無法確定整個表格的和,因為在每個格中都放0,或100或-100或每一行只有一個是正數(shù)100,其他還是可以隨便放,可都放0或-100,結(jié)果就不同,前者和大于0,后者和小于0.同樣地條件一和二都無法確定和的正負情況.

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】主要考慮到這樣的數(shù)字,如:通過條件一N可能為根號2, 可是根號2是無限不循環(huán)小數(shù),是無法用分數(shù)表示的.只有循環(huán)小數(shù)和分數(shù)都是有理數(shù),可以互相轉(zhuǎn)化.

10、|a-b|>|a+b|?

(1) ab<0;

(2) a>b;

【答案】A

【思路】(1)知A與B是異號,可得|a-b|>|a+b|