【求助】prep2道

129.  13872-!-item-!-187;#058&010142
If t is a positive integer and r is the remainder when t^2 + 5t + 6 is divided by 7, what is the value of r ?
 
(1) When t is divided by 7, the remainder is 6. 
 
(2) When t^2 is divided by 7, the remainder is 1.

还有一道：A certain list contains of different integers. Is the product of all integers in the list positive?

                (1) 最小的乘以最大的是正的

              （2）有一个数是偶数 

第一题选a第二题选c；

没思路呀...请求指点...

If t is a positive integer and r is the remainder when t^2 + 5t + 6 is divided by 7, what is the value of r ?
 
(1) When t is divided by 7, the remainder is 6. 
 
(2) When t^2 is divided by 7, the remainder is 1.

答案是A

条件(1):T被7除的时候,余数为6,说明T=6或者13,20....(就是7的倍数再加6),然后把这些数代入提干里t^2 + 5t + 6 ,可以算出余数都等于2.充分

条件(2):同理条件1,t^2 被7除的时候,余数为1,说明t^2 =1或者,8,15,22,29,36,43,50,57,64...而这些数中有36和64是可以被完全平方的,就是说T可能等于6也可能等于8,代入t^2 + 5t + 6,得出的余数是2和5,条件2不充分

还有一道：A certain list contains of different integers. Is the product of all integers in the list positive?

                (1) 最小的乘以最大的是正的

              （2）有一个数是偶数(这里应该是说一共有偶数个数包括在这个LIST里,而不是有一个数是偶数吧)

条件(1)可以知道最小的和最大的数同号,都为负或者都为正,但是不知道数列里有多少个数,比如全都为正的,那么乘积为正,但是如果都是负的,那么如果有偶数个数乘积为正,有奇数个数则乘积为负.因此条件1不充分.

条件(2)弥补了条件一的不充分

因此答案选C

懂了，谢谢！