求教prep-ds1-145，149，159

145. 14689-!-item-!-187;#058&010088
On her way home from work, Janet drives through several tollbooths.  Is there a pair of these tollbooths that are less than 10 miles apart?

(1)  The first tollbooth and the last tollbooth are 25 miles apart.

(2)  Janet drives through 4 tollbooths on her way home from work.

本题答案C，题目没有说收费站之间的距离是相等的，为什么会是C？

149. 14908-!-item-!-187;#058&010196
If m, r, x, and y are positive, is the ratio of m to r equal to the ratio of x to y ?

(1)  The ratio of m to y is equal to the ratio of x to r.

(2)  The ratio of m + x to r + y is equal to the ratio of x to y.

答案B

159. 15957-!-item-!-187;#058&010660
If n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what is the value of r ?

(1) n is not divisible by 2.

(2) n is not divisible by 3.

答案C

求教解法！

145. 14689-!-item-!-187;#058&010088
On her way home from work, Janet drives through several tollbooths.  Is there a pair of these tollbooths that are less than 10 miles apart?

(1)  The first tollbooth and the last tollbooth are 25 miles apart.

(2)  Janet drives through 4 tollbooths on her way home from work.

本题答案C，题目没有说收费站之间的距离是相等的，为什么会是C？

根据1＋2，中间有4个tollbooths，一共是25miles，那么必定有2个之间距离<10,因为如果3个或者4个>10miles的话，总数必将超过25miles

149. 14908-!-item-!-187;#058&010196
If m, r, x, and y are positive, is the ratio of m to r equal to the ratio of x to y ?

(1)  The ratio of m to y is equal to the ratio of x to r.

(2)  The ratio of m + x to r + y is equal to the ratio of x to y.

答案B

(m+x)/(r+y)=x/y,->(r+y)x=(m+x)y->rx=my->x/y=m/r

159. 15957-!-item-!-187;#058&010660
If n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what is the value of r ?

(1) n is not divisible by 2.

(2) n is not divisible by 3.

答案C

根据1和2分别都推不出来，根据1：n是奇数－>n-1 或者n+1一个是2的倍数，一个是4的倍数，所以含有因子8；

根据2：n不是3的倍数－>n-1 或者n＋1肯定有个3的倍数

1＋2：(n - 1)(n + 1) 肯定是8X3＝24的倍数－>r＝0充分