以下是引用Luluisland在2007-4-29 18:56:00的发言:1. DS:If t is a positive integer and r is the remainder when t平方+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平方 is divided by 7, the remainder is 1
====》 有题目可以知道:
1)假设 t = 7k+6 ===> t平方+5t+6 = 49k^2 +84k+36+35k+30+6= 49k^2 + 119k+72 ===> t平方+5t+6 除7 的余数是2.
2)假设 t^2 = 7k+1 ==> t平方+5t+6 =7k+1 + 5(7k+1)^(1/2) + 6 ===> 由于 5(7k+1)^(1/2) 除7的余数不确定(取k=5, 余数为2;取k=9, 余数为5; ,所以 2) 无法得出结论。
===》 答案为 A.
2. DS:Store S sold a total of 90 copies of a certain book during the seven days of last week, and it sold different numbers of copies on any two of the days. If for the seven days Store S sold the greatest number of copies on Saturday and the second greatest number of copies on Friday, did Store S sell more than 11 copies on Friday?
1) Last week Store S sold 8 copies of the book on Thursday
2) Last week Store S sold 38 copies of the book on Saturday
==> 有题目设Starday 销售为n, Friday 为 m, 其余5天为k. (k,m,n 为正整数)
则有 90 = 5k + m + n 且 n > m > = k . 题目要求判断 m 是否大于11
1) ===》 k = 8 ===> m + n = 40 . 无法确定 m 的值是否大于11.
2) ===》 n =38 ==> m+5k = 52 , 由于k,m,n 为正整数,且 n > m > = k ,则k 和m 的组合中 k 最大只能取值8 ,此时m=12, 大于11(如果k =9 ,则 m = 7 , m< k )
==> 有题目设Starday 销售为n, Friday 为 m, 其余5天为k. (k,m,n 为正整数)
则有 90 = 5k + m + n 且 n > m > = k . 题目要求判断 m 是否大于11
1) ===》 k = 8 ===> m + n = 40 . 无法确定 m 的值是否大于11.
2) ===》 n =38 ==> m+5k = 52 , 由于k,m,n 为正整数,且 n > m > = k ,则k 和m 的组合中 k 最大只能取值8 ,此时m=12, 大于11(如果k =9 ,则 m = 7 , m< k )
==》 答案为 B.3. PS: For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75=3*5*5. How many two-digit positive integers have length 6?
a. None b. One c. Two d. Three e. Four
==》 要positive integers have length 6,而且为two-digit positive integers 。 ===》 即为求小于100 且质数因子个数等于6的数的个数
==》 最小的质数因子为2 则 可以接受的是 2^6 = 64, 和 2^5 * 3 = 96 这两个数。如果取2^4 * 3^2 = 144 > 100
==》 答案为C
答案1. A 2. B 3. C
还有两道verbal题在附件里。