Math problems for October 7 2011

Problem #1


Suppose the time is now 2 o'clock on a twelve-hour clock which runs continuously. What time will it show 1,000 hours from now?


Problem #2
The average of five numbers is 6. If one of the five numbers is removed, the average of the four remaining numbers is 7. What is the value of the number that was removed?


Problem #3


If you start with 3 and count by 7s, you get the terms of the sequence 3, 10, 17, ..., 528 where 3 is the 1st term, 10 is the 2nd term, 17 is the 3rd term, and so forth up to 528 which is Nth term. What is the value of N?


Problem #4


When a counting number is multiplied by itself, the result is a perfect square. For example 1, 4, 9 are perfect squares because 1 x 1 = 1, 2 x 2 = 4, and 3 x 3 = 9. How many perfect squares are less than 10,000?


Problem #5


A restaurant has a total of 30 tables which are of two types. The first type seats two people at each table; the second type seats five people at each table. A total 81 people are seated when all seats are occupied. How many tables for two are there?