1) Suppose the time is now 2 o'clock on a twelve-hour which runs continuously. What time will it show 1,000 hours from now?
2) When a natural number is multiplied by itself, the result is a perfect square. For example, 1, 4, and 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?
3) A work team of four people completes half of a job in 15 days. How many days will it take a team of ten people to complete the remaining half of the job? (Assume that each person of both teams works at the same rate as each of the other people).
1) The time 2 o'clock is repeated every twelve hours. There are 83 twelves in 1,000 plus a remainder of 4. Therefore the clock will show a time of 6 o'clock 1,000 hours from now.
2) Since 10,000 = 100 x 100, each of the perfect squares 1 x 1, 2 x 2, 3 x 3, . . . , 99 x 99 is less than 100 x 100. There are 99 numbers in the above sequence.
3) Four people working 15 days is equivalent to one person working 60 days. To complete the other half of the job, ten people would have to work 6 days which is also equivalent to one person working 60 days.