31. A man has a metal pole which is 1.05 meters long and he wants to get on a bus, but it is the rule of the bus that passengers are not allowed to carry any items more than 1 meter in length, breadth or height on the bus. He runs into a store and comes out with a package containing the pole. The bus driver allows him on the bus. Why?
33. A man decides to buy a nice horse. He pays $60 for it, and he is very content with this strong animal. After a year, the value of the horse has increased to $70 and he decides to sell the horse. But already a few days later he regrets his decision to sell the beautiful horse, and he buys it again. Unfortunately he has to pay $80 to get it back, so he loses $10. After another year of owning the horse, he finally decides to sell the horse for $90. What is the overall profit the man makes?
34. When you travel to work going 50 mph, you arrive too early when you leave at a specified time. When you travel 40 mph, you arrive too late, leaving at that same time. In both cases, you arrive exactly as early as you arrive late (i.e., time early = time late). How fast should you go to get to work on time, leaving at the same time?
35. A ship is battling against the tide to safety. It uses 9.5 gallons of fuel every hour and sails at 23 mph. It is 34 miles from safety but the flow against it is 12 mph. It has 30 gallons of fuel left. Will it reach safety?
36. There are four numbers that are equal to the sum of the cubes of their
digits. Below are three of them. What is the missing equation?
153 = 1 cubed + 5 cubed + 3 cubed
370 = 3 cubed + 7 cubed + 0 cubed
407 = 4 cubed + 0 cubed + 7 cubed
38. Two brothers went to a stamp-collecting exhibit where they wanted to buy some old stamps to add to their collections. On one table Marcus found sets of 12 stamps selling for eight dollars; the stamps could also be bought individually. Julius went to another table that offered 32 stamps for 20 dollars. They too could be purchased individually. On the way home from the exhibit, Marcus remarked that he had spent only two dollars more for his stamps at one than had Julius, who had purchased his stamps at table two. Both boys had purchased the same number of stamps. How many did each have?