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?

A metal pole which is 1.05 meters long, if placed diagonally can easily fit into a square or a rectangular package that is less than 1 meter in dimensions. For example, a 75 centimeters x 75 centimeters square package can contain the pole.

32. What is the next number in the sequence below?

1
4
9
7
7
9
4 1 ?

9. The sequence reflects a single-digit sum of the digits of the squares of the first 9 counting numbers, obtained by adding the two digits together until a single digit results...... 1 squared = 1 2 squared = 4 3 squared = 9 4 squared = 16 ( 1 + 6 = 7 ) 5 squared = 25 ( 2 + 5 = 7 ) 6 squared = 36 ( 3 + 6 = 9 ) 7 squared = 49 ( 4 + 9 = 13 ) ( 1 + 3 = 4 ) 8 squared = 64 ( 6 + 4 = 10 ) ( 1 + 0 = 1 ) 9 squared = 81 ( 8 + 1 = 9 ).

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?

The man makes an overall profit of $10 + $10 = $20. In the first trade, the man buys the horse for $60 and sells it again for $70, so he makes a profit of $10. In the second trade, the man buys the horse for $80 and sells it again for $90, so he again makes a profit of $10.

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?

44.44 mph. For the sake of easy mathematics, let's say you need to go 200 miles to get to work. At 50 mph it will take you 4 hours; at 40 mph it will take you 5 hours. The essence of the problem is that you need to find the average speed of traveling 400 miles in 9 hours, which is 44.444....mph.

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?

Yes. And, it there will be .63 gallons of fuel left.

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

371. 3 cubed + 7 cubed + 1 cubed.

37. Which is larger, the number of seconds in a day or the number hours in 10 years?

Hours in 10 years. There are 86,400 seconds in a day and there are over 87,000 hours in 10 years - including leap years.

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?

48. On table one, each stamp could be purchased for 66 2/3 cents or 2/3 of one dollar.
On table two, each stamp could be purchased for 62 1/2 cents or 5/8 of one dollar, the difference between 2/3 and 5/8 of one dollar is 1/24. 2/3 - 5/8 = 16/24 - 15/24 = 1/24. One-twenty-fourth of one dollar is 4 1/6 cents. Since Marcus purchased two dollars worth of stamps more than Julius, and he paid 4 1/6 cents more for each stamp, divide 200/4 1/6 = 200/25/6 = 200 x 6/25 = 48 stamps.

39. What is the next number in this series:

1248 1632 6412 8256 ?

Regrouping the series as 1, 2, 4, 8, 16, 32, 64, 128, and 256, the next two terms in this series are 512 and 1024. The answer to the question is 5121.

40. How many different ways can seven people arrange themselves in a row of seven seats?

5,040 ways. 7 x 6 x 5 x 4 x 3 x 2 x 1. The first person can choose any of 7 seats, the second person any of 6 seats, the third any of five seats, etc.