51. A grandfather clock chimes the appropriate number of times to indicate the
hour, as well as chiming once at each quarter hour. You are in another room and hear the clock chime just once, figuring that it could be any time of
day, which period of time (hours and minutes), or how many minutes total would be the longest period of time you would have to wait in order to determine the
correct time?

Between 12:15 and 1:45 you would have to wait 90 minutes. You would have to wait until you hear 7 single chimes before you would hear the 2 chimes for 2 o'clock.

52. Traffic was really bad going to work this morning. I only managed to average 30 mph. At what speed must I travel home tonight to average 60 mph for the entire round trip?

This cannot be done. It does not matter how far the trip is, for instance, if we use 30 miles, then the morning trip took 1 hour. Now, we are asking that the entire trip average 60 mph, but we have already used up an hour in the morning; so it is impossible. Any speed, (which will also requires time) increases our already used one hour; therefore, we can never average one hour for the entire trip.

53. There are 2 numbers that total 225 and have a ratio of 2 to 13. What are the numbers?

30 and 195. Think of it like this: If there is a ratio of 2 to 13, then there are 15 total parts (2 + 13). One fifteenth of 225 is 15 or one part. Two parts are 2 x 15 or 30, leaving 13 parts x 15 or 195. 30/195 = 2/13.

54. A man bought a number of turkeys at a cost of $60.00, and after reserving
fifteen of the birds he sold the remainder for $54.00, thus gaining .10¢ a head by these. How many turkeys did he buy?

The man bought 75 turkeys at .80¢ each, making $60.00. After retaining 15 he sold the remaining 60 at .90¢ each, making $54.00, as stated. He thus made a profit of .10¢ each on the 60 birds he resold.

55. What 3-digit number (including a decimal point) will give you the same answer whether you subtract 5 or divide by 5?

56. If there are 4 empty seats in a movie theatre, how many combinations are there for the number of ways 4 people could sit in these seats?

24. The answer can be found by starting with 4 numbers or letters, such as 1234, & counting upward using only these 4 numbers to find all of the possible combinations: 1234, 1243, 1324, 1342, etc.

57. What is the 4-digit number (no zeros) in which the third and fourth
digits are a baker's dozen; the second digit is the sum of the third and fourth, and the first digit is double the last?

58. The speed of one train is 6 mph slower than the speed of a second
train. The first train travels 198 miles in the same time it takes the second train to travel 264 miles. What is the speed of the first train?

18 mph. First train mph = x - 6 Second train mph = x set up the proportion: X - 6 / 198 = x / 264 then cross multiply 264(x - 6) = 198x 264x - 1584 = 198x 66x = 1584 x = 24 mph x - 6 = 18.

59. In a recent contest, 45 participants were awarded $300,000 in prize
money. The money was divided into prizes of $4,000 and $8,000. Each of the participants received one prize. How many participants received the
$4,000 prize and how many received the $8,000 amount?

Let's say A = participants receiving $4,000 in prize money and B = participants receiving $8,000 in prize money. A + B = 45. 4,000(A) + 8,000(B) = 300,000 substituting: 4,000 (45-B) + 8,000(B) = 300,000 180,000 - 4,000(B) = 300,000 180,000 - 4,000(B) + 8,000(B) = 300,000 4,000(B) = 120,000 (B) = 30 So, 15 people each received $4,000 and 30 people received $8,000.

60. What is the four-digit number in which the first digit is one-third the
second, the third is the sum of the first and second and the last is three times the second?