81. My father is three times as old as my sister, who is twice as old as my
brother, who is twice as old as our nephew. The total of all ages is divisible by five and less than 100. How old is my father?

60. Here is how to get it: nephew = x, brother = 2x, sister = 4x, father = 12x total of 19x = some number divisible by 5 but less than 100. The only number that fits is 95; so 19x = 95; so x = 5. nephew = 5, brother = 10, sister = 20 and father = 60.

82. Kevin treated his girlfriend to a bus ride, but because of his limited
resources they had to walk back. Now, if the bus goes at an average speed of 9 miles per hour and they can walk back at the rate of three miles per hour,
how far did they ride so that they made it back in eight hours?

They can ride 3 times as fast as they can walk, so 3/4 of their time must have been spent walking, and only 1/4 in riding; therefore, they rode for 2 hours, going 18 miles, and walked back in 6 hours.

83. Using the numbers 1 through 9, how many three-digit palindromic numbers can
you make? A palindrome reads the same forward and backward. Examples: 181, 545, 858.

81 palindrome numbers can be made.

84. Which set of numbers would most logically come next in the following sequence?

10 1 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2

(a) 9 1 (b) 9 3 (c) 8 5 (d) 6 7

(a) 9 1. There are two series, one starting with 10 and going down one number each time, and one starting with 1 and going up one number each time.

85. Can you think of a geometric series of whole numbers with three or more
numbers which add up to a square? Start with 1. Example: 1 + 3 + 9 + 27 + 81 = 121 = 11 squared.

Here is one answer: 1 + 7 + 49 + 343 = 400 + 20 squared. You may have found others.

86. Two ferries start at the same time from opposite sides of a river, traveling across the water on routes at right angles to the shores. Each boat travels at a constant speed, though their two speeds are different. They pass at a point 720 yards from the nearer shore. Both boats remain at their slips for 10 minutes before starting back. On the return trips, they meet 400 yards form the other shore. How wide is the river?

The river is 1760 yards wide ( one mile ). How long they stayed at their slips is irrelevant.

87. What is the significance of this sequence?

235, 711, 131, 719, 232, 931, 374, 143

The sequence is a list of some of the prime numbers (numbers divisible only by themselves and 1) starting at 2 and them lumping their digits into sets of 3: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43.

88. A man left a legacy of $10,000 to three relatives and their wives.
Together, the wives received $3960. June received $100 more than Camille, and Martha received $100 more than June. Jack Smith was given just as much
as his wife, Horace Saunders got half as much again as his wife, and Terry Connors received twice as much as his wife. What was the first name of
each man's wife?

As it is evident that Camille, June and Martha received respectively $1220, $1320 and $1420, making the total of $3960 left to the three wives, if Jack Smith receives as much as his wife Camille, $1220; Horace Saunders half as much again as his wife June, $1980; and Terry Connors twice as much as his wife Martha, $2840, then we have correctly paired the married couples and accounted for exactly $10,000.

89. What is the number that is one more than one-fifth of one-third of one-half of one-tenth of 2,700?

10. (2,700 ÷ 10 = 270; ÷ 2 = 135; ÷ 3 = 45; ÷ 5 = 9; + 1 = 10).

90. What is the number which is 5 more than one-fifth of one-tenth of one-fourth of 1000?

10. (1000 ÷ 4 = 250 ÷ 10 = 25 ÷ 5 = 5 + 5 = 10).