# Thomas Paine "Rights of a Man

A book is to have 250 pages that will be numbered with Arabic numerals. How many times will the digit 2 be used in numbering the pages?

John and a group of his friends took a bus trip. Each person paid the bus driver with the same combination of 9 coins. If the bus driver received $8.41 from the group, how many dimes did he receive?

A man walks 3 miles east, then 3 miles north, and then 2 miles northeast. How far is he from his starting point?

A culture of bacteria doubles in size twice every day. A dish with 1 million bacteria is full after 15 days. How long will it take for a dish with 2 million bacteria to fill?

1

Two clocks now indicate the true time. One gains a second every hour, and the other gains 3 seconds every 2 hours. In how many days will both clocks again indicate the true time?

2

In his last game, Joe bowled a 199, raising his average by one pin (one point in bowling) to 178. What must he bowl in his next game to raise his average to 179?

3

It takes 1140 digits to number the pages of a book. How many pages are there in the book?

4

The owner of a bicycle shop took inventory of his bicycles and tricycles. He counted 153 wheels and 136 pedals. How many bicycles and tricycles did he have?

5

A large square has a smaller square cut from its corner in such a way that the area of the square removed equals the area of the remaining region. If x represents the length y x of a side of the removed square, and y represents the remaining length, find the ratio x/y.

6

A large circular piece of plywood has an area of 9p square feet. A carpenter plans to cut four congruent, maximum-sized circular pieces from the plywood. What is the length of the radius of each of the four congruent circular pieces?

7

If a rectangular region having an area of 500 square units has its length increased by 20 percent and its width decreased by 10 percent, what is the area of the newly formed region?

8

Two positive numbers may be inserted between 3 and 9 such that the first three numbers in the sequence form a geometric progression and the last three form an arithmetic progression. Find the sum of these two positive numbers.

9

10

Given is a square with each side 2 units long. Arcs are drawn tangent to each other at the midpoints of the sides of the square, as shown. What is the exact area of the shaded region?

11

If x + y = 5, and xy = 3, what is the value of x 2 + y 2 ?

A bag of 3 apples, 7 oranges, and 11 pears costs $6.04, while a bag of 2 apples, 5 oranges, and 8 pears costs $4.31. What is the cost of a bag of fruit consisting of 1 apple, 1 orange, and 1 pear?

12

A number leaves a remainder of 3 when divided by each of the following: 8, 7, 6, 5, and 4. What is the smallest positive integer greater than 3 that satisfies these conditions? Solve for x: 1+ 2 + x = 3

13

14

The radius of each circle is r. Find the area of the shaded region.

15

Strips of width w are cut off the length and width of a rectangle 10" by 12". How wide must each strip be in order to reduce the rectangle to one having an area of 80 square inches?

16

During a vacation it rained 13 days; but when it rained in the morning the afternoon was sunny, and every rainy afternoon was preceded by a sunny morning. There were 11 sunny mornings and 12 sunny afternoons. How long was the vacation? If a*b = a – b, find (2*3)*4. b

17

2

18

Given the expression xy , if the values of x and y are each decreased by 50 percent, find the percent of decrease in the value of the original.

19

A car travels a distance of 1742 miles at an average rate of 40 mph and returns at an average rate of 55 mph. Find the average rate for the round trip to the nearest tenth.

20

A man invests some money at 8 percent interest and twice as much at 6 percent. If the total income from the two investments is $250, how much is invested at the lower rate?

21

The product of five prime positive integers is a six-digit...

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