At Wal-Mart, CDs cost $0.50 per disk, and pens cost $1.00 each.
Which inequality best describes the number of CDs, c, that can be purchased for $5.00 or less if you have spent a part of the money on v pens?
A father wishes to divide a square piece of land among his five sons.
He gives one quarter of the land to the first son, as shown.
He divides the remaining land into four plots of equal size and shape.
Find the plot.
Source: Fixx, James F Solve It!, 1978
John's dad pays him $8 for each correct answer he gives in his math homework and fines him $2 for each incorrect answer.
Today, John received nothing after doing 50 problems.
How many problems did John answer correctly?
Bob is looking for a new job. He has three offers with the same starting salary.
Bob wants to be better paid in the first year.
Please help him to make a decision about his monthly salary raise.
A restaurant sells a 30 cm (in diameter) pizza for $9, while their large 40 cm pizza is specially priced at $12.
What is the percent discount the restaurant is offering for the large pizza?
A real estate agent receives a 5% commission on the selling price of a house from the buyer.
You can borrow 80% of the house price from your bank.
If you have $250 000, what is the most expensive house that you can afford?
The traveling salesman problem: a salesman has to visit eight towns and return home.
What is the shortest available route between the towns?
Blind people use a special method to read texts.
The method was invented by the Frenchman Louis Braille in 1829.
Each symbol is raised on a base of six positions, two across in three lines.
The picture shows six first letters of the Braille alphabet.
How many different symbols can you produce on the base of six positions?
I use a room that is 7 x 11 to arrange five boxes.
I would like to move the boxes to a smaller room.
What is the smallest possible area of the new rectangular room?
I placed seven balls into a square box.
Is it possible to rearrange the balls in order to use a smaller square box?
If yes, how much does the box side length decrease?
Brad is framing a small flower box by four rectangular bricks.
Each of the rectangles has a perimeter of 80 cm.
What is the area of the flower box including the bricks?
Yesterday, I caught 30 fish of a certain size in a pond.
I marked and released them without any harm.
Today I also caught and released 80 fish of the same size and noticed that there were 6 marked fish in the second catch.
How many fish of the same size are there in the pond?
In a casino on a Sunday, 90% of the visitors lost $100 each,
9% of the visitors lost $1,000 each, and
the rest won $10,000 each.
If the profit of the casino is $80,000, how many people visited the casino?
Several plumbers work on a pipeline installation, which 1 plumber is able to complete in 120 days.
If 2 plumbers are sick, then others work 10 days more.
How many plumbers are in the team?
John works on a 12-month project.
Forty percent of the first 3-month activity is completed.
Seventy percent of the second 4-month activity is completed.
The third 5-month activity has not been started.
What part of the project is completed?
A project manager needs a car 3 days per week.
The daily cost of car renting is $200.
To purchase the car, it costs $26,000, and the daily car expenses are $50.
What should the project manager do if the project lasts 52 weeks?
The car is used in a toxic environment. If it is used for 6 months it is economically salvageable. If it is used for the whole year it is economically infeasible to clean it, so the vehicle is effectively worthless.
The average hourly wages of men and women in company A are $21 and $16, respectively.
The average hourly wages of men and women in company B are $20 and $15, respectively.
Twenty percent of company A employees are men.
Forty percent of company B employees are men.
Which company pays a higher average wage to their employees?
In an investment club,
90% of the members bought stock in company A,
80% bought stock in company B,
70% bought stock in company C, and
60% bought stock in company D.
What is the smallest possible percentage of members who bought all four stocks?
If 9 workers can build 9 houses in 9 months,
then how many months would it take 9 workers to build 11 houses?
Jim sells 60 percent of pineapples he had and throws away 10 percent of the remainder. On the next day, he sells two-thirds of the remainder and throws away the rest.
What percent of his pineapples does Jim discard?
A space rocket has 4 critical components, the failure of all of which will cause the rocket to crash after lift-off. The probability that any one critical component will fail is 1/10.
If the rocket has lifted off, what is the probability that it will not crash?
A city hall floor is to be tiled in the following pattern.
The hall measures 91 tiles x 61 tiles.
How many green tiles do we need?
It costs $24 to paint a cube.
Before painting, it was cut in four pieces by two planes.
What is maximum possible cost to paint these four pieces?
A full box with 70 matches weighs the same as four boxes with 10 matches each.
How many empty boxes weigh the same as a full box?
If 5% of the people get 95% of the total salary paid in a county, and the average salary is $50,000, what is average salary of the highest paid people?
Anna can complete a project in 40 days.
Bill can complete the project in 50 days.
Cindy can complete the project in 60 days.
Daniel can complete the project in 120 days.
Their daily wages are proportional to their performance.
Find two people who together complete the project in exactly 40 days.
I want to construct a solid brick from wooden cubes.
Its side ratio is 1 : 2 : 3.
I have 200 wooden cubes.
What is the maximum number of cubes I will use?
There are 8 people in a village.
They have 8 coconuts altogether.
Each man eats two coconuts, each woman eats a half, and each child eats a quarter.
How many men are there?
Inspired by Morozkin's problem :
Two children started at 6:00 and each walked at a constant (different) speed.
A boy went from A to B and a girl from B to A. They met at noon and continuing with no stop. The boy arrived at B at 4 p.m.
At what time did the girl arrive at A?
Anna and Bill roll a six-sided die.
The first person to roll a six wins.
Anna goes first.
What is the probability that she will win the game?
The picture shows the rectangular floor plan of the first level of a house.
Both the bathroom and the kitchen are square with areas of 4 square meters and 64 square meters, respectively.
The dining room is rectangular with an area of 96 square meters.
What is the area of all 4 rooms?
I am placing round beads: 1 blue and 1 red; then 2 blue and 2 red; then 3 blue and 3 red; and so on.
If there are 95 beads in total, how many of them are blue?
The rear tires of my car wear out after 60,000 miles, whilst the front tires wear out twice as fast.
Estimate how many miles I can drive if I change the tires (front and rear) at the best moment.
80% of the women in company A are under 25 years old, 40% of the men in the company are under 25 years old, and 50% of all employees are under 25 years old.
What percentage of the company are men?
If Mark had driven at 6 miles per hour (mph) faster than the state speed limit on a trip, it would have taken him 6 minutes less.
When does he arrive if he starts at 7:00 and the state speed limit is 70 mph?
Since the day he was born, Bill's parents have put $1000 in his bank account every year.
Each year the account earns 1% simple interest.
How much money will he get after 20 years?
In selling stock, John made a profit of 19% of the amount originally paid for the stock.
He pays $99 for the transaction.
If the cost of the stock was originally $25,000 what was his final profit?
The size of an NBA basketball court is about 29 by 16 meters.
How many courts can be planned in an 80 x 54 meter school yard, given that at least 3 meters must separate the courts?
The population density of the Italian capital Rome is about 2,000 people per square kilometer.
How many square meters does a citizen of the city get?
There are 1000 meters in one kilometer.
Don't count tourists.
Each week, Mrs. Smith gives her students as many worksheets as their age.
For example, Jane, who is 7-years old, gets 7 worksheets for this week.
If there are 20 students aged 7 - 10 years, how many worksheets should Mrs. Smith prepare for this week?
Jane pedaled downhill at 20 km/h (kilometers per hour) and it took 2 hours to travel from a Swiss mountain village to another village.
If she pedaled back at 12 km/h how much time did it take?
If a real estate agent received $60,000 as a 5% commission on the selling price of a house, how much was the house sold for?
How much paint do you need to paint the pyramid if you need 1kg for 1 square surface?
Don't count the bottom and the internal surfaces.
A district sends, on average, a total of 200 million gallons of water each month to its 20,000 residential customers.
In the winter months, it sends an average of 100 million gallons per month.
Assuming the winter period lasts three months, what is the average number of gallons sent in each nonwinter month?
Gerry was born at 11:55 P.M. on December 31, 2000.
Jane was born 6 minutes later.
Which statement below is true?
Anna (A), Bill (B), Cindy (C), and Daniel (D) work on a project.
(1) Together, A, B, and C can complete it in 100 days.
(2) Together, B, C, and D can complete it in 101 days.
(3) Together, C, D, and A can complete it in 102 days.
(4) Together, D, A, and B can complete it in 103 days.
Rank them from the best to the worst performer.
The picture shows a composite structure under stress.
Estimate the percentage of strands that are broken.
Computer Update Problem suggested by Leslie Green
I spot a computer at work which is doing updates.
When I arrive it says '93% complete'.
I immediately start timing the activity and it takes 8 minutes to change to '95% complete'.
Assuming the 'percentage complete' relates directly to time, how much longer will it take to reach '100% complete'?
A plastic ruler is much easier to bend in one direction than another according to the proportionality shown, where b is the breadth and d is the depth of the rectangular cross-section.
The ruler can be approximated as being 1mm thick and 20mm wide.
How much stiffer is it in the hard-to-bend direction?
The problem was suggested by Leslie Green.
WARNING: Unless the ruler has some sort of anti-shatter statement written on it, do not try bending it like this without using eye protection. Older designs of rulers are known to shatter and eject bits of plastic into nearby eyes.
Leslie Green asks:
Income tax is a strange concept when inflation is taken into account.
At the end of one year with a 1% interest rate and a 2% rate of inflation, what is the tax owed on a $10,000 saved amount, given a 20% income tax rate?
Leslie Green, Oxfordshire, UK, asks:
"My neighbor a famous Professor of Physics has an excessively old and doddery gardener who knows absolutely nothing about basic science. Nevertheless this disrespectful old gardener insists that the Professor does not need to install an electric power cable all the way down to the ponds to power a fountain pump. The decrepit gardener insists that he has seen such a setup when he was a child and that it required no external power, had no electric motor, and could spray water well above the height of the source pond - but has no idea how. The Professor is still listening because the power cable will cost thousands of dollars to install.
What should he do?"
Bob worked for 45 years. He did not work on weekends, had a 3-week summer vacation, and 7 days of official holidays. The hourly rate was $5 in the first year and it increased by $0.5 every year.
He worked 8 hours per day.
What is his total income?
There are two gods named Mendax and Fidelis, one on your left, the other on your right, but you do not know which is which. Fidelis always answers correctly. Mendax only answers one question in 7 correctly in a repeating cycle. You do not know which part of the cycle Mendax is currently on.
You must determine which god is which using the minimum number of YES/NO questions. How many questions do you need to be certain?
To clarify the matter, if Mendax is answering incorrectly, your entire question is evaluated correctly and then the answer is reversed. A single question to both gods counts as two questions.
Author : Leslie Green
Inspired by G. Boolos. 'The hardest logic puzzle ever', The Harvard Review of Philosophy (6), 1996.
An elephant weighing 2 tons and a rabbit weighing 1kg are balanced on a very long, perfectly rigid board.
If the elephant starts walking toward the center at the uniform rate of 1 meter per minute, how many km per hour must the rabbit run in order to maintain balance?
Remember 1 ton = 1000 kg
If $1 equals 0.9 Euros, $1 equals 1.02 Swiss francs, and 1 euro equals 9.5 Norwegian krones, who has the largest amount of money?
The ratio of women to men at a 100-employee company is 1 : 4.
The company wants to change the proportion to 1 : 2.
How many men must be fired to reach the goal?