Which has the most volume?
It costs $24 to paint a cube.
Before painting, we divide the cube into two rectangular boxes.
How much will it cost to paint these two boxes?
The original price of an umbrella was $16.
What was the price of the umbrella after two 5% markdowns?
A food stand buys ice cream cones in packages of 8 and cartons of 14.
What is the least number of packages and cartons of ice cream cones that need to be bought to have an equal number of ice cream cones from each source?
500 employees work for company XYZ, where the ratio of men to women is 6 to 4.
If 20 men leave the company and 10 women are hired, what is the new ratio of men to women?
Anna is a member of Greenland Velo's race team.
This summer, she has won only 6 out of 16 races.
How many races must she now win in a row to achieve a winning record of exactly 60%?
A $10 million lottery pot is divided into equal increments over 20 years. The government retains 35% of the total for taxes.
How much could the winner expect to receive after taxes each year?
If three students eat three apples in 33 seconds, how long will it take nine students to eat 19 apples?
NOTE: They do not cut the apples into small parts.
A 2-meter wide path is constructed around the outside of a rectangular garden that is 50 m by 100 m.
What is the area of the pathway?
A lottery has one $8000 prize, two $2000 prizes, and twelve $500 prizes.
The organizers retain 10% of the ticket price.
Two thousand tickets are sold.
What is the price per ticket?
The picture shows four supermarket lines, viewed from above.
The numbers are estimations of the items in the shoppers' baskets.
It takes two seconds to count one item and 30 seconds for a customer to pay.
Which line do you choose?
Apples are sold in bags of eleven that cost $11 per bag, or bags of nine that cost $10 per bag.
What is the lowest cost for 111 apples?
The area of the white cross is 45% of the area of the square flag.
Five white squares form the cross.
Which is the side length of the white square?
The picture shows an example of the Aztec code for Wikipedia.
Estimate the area of the design that is black.
A jigsaw puzzle consists of 250 identically shaped pieces to spread on a plane.
A link is a connection between two pieces.
What is the largest possible number of links required to assemble the puzzle?
I completely covered a one square meter area with $100 bills without any overlap or gaps.
What is the least amount of money that I spent if the bill size is 157 x 66 mm and its area is 0.01036 m2?
A chain with 3 links is 10 cm long.
A chain made from 5 links of the same type is 16 cm long.
How long is a chain with 35 such links?
All sizes can be 1% bigger or smaller compared with the initial design sizes.
Find the maximum possible size X.
I can buy gold bars in boxes of 25 kilograms, 45 kilograms, 65 kilograms, and 85 kilograms.
What is the smallest number of boxes I will buy if I want exactly 500 kilograms?
In a survey of customers, 2/3 of the female clients and 3/4 of the male clients preferred using antiglare display computers over glossy display computers.
Women make up 36% of the clients in the region.
What percent of the clients prefer to use antiglare display computers?
Americans measure the temperature in oF.
Europeans measure the temperature in oC.
The formula to convert Fahrenheit to Celsius is:
c = 5 (f - 32) / 9
where / is the symbol for division, f represents the temperature in oF and c represents the temperature in oC.
What is the temperature in oF when it is 10oC?
Jim bought a laptop at 25% off the regular price of $500.00.
He also bought a printer at 40% off the regular price of $250.00.
Find the amount of his discount.
The drama club is selling tickets to a play for $9 per ticket.
The cost to rent the theater and costumes is $500.
In addition, the printers are charging $1.5 per ticket to print the tickets.
How many tickets must the drama club sell to make a profit?
A particular stock is valued at $40 per share.
The value increases by 25% and then decreases by 16%.
What is the value of the stock per share?
Three friends visited a restaurant where everything costs $0.50.
They ordered four teas, five cakes, and a coffee.
They gave the waiter 15% of the sum of the bill as a tip.
They paid with a $10 note.
What was the change?
A stadium security system consists of two stages.
In the first stage, 70% of the spectators are inspected.
In the second stage, 90% of the people undergo an inspection.
Estimate the percentage of the spectators who do not undergo any inspection.
Sixty carpenters and forty plumbers work together.
The average daily rate of a carpenter is $200 while the average daily rate of a plumber is $300.
What is the average daily rate of all those involved in the project?
There are 130 cars in a village of 30 families.
Each family has either 4 or 5 cars.
How many families have 5 cars?
John buys shares in the stock market for $1000.
He sells the shares when the value of the shares doubles.
He pays a 5% transaction fee on both his purchase price and sale price.
How much profit does John make?
NOTE: When a transaction fee is paid for a stock purchase, the amount of stock
purchased is reduced by that commission.
A girl drives from home to her school at an average speed of 50 miles per hour, and she drives back at an average speed of 70 miles per hour.
What is her average speed for the whole journey?
A 100-liter vessel is full of a mixture of juice concentrate and water, in which there is 60% concentrate.
50 liters are sold, and the vessel is filled up with water.
What is the new fraction of the juice concentrate?
A 100-liter vessel is full of a mixture of juice concentrate and water, in which there is 60% concentrate.
40 liters are sold, and the vessel is filled up with water.
What is the new fraction of the juice concentrate?
A stadium contains 20,000 seats. At a match, 20% of the seats remain empty.
One ticket costs $20.
Find the cost of the total tickets sold.
Normal milk has 36 grams of fat in a bottle.
Fat free milk has 6 grams of fat in the same bottle.
Estimate the approximate percentage of fat that is removed from normal milk to produce 'fat free' milk.
A car that originally sold for $40,000 depreciates at a rate of 50% per year.
What is the value of the car after eight years?
John put $10,000.00 in a savings account at an annual interest rate of 5%. He pays 20% tax on earnings.
How much will he have in 1 year?
In a basketball tournament, a team is eliminated after a defeat.
There can be no draws, and twenty teams participate in the tournament.
What is the number of games that can be played?
A class picnic is estimated to cost $192.
The boys agreed to contribute $1 more than the girls.
If there are 12 boys and 8 girls in the class, how much money should each boy contribute?
A total of 321 employees work for company XYZ and two thirds of them are men.
To obtain a workforce in which the number of men and women are equal, how many women should be hired?
A man and his equipment weigh 180kg on Earth.
If he takes the same set of scales to the moon and weighs himself there, the scales would read 30kg.
If the Great Pyramid of Pharaoh Khufu weighs about 6.6 million tons, what would be its weight on the moon?
The picture shows a simplified statement of income for company ABC in millions.
How does the profit change if the revenue decreases by 7% and the expenses increase by 10%?
A race car is constructed from ultra-lightweight materials.
The car weighs 640kg (1,411 lb) including the driver and a full fuel tank.
The fuel is 25% of the total weight.
What will the car weigh with 20% of the maximum fuel?
I bought a 15''-screen laptop with a screen width to height ratio of 4 : 3.
What is the screen's width?
To unlock his mobile device, Alex must enter the four different digits of his security code in the correct order.
He remembers the four different digits.
However, since he cannot recall the order of the last three digits, he correctly enters the first digit followed by the last three digits in a random order.
What is the probability that Alex unlocks his device in three attempts?
Anna has 8 biscuits, Bill has 6, and Cindy has 1. They share them out equally. Cindy pays for her biscuits by leaving 8 wafers.
What is the fairest way for Anna and Bill to share out their wafers?
What is the minimum number of cuts needed to cut a log into 24 equal pieces?
(NOTE: The pieces cannot be rearranged between cuts.)
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 foyer area?
A revolving door with three wings makes 5 complete rotations in a minute.
There is room for a maximum of three people in each of the door sectors.
What is the maximum number of people that can leave the building through the door in 5 minutes?
On a trip, Evguenia cycled 5 km in the first 15 minutes and then 4 km in the next 12 minutes.
Which one of the following statements is correct?
The question is typical for PISA Test.
PISA stands for Programme for International Student Assessment.
Mr. Smith bought glasses for all members of his family including animals and him.
If every pair of glasses costs $10 and the tax is 8%, how much money did he spend?
Jim can eat a 10-inch pizza in 16 minutes.
How long will it take for Jim to eat a 15-inch pizza at the same rate?
You have 3 coins.
One is counterfeit and is either heavier or lighter than the other two.
How many moves are needed with a balance beam scale to isolate the counterfeit coin?
Tickets for a football game are available for $29 in advance or $39 if purchased on the day of the game.
The organizers had revenue of $68,000 for the game and they sold 2,000 tickets.
How many tickets were sold in advance?
John starts a taxi business and rents a car for $77 per day.
The rent includes gas and insurance.
He plans to charge $9 for a ride inside his town borders.
What is the minimum number of rides he needs to drive if he wishes to earn a daily profit of at least $29?
Food is 24% of the Smith family (8 members) monthly budget of $15,000.
Next month, two dogs will join the family.
How much must Mr. Smith earn to keep the same cash balance for the family?
Jane and Gerry are lost in a forest.
Gerry walks east, while Jane walks south 25% slower than Gerry.
After 49 min, Gerry is 4 km from the starting point.
How far is he from Jane?
John is Jim's son.
Jay is John's son.
John is a doctor's son.
His father is not a doctor.
Who is the doctor?
A pavement stone's side length is 9 cm and it weighs 20kg.
How much stone do I need to pave a city square 10 m x 10 m if the distance between the stones is 1 cm?
Just to remind you 1 m = 100 cm.
Gerry puts 1/10 of his weekly allowance in the bank for college.
If he has $208.00 dollars in the bank from a full year's deposits alone, how much is his weekly allowance?
Australia defeated American Samoa and set a world record for the largest victory in an international football (soccer) match, winning the game 31 – 0.
If the match lasted 93 minutes, how many goals did the audience watch in an hour?
Estimate the volume of Bob if he weighs 100kg.
1kg = 2.2 pounds
1 liter (1 l) is the volume of 1kg of water.
A boat has a ladder that has eight rungs. Each rung is 20cm apart. The bottom rung is 20cm from the water. The tide rises at 20cm every 10 minutes. High tide peaks in one hour.
When the tide is at its highest, how many rungs are under water?
Use of composite materials decreases the weight of passenger airplanes.
How does the weight of a passenger airplane change if 40% of its structure are composite materials?
Modern petrol-electric hybrid cars typically have so many sensors that you can do interesting things like measure, log, and plot the power going to the wheels. This is such a plot, measured on level ground during the course of one day with relatively constant temperatures, no rain, and not especially windy.
Below 30 mph the car was running on electric power only. Above that it was doing its own hybrid thing with the engine running.
What can you conclude from the plot alone?
(NOTE: The power should at least double every time you double the speed since at twice the speed that part of the journey is half as long.)
The problem was suggested by Leslie Green
Dieter's new design of frequency-doubling power converter has an efficiency of 40%, a good figure for this particular type of device.
Kerstin's design is half the price so it is worthy of consideration, despite the fact that for the same power input, Kerstin's design produces 25% less output power than Dieter's.
What is the efficiency of Kerstin's design?
[ NOTE: Efficiency = 100% x (output power) / (input power) ]
Author: Leslie Green
A frog jumps around the outside edge of a room from a dark tile to the next dark tile.
It jumps 8 times to arrive to the initial tile.
How many times does it jump in a similar 9x9 tiled room?
A 2-hour-long television program included 12 minutes of commercials.
What percentage of the program was not commercials?
Leslie Green asks:
Scientists and engineers need to use quantities which can vary over at least 30 orders of magnitude. Using zeros such as 12300000000000 is impractical. Scientific notation uses a number between 1 and just less than 10, multiplied by a power of 10.
What is the scientific form for 567001?
Make up one dollar by using 50 coins.
What is the number of dimes that can be used?
Penny = 1 cent.
Nickel = 5 cents.
Dime = 10 cents.
Quarter = 25 cents.
Leslie Green asks: "Symmetry is a very big subject, involving much more than geometry alone. Spotting patterns, and breaks in patterns, is a valuable skill.
Without worrying about what the function is, or what the programming language is, can you spot the error in this code simply by spotting a break in the symmetry?
The error is on line . . . "
You are making a bank deposit of $995.
You have an unlimited number of $50s, $10s and $5s bills.
What is the minimum number of bills you need to bring to the bank?
A large cylinder can hold 6 L of water when full. The tick marks show the division of the cylinder into five equal parts.
Which of the following is the best estimate for the volume of water in the cylinder?
Most people use about 30 gallons of water for a bath, according to industry estimates.
A standard showerhead uses 2.5 gallons a minute.
Until what time is the use of a shower more environmentally friendly than taking a bath?
The ancient game of GO, which originated in China, consists of 180 white stones, 180 black stones, and a board with a 19 x 19 grid of lines.
My set weighs 9 kg (9,000 grams) if you don't include the box. The board (a goban in Japanese) weighs 720 grams.
How much does a stone weigh, assuming black and white stones have equal weights?
The radius of the Earth is about 6400 km.
What is the speed of a tree on the equator relative to the Earth's axis?
Note:
The speed of sound is 1,235 km/hour.
The maximum speed of conventional cars is about 175 km/hour.
One scoop of fish food can feed 7 fish for two days.
How many fish can 6 scoops of fish food feed for a week?
Evguenia’s hand length is 20 cm.
She measures the dimensions of her rectangular table to be 5 by 4 hand lengths.
Which of the following is the closest to the area of the table?
A season theater pass costs $495.
A ticket costs $45.
How much money is saved with a season pass compared to 18 tickets?
I sold 2/3 of my pencils for $0.25 each. I sold the remaining 8 pencils at $0.25 per pair.
How much money did I collect for the pencils?
It might not seem like it, but air has weight.
A cubic meter of air weighs 1.25kg at sea level.
A cubic meter of water weighs 1000kg.
How many people with an average weight of 100 kg can a one-cubic meter air mattress keep afloat if it weighs 20 kg when it is packed?
In a village of 250 houses, 80% of houses contains two or more people.
Of those homes containing only one person, 20% contained a female.
How many houses are there in the village with a single man, living on his own?
Evguenia, her parents and her teacher agree that she should do 1.5 hours of homework every school evening.
This year is not a leap year, there are 5 school days per week, and there are no official holidays in February.
How much homework does she get in February?
What is the main advantage of using obtuse-angled parking spaces compared to right-angled parking spaces?
There are 50 houses on the Straight Street.
FastInternet Company installs optical fiber Internet connection in all houses of the street.
If the average distance between two house doors is 10 meters, and a house needs an additional 4 meters of the cable on average inside the house, how much cable does the company need?
My collection contains British, Russian and Swiss stamps.
The ratio of British to Russian stamps is 4 to 3, and the ratio of Russian to Swiss stamps is 2 to 3.
Which number of stamps is the largest?
"The Russian adventurer Fedor Konyukhov has broken the record for the fastest circumnavigation of the earth in a hot air balloon in 2016. The 64-year-old has beaten the late Steve Fossett’s record of circumnavigating the world by two days, making the 34,000km journey in just 11 days flying at heights of up to 10km." - The Guardian.
Estimate the average speed of the journey.
A car has accelerated from 0 to 144 km per hour in 10 seconds and traveled at the constant speed.
How far does it go in the 1 minute from starting?
Hydraulic pumps pump cleaned water from a filled tank into a special pond via tubes that have an input diameter of 8 cm and an output diameter of 16 cm.
How much water per minute goes through the output outlet compared to the input tube?
Mountain View is a city located in Santa Clara County, California, United States, named for its views of the Santa Cruz Mountains. The table shows the population of the city. The source is U.S. Decennial Census data from Wikipedia.
During what decade was the rate of population growth the largest?
A 99-people city chooses its mayor between Anna and Bill.
They have a strange rule: the first person chooses a candidate and the next two people always choose another one and so on. If the first person casts a ballot not marking anything at all, the next two people choose whatever they want.
What is the best strategy for Anna to win if she starts first?
The ball's design stitches together hexagons with pentagons. The ball made its World Cup debut as Adidas' Telstar in 1970 in Mexico. The ball's pattern of white hexagons with black pentagons made it easily visible on television.
If there are 12 pentagons, how many hexagons are there?
Four large pipes will drain a pond in six hours and twelve small pipes will drain the same pond in four hours.
How long will it take 2 large pipes and 2 small pipes to drain the pond?
Jane and Gerry left their home at the same time. They drove towards Oxford, which is 240 km away from their home. Jane drove at an average speed of 80 km/h. The average speed of Gerry's sport car was 20 km/h higher. He stopped along the way to arrive at Oxford at the same time as Jane.
For how long did Gerry stop to rest?
Jane received 56% of the votes of her class to become the class representative in the School Committee.
If she received 3 more votes than the other candidate Gerry, what was the total number of votes?
The distance from the heel print of one foot to the heel print of the other foot is the distance traveled forward by a single leg / step. An average step is 2.2 feet (0.67 meters) for women and 2.5 feet (0.762 meters) for men, but it depends very much on height.
How many steps are needed for Jane to walk 100 meters?
At a school, 40% of students are boys. Of those, 20% play hockey. Of those, 12% or 24 students are on the school hockey team.
How many students are there in the school?
Gerry has Swiss coins:
5 francs,
2 francs
50 centimes = 0.5 franc
20 centimes = 0.2 franc
He has equal numbers of each coin.
How much money does he have if the total number of coins is 48?
In a country, a ticket is considered to have a "lucky" number if the sum of the first 3 digits is equal to the sum of the last 3 digits for a six digit number.
For example, the number 376079 marked green is lucky.
Estimate the probability of getting a lucky ticket.
Five percent of the solar panels must be repaired.
If the set is a rectangle 32 panels in length and 15 panels in width, how many panels must be repaired?
Gerry does not know how much money he has in his wallet.
He asks Jane to check it. She says that he and she have the same amount of money and asks him to give $20 to her. He agrees.
Now she has twice as much money as he has.
How much cash is there in his wallet now?
Three parrots sleep one after another.
Sunny sleeps 3 hours, then
Buddy sleeps 4 hours, and then
Twitty sleeps 5 hours, then Sunny takes the lead again.
How much time does Buddy sleep in a week?
Certain scientists think that love is a chemical state of mind and the formula for love is as follows:
C8H11NO2 + C10H12N2O + C43H66N12O12S2
dopamine + seratonin + oxytocin
If a letter stands for a chemical element, how many different chemical elements are there in the formula of love?
I saw the wrist watch of my friend in the rear view mirror of my car. The picture shows what I saw.
What was the time at that moment?
John (left) weighs himself, eats 100g of cooked rice, drinks 1 kg of water, then weighs himself again.
Peter (right) weighs himself, eats 100g of super-high-calorie energy bar, drinks 1 kg of water, then weighs himself again.
All of this activity takes place within the space of a few minutes, and no significant activity has not been mentioned.
Who gains the most weight?
Author: Leslie Green
Chocolate Easter Eggs are packed in boxes of 3 or boxes of 7.
What is the smallest number of full boxes required to pack exactly 2000 Easter Eggs?
John's age is 33 years, 33 months, 33 weeks and 33 days old.
What age will he be on his next birthday?
One hundred eleven measures of corn must be divided among 3 peasants, such that the second peasant gets the same factor more than the first peasant, as the third gets more than the second.
How many measures of corn shall the second peasant get?
The puzzle is inspired by one of the most ancient math puzzles known on the Earth. About 1650 B. C., Egyptian scribe Ahmes, made a transcript of even more ancient mathematical scriptures dating to the reign of the Pharaoh Amenemhat III.
Image source of the Rhind Mathematical Papyrus : Wikipedia
The team behind Lawson's Pasta Restaurant (Japan) achieved the World Record for the longest pasta in the world (3776 meter) in 2012.
For how many years will Gerry eat the noodle if he usually consumes 3 meters, five times per week?
Mr. Cheeseman takes a taxi home from his shop every Saturday evening. The fare is $2 for the first km, and $0.80 for each additional km. He lives 16 km away. The taxi driver always accepts Mr. Cheeseman's excellent cheese at $20 per kg. The shopkeeper always tips 200 grams of cheese (0.2kg).
How much cheese does the shopkeeper give to the taxi driver?
Three types of cubes are used to form a large cube, using as many orange cubes as possible, followed by using as many blue cubes as possible.
How many cubes are there?
Mary has devised a rope and pulley hoist system to lift her 2 tonne (2000kg) boat out of the water. She has to pull the rope with a force equivalent to a 10kg weight to lift the boat.
How far does she have to pull the rope to lift the boat 1m out of the water?
For simplicity we assume that the rope and pulley system is lossless.
Author: Leslie Green
Leslie Green asks:
List the following storage technologies in order of their data retention capabilities, the longest storage being listed first:
USB flash drives
paper/books
stone tablets
magnetic tape
If 20 kg of a bay's water is evaporated, 700 grams of salt is obtained.
What is the salt percentage of the bay’s water?
1 kg = 1000 grams
Gerry leases a car. The initial down payment is $4,996 and the amount of the monthly payment is $299.
How much does he pay for the three-year lease in total?
Two young ladies are running on straight parallel paths, about 2m apart, with neither of them in the lead.
They are running at about 3m/s.
Ann throws a tennis ball to Betty, and it takes about half a second to reach her.
How fast is the tennis ball travelling relative to the ground?
Leslie Green asks:
You see a person apparently swimming vigorously in the sea near to a jetty. The strange thing is that he is swimming backwards, by which I mean his head should be getting closer to the jetty, but it is actually getting further away.
What should you reasonably conclude?
Grandpa drives a dilapidated old banger which only gets 10mpg (miles per gallon). The City Slicker drives the very latest Eco car which achieves an impressive 100 mpg. The City Slicker is always bragging about how his car choice is so good for the environment.
Grandpa does a 1 mile round trip 5 times a week to visit his pals at the retirement home. The City Slicker drives 50 miles to work each day, again 5 times a week.
Compare the fuel usage of these two life-styles.
Author: Leslie Green
Two coins have the diameters of 30mm and 15mm.
If they have the same thickness and they are made of the materials of the same density, how much heavier is the larger coin?
Gerry made 6 snow balls of size 1.2m, 0.7m, 0.7m, 0.7m, 0.4m, and 0.3m and built two snowmen by stacking three balls.
How much taller is the tallest snowman compared to the other one?
Jennifer wishes to transform her rooms from the existing Dungeon Grey to a bright pastel color. She knows from experience that this large a color change will require 3 coats. Her chosen paint is an expensive type with double the reflected light compared to ordinary paints. It also costs twice as much per tin.
Assuming the paint is applied in the same thickness per layer, what is the cost reduction (as a ratio) by using two layers of a cheaper ordinary reflectivity paint before putting on a top coat of the more expensive high reflectivity paint?
by Leslie Green
A submarine travels at 40mph (65 km/h or 35 knots) while submerged, but twice as slow on the surface.
If the total distance is 1,200 miles and it travels only 20% on the surface, what is the expected time of the trip?
Mount Everest is 29,028 feet high.
Mount Kilimanjaro is 19,340 feet high.
If you travel from one peak to the other on foot, how many feet up and down do you walk?
A camel can carry a maximum weight equal to either 18 large gold bars or 225 small gold bars.
If the camel is loaded with 100 small bars, how many additional large gold bars can the camel carry?
Olympia and Sparta are 858km apart. Achille runs at 10km per hour from Sparta to Olympia with 11-hour daily breaks, while a tortoise travels at 2km per day from Olympia to Sparta.
If they set out at the same time, how much time will they have to travel before meeting each other?
You can change pounds into kilograms by multiplying by 0.45.
For example, 20 pounds ≈ 20 x 0.45 = 9 kg
If John, his clothes, and instruments weigh 100 kg, how much is it in pounds?
Share prices are notorious for going up and down, but on a long average they consistently go up in value over time. From year to year you see rises and falls. Suppose the annual changes were of
+10%, +15%, -5%, +2%, +7%, -3%, +10%.
Which is the best sequence to maximise your profit?
by Leslie Green
At the teacher’s faculty meeting, 40 drinks were served: 18 cups of coffee, 16 glasses of apple juice, and the rest were just water. Five people took 2 drinks. Seven people did not have anything to drink.
How many teachers were there at the meeting?
One landowner has a mile square property, while the other has a square mile.
Is there a difference between the two pieces of land?
Small ducklings must take seven steps for every two steps Mother Duck takes.
One of Mother Duck steps covers 10 centimeters (0.1m).
How many steps will a baby duckling travel when his mother has walked 10m?
Which spring wire is longest?
Which is the side view of the 3-D shape?
Estimate the length of the blue cord.
A $160 watch is on sale for $96. 
I composed the numbers from strips of paper. 
Find the total discount which is equivalent to a discount of 25% followed by a 20% discount.
What day of the week is it 777 hours after noon on Monday?
How many seconds are there in a day?
An elevator sign reads " Maximum weight 250kg."