ID 805

The slice that has been eaten had 11 mushrooms on it.

What is the estimated number of mushrooms on the entire pizza?

ID 806

The population of Funnytown increased from 9,999 people in 1999 to 11,111 in 2001.

What was the percentage increase?

ID 816

Bob is rolling two dice and adding the numbers on the top faces.

What sum is Bob most likely to roll?

ID 823

The average of eleven numbers is 9 and the average of another set of nine numbers is 11.

What is the average of all these numbers?

ID 825

Fifteen numbers have an average of 15.

Five of these numbers have an average of 5, four other numbers have an average of 4, three an average of 3, and two an average of 2.

What is the remaining number?

ID 829

What is the probability that the x-coordinate of a point randomly selected within the triangle is less than the y-coordinate?

ID 831

The average (arithmetic mean) of the 9 numbers is 60.

Which pair of numbers could be removed from the list without changing the average?

ID 833

The average (arithmetic mean) of a set of 10 different numbers is 100.

If the numbers 48 and 160 are removed from the set, what is the average of the remaining numbers?

ID 838

In a class, 90% of the students earned As grades on the first test, 80% earned As grades on the second test, 70% on the third test, and 60% on the fourth test.

What is the smallest possible percentage of students who earned As grades on all the tests?

ID 842

Three boxes contain two coins each.

One contains two nickels, one contains two dimes, and one contains a dime and a nickel.

All three boxes are mislabeled.

If you are permitted to remove only one coin at a time, how many must you remove in order to be able to label all three boxes correctly?

Source: Fixx, James F Solve It!, 1978

ID 1018

Everyone in tenth grade classes voted on a motion.

Sixty percent of the girls voted YES.

Forty percent of the boys voted YES.

The motion passes if over 50% of the votes are YES.

In what class did the motion pass?

ID 1051

John earned an average of 80% on his five exams.

What is the lowest possible percentage score he could have received in any one of the exams?

ID 1056

By drawing two marks on a wooden ruler, we can measure 1, 2, 3, 4, 5 and 6 units. We can measure ALL units from 1 to 6.

What is the maximum number of units we can measure in such manner if we draw three marks on a longer ruler?

ID 1173

ID 1311

Statistics at statemaster.com shows the numbers of elementary and secondary school pupils per teacher in different states of the USA.

If the quality of education depends only on the ratio of teachers to students, which state has the best education system?

ID 1315

The Smiths and Petersons went out to dinner.

The two couples chose a round table and randomly picked their places.

What is the probability that Mr. Smith is in front of his beloved wife?

ID 1344

ID 1424

ID 1425

A pass code must comprise four different numbers from 0 to 9.

How many different pass codes can you use?

ID 1503

There are 4 male and 3 female players on a national tennis team.

How many sets of 3 mixed doubles teams can be formed?

ID 1556

ID 1777

One person is chosen at random from the list.

What is the probability that his/her name contains the letter 'a'?

ID 1828

ID 1886

Bob the plumber has 10 pockets and 60 nuts.

He wants to put the nuts in all of his pockets so that no two pockets have the same number of nuts.

What is the largest number of nuts that a pocket can possess?

ID 1950

A frog jumps one meter 3 times, and every time he randomly chooses one of four directions (either north, south, east, or west).

What is the probability that the frog is 3 meters away from where he started?

ID 1970

Henry has 100 roses.

He gives them to his dancing partners in such a way that each girl gets at least one flower and no two girls get the same number of flowers.

What is the largest number of girls with whom he could dance?

ID 2047

The Venn diagram shows the result of a survey of 80 students.

It indicates the number of people listening to 4 popular music genres.

If the proportion is the same in a school of 500 students, how many are expected to listen to only one music genre?

ID 2069

I put 100 pennies, 20 nickels, 10 dimes, and 4 quarters in a bag.

I take 4 coins from the bag without looking.

What is expected the value of these four coins?

Penny = 1 cent.

Nickel = 5 cents.

Dime = 10 cents.

Quarter = 25 cents.

ID 2083

This is a standard set of dominoes.

One domino has no spots and the greatest number of spots is 12.

If I randomly choose a domino, which number of spots has the greatest probability of appearing?

ID 2151

Place the number tiles in the squares so that no two consecutive numbers are next to each other horizontally, vertically, or diagonally.

What is the sum of the two numbers in the red squares?

ID 2166

The Venn diagram shows the result of a survey of 80 clients.

It indicates the number of people using 4 different service providers.

There are 8 clients who use all four providers.

If the proportion is the same in a region of 10,000 clients, how many are expected to use at least 2 providers?

ID 2174

John sent an email to his three partners.

Everybody answered and copied the answer to all others.

A total of 12 emails were sent.

How many emails are sent if there are 40 people communicating in the same manner?

ID 2189

There are four referees on a rectangular pitch, with one at each corner.

They all set off for a different corner along a side at random at 19:00.

What is the probability that none of the referees meet another referee?

ID 2191

There is a legend that a stork brings babies to a village.

All parents continue to have children until they have a boy.

If they have a girl, then they try to have another child.

They stop if they have a boy.

The probability of giving birth to a boy is 50%.

What is the proportion of boys to girls in the vilage?

The photograph courtesy of Roland Sauter

ID 2197

I arranged eight wooden sticks in the shape of a fish.

What is the minimum number of sticks that must be moved to make the fish face another direction?

ID 2209

I have four boxes, each containing identically shaped balls: one of them is black.

A ball is randomly drawn out of each box.

What is the probability that at least one of the four balls is black?

ID 2211

In a bakery store, 400 customers participated in a survey on Tuesday.

On Wednesday, 500 customers were asked at random, of which 40 confirmed that they were surveyed the day before.

Estimate the number of customers per day in the store.

ID 2230

There are 9 children in a class and each knows a different piece of a short story. They are allowed to exchange what they know via email.

What is the minimum number of emails required to enable each child to know the whole story?

ID 2249

ID 2251

The binary numeral system represents numeric values using two symbols: 0 and 1.

How is the number 999 written in binary code?

ID 2257

ID 2289

Bob shaves himself 4 minutes per day.

If he lives 70 years, what is the total amount of time spent shaving?

ID 2291

There are 10 green and 10 red jellybeans in a jar.

If I randomly remove 2 jellybeans, what is the probability that both are the same color?

(Note: the jelly beans are not replaced in the jar after having been removed.)

ID 2296

The national debt of a country is 16.5 trillions.

It has a population of 300 million.

If each person paid back $100 per month how long would it take to pay off the national debt?

ID 2299

ID 2304

I participate in a Formula 1 race.

One second before the finish I am the first who overtakes the last.

What position do I finish?

ID 2307

ID 2309

A two-digit integer is 4.5 times is larger than the same number read from right to left.

Find the number.

ID 3119

The slice that has been eaten had 16 mushrooms on it.

What is the estimated number of mushrooms on the entire pizza?

ID 3145

Five percent of the marbles in a jar are black.

One fourth of the marbles are green.

One half of the marbles are yellow.

The rest are white.

If there are 12 white marbles, how many marbles are in the jar?

ID 3149

A bag contains 6 green, 5 gray, and 4 violet marbles.

If a marble is drawn at random from the bag, what is the probability that the marble drawn is not green?

ID 3151

If two dice are rolled 72 times, how many times is the sum of the two top numbers expected to be 10?

ID 3154

Which number could be added to the set without changing the average (arithmetic mean of all the numbers)?

ID 3156

The first person is 100 cm tall.

Each next person is 10% taller than the person before.

Who will be taller than 2 meters first?

ID 3179

Four kinds of apples are combined in a box.

I select apples from the box without looking.

How many apples must I draw to be sure of getting at least two of one kind?

ID 3196

Alex received a 70 on his essay and a 80 on his final.

He got an 90 on class participation.

The essay counts as 30% of his grade.

Class participation counts as 20% of his grade.

What is his grade?

ID 3204

Statistics show that for every 100 babies born in Funny Town, there are 10 more boys than girls.

What is the probability that Mr. Smith's newborn twins are girls?

ID 3207

As each of five eggs is weighed, the average weight increases by two grams each time.

If the first egg weighs 50 grams, what is the weight of the last egg?

ID 3282

One person is chosen at random from the list.

What is the probability that his/her name contains the letter "n"?

ID 3327

John arrives at a crossroad A from the North.

He makes moves each time randomly choosing one of three directions.

For example, he could be at point B making four moves.

What is the probability that he finds himself at point A after 5 moves?

ID 3336

99 numbers have an average of 100.

Ninety of these numbers have an average of 99.

What is the average of the other nine numbers?

ID 3337

The average of a set of 12 numbers is 1.

If 18, 35 and -20 are added to the set, what is the new average?

ID 3380

Eugenia earned 60, 65, 71, 79, 85 and 90 on her mathematics examinations.

If she receives a score of 68 on the seventh exam, then the average will . . .

ID 3407

I have ten dimes; nine are real, and one is fake.

Whenever a real dime is flipped, it comes up heads with a probability of 0.5.

A fake dime comes up heads up with a probability of 9/10.

What is the probability that a randomly chosen coin will come up heads?

ID 3420

A chip is placed at the bottom left corner square of a 5 x 5 grid.

The chip is moved one space upwards or to the right. One of the directions is randomly chosen, for example, by flipping a fair coin.

What is the probability that the chip does not reach the center square of the grid in 4 moves?

ID 3463

John answered 100 4-option multiple-choice questions.

He is sure that he correctly answered 60% of the questions.

In 30% of the questions, he chose the answer among two options, and he answered all other questions by randomly guessing among the four options.

What score does John expect to receive on the exam?

ID 3465

There are six traffic lights on Speedup Avenue.

In how many ways can the lights be set so that no neighboring lights have the same color?

(We assume a traffic light sequence where only one colour is lit at a time. This would not be the case for traffic lights in the United Kingdom and some other countries.)

ID 3473

Three apples were weighed in pairs and the weights were 200, 212, and 224 grams.

What is the weight of the lightest apple?

ID 3512

Four bugs are at the four corners of an equilateral tetrahedron.

Each bug randomly picks a direction and moves along the edge of the tetrahedron until it reaches the next corner.

What is the probability that none of the bugs will meet another?

ID 3517

ID 3523

ID 3557

ID 4052

ID 4053

ID 4215

What is the average (arithmetic mean) of all the multiples of ten from 10 to 1000 inclusive?

This is typical SAT question.

ID 4233

ID 4307

The amount of water flowing into a tank doubles every minute.

The tank is full in an hour.

When was the tank a quarter full?

ID 4332

Seven soldiers have lined up in order of height, tallest to shortest.

They have to be lined up from small to tall.

This will be achieved by a number of interchanges of two soldiers next to each other.

How many
interchanges are needed?

ID 4418

The average IQ of 10 students is 101.

If nine of these students each have an IQ of 100, what is the IQ of the tenth student?

This is a typical SAT question.

ID 4441

John and Mary borrow $3,000 to pay for new furniture.

They will pay back the loan by making 12 monthly payments of $333.

How much does the loan cost?

Compare the loan with the original price of the furniture.

ID 4488

In a country, there is a baby born every 20 seconds, 1000 deaths every day and 6,000 people immigrate to the country every month.

To the nearest hundred, how many people are added to the population of the country each day?

ID 4545

ID 4565

Jane picks a random integer between 1 and 5 (inclusive) and Gerry does the same.

They then compared their numbers.

What is the probability that Jane's number is greater than Gerry's number?

ID 4567

ID 4578

According to Wikipedia Mrs. Vassilyeva holds the record for most children: she gave birth to a total of 69 children: sixteen pairs of twins, seven sets of triplets and four sets of quadruplets between 1725 and 1765, in a total of 27 births.

What is the average number of children per birth?

ID 4695

If the ratio of men to women in a company is 5 : 7, which of the following could not be the number of employees in the company?

ID 4734

ID 4805

Gerry wants to buy Jane a $100 gift in a pet shop.

If the sales tax is 10% and Benny is on 10% sale today, how much would he have to pay to buy Benny?

ID 4840

ID 4923

ID 4951

If you toss eight dimes and three of them land heads up, what are the chances the ninth dime will land heads up?

ID 5032

ID 5048

A survey shows that 85% of the population of a country speak English, 75% of the population speak French.

How many per cent of the population can speak both these languages if 5% of the population speak none of them?

ID 5084

There is a 6% sales tax in a state.

How much tax did I pay for a car, if the check was $265,000 in total?

ID 5173

Jane and Gerry work at a call center selling worthless rubbish to unsuspecting customers. They are in competition with each other to be the best seller today. In the morning they work from the *easy customer* list and in the afternoon they are forced to work from the *difficult customer* list.

In the morning Jane sells to 90 out of her 100 calls, whereas Gerry sells to 85 out of his 100 calls. 90% to 85% means Jane wins.

In the afternoon Jane sells to 30 out of her 100 calls, whereas Gerry, who is sad that Jane is winning, only makes 20 calls, and only makes 5 sales. With 30% to 25% sales figures, Jane again wins.

At the end of the day the boss totals the sales, totals the calls, and computes the aggregated percentage successful sales figure for each seller.

Who wins the competition?

The problem was suggested by Leslie Green