ID 862

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 16 white marbles, how many marbles are in the jar?

ID 883

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

If 2 marbles are drawn at random from the bag, what is the probability that the marbles drawn are green?

ID 890

If two dice are rolled 72 times, how many times is the sum of the two top numbers expected to be 12?

ID 899

A city hall contains 165 chairs. The first row has 10 chairs.

Each additional row has one more chair than the row before it.

How many rows are there?

ID 900

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

ID 907

The first person is 100 cm tall.

Each next person is 20% taller than the person before.

Who will be taller than 2 meters first?

ID 986

Five students put their sandwiches into five paper bags.

The bags are randomly distributed to the students.

What is the probability that exactly 4 students receive the correct bag?

ID 989

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 three of one kind?

ID 1019

Alex received a 70 on his essay and a 90 on his final.

He got an 80 on class participation.

The essay counts as 30% of his grade.

Class participation counts as 20% of his grade.

What is his grade?

ID 1035

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 boys?

ID 1266

John arrives at a crossroad A from the North.

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

For example, he could be at point B.

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

ID 1277

99 numbers have an average of 101.

Ninety of these numbers have an average of 100.

What is the average of the other nine numbers?

ID 1278

The average of a set of 12 numbers is 1.

If 18, 50 and -20 are added to the set, what is the new average?

ID 1318

Anna has a bag with 90 wafers.

She eats 14 wafers on the first day.

Every day, she eats one wafer less than the day before.

In how many days does she eat all the wafers?

ID 1360

Bobby takes five tiles with the letters of his name and places them into a bag.

He randomly picks one tile after another from the bag, and does not replace them in the bag.

What is the probability that he chooses the tiles in the same order as his name?

ID 1380

Six standard dice are rolled and the numbers on the top faces are added together.

What sum is the most probable?

ID 1394

Two princes and two princesses are ready to marry.

Everybody independently chooses a partner without telling anyone.

What is the probability that at least one princess chooses a prince that chooses her?

Assuming that boys choose girls and girls choose boys.

ID 1460

ID 1522

I have eight dimes; five are real, and three are 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 5/6.

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

ID 1523

A team of three children, Anna, Bill and Cindy, independently answers true-or-false questions.

Anna answers 90% of the questions correctly.

Bill and Cindy answer 50% of the questions correctly.

The answer is accepted as the team's response when the children give the same answer.

If their answers are different, then the result is ignored.

What is the probability that a team response is correct?

ID 1529

Dueling Idiots Problem: three idiots participate in a duel.

They shoot at the same time.

If each idiot randomly chooses one of the other two idiots and successfully shoots him, what is the probability that at least one idiot will survive?

ID 1605

There are 10 girls and 10 boys in a class.

A teacher randomly chooses two students.

What is the probability that they are a boy and a girl?

ID 1609

Two dice are thrown.

You can see all 12 numbers except 2 faces that are on the table.

All the numbers on the ten visible faces are added.

Which sum of the numbers on the faces is best to bet on?

ID 1620

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.

Find the probability that the chip reaches the center square of the grid in 4 moves.

ID 1671

After a gun is fired in a saloon, 75% of the cowboys have a wounded ear, 80% have a wounded eye, 85% have a wounded arm, and 90% have a wounded leg.

What is the smallest percentage possible of cowboys who have all four wounds?

ID 1672

If we set out by ranks of 10, we will be one short.

We will also be one short if we set out by ranks of 9, 8, 7, 6, 5, 4, 3, and even 2.

Yet there are fewer than 5000 participants.

How many are we?

Source: Marie Berrondom, Mathematical Games, 1983

ID 1675

It takes 2 cards to build 1 floor of a card house.

It takes 7 cards to build 2 floors of a card house.

It takes 15 cards to build 3 floors of a card house.

How many cards does it take to build a 10-story house?

ID 1754

Anna earned an average of 80% on her four exams.

If she never earned more than 90% what is the lowest possible percentage score she could have received in any one of the exams?

ID 1829

ID 1968

John answered 100 4-option multiple-choice questions.

He is sure that he correctly answered 50% 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 1995

Forty non-zero positive numbers are written in a row.

The average of the first two numbers is 1.

The average of the second and third numbers is 2.

The average of the third and fourth numbers is 3 and so on.

What is the last number in the row?

ID 2018

This picture shows the first five rows of Pascal's triangle.

What is the sum of the numbers in the 10th row of the triangle?

ID 2033

San Jose Scrabble® Club No. 21 published a three-letter word list that included 1014 English words.

Estimate the percentage of these words compared with all possible three-letter combinations?

ID 2157

In a city, there were seven bridges.

There was a tradition to walk and cross over each of the seven bridges.

If a person starts and finishes at the same point, what is the smallest number of crossings the person would have to make?

ID 2213

An entrepreneur wants to hire the best person for a position.

He makes a decision immediately after the interview.

Once rejected, an applicant cannot be recalled.

He interviews N randomly chosen people out of 100 applicants, rejects them and records the best score S.

After that, he continues to interview others and stops when the person has a score better than S.

What number N do you recommend to the cruel man?

ID 2256

A group of kids with dogs go for a walk.

There are 49 feet and heads altogether.

There are more dogs than kids.

How many dogs are there?

ID 3125

Bob is rolling two dice and will subtract the second number from the first number.

What result is Bob most likely to roll?

ID 3128

The average of twelve numbers is 8 and the average of another set of eight numbers is 12.

What is the average of all these numbers?

ID 3129

Fifteen numbers have an average of 10.

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 3131

The average (arithmetic mean) of a set of 10 different numbers is 98.

If the numbers 40 and 140 are removed from the set, what is the average of the remaining numbers?

ID 3164

Anna has 3 bags of marbles.

The first contains 5 white marbles and 5 green marbles.

The second contains 2 white marbles and 8 blue marbles.

The third contains 16 white marbles and 4 green marbles.

If she randomly selects a single marble from each bag, what is the probability that all three marbles will be white?

ID 3175

John has an average of 87 on his two math exams.

To earn an A, he must have a 90 average.

What is the lowest grade he must earn on the next exam to raise his average to 90?

ID 3177

ID 3195

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 the motion was rejected?

ID 3197

Alex received a 60 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 3240

Gerry and Jane are younger than 25.

The probability that two randomly chosen people in their city are younger than 25 is 25%.

What is the probability that 4 randomly chosen people from the city are younger than 25?

ID 3247

Jane and Gerry visit a casino.

In one game, they have a 1/5 probability of winning $100 and 1/2 probability of losing $50.

They have also a chance of no win / no loss.

What is the most likely amount of money they will win (or lose) at the end of 100 games?

**Gambling is bad!**

ID 3338

John is sick 12 days per year.

The probability of being sick on a Saturday or a Sunday is two times less than on any other day.

What is the probability that John will be sick on a Monday?

ID 3374

Abbey has a dog Abby.

She places 5 tiles with the letters of her surname into a bag.

She picks up one tile after other without looking.

What word has the greatest probability of appearing in the correct order from the beginning?

ID 3484

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 20 people communicating in the same manner?

ID 3492

An average baby is about 20 inches (51 cm) long and weighs approximately 6 to 9 pounds (2700 to 4000 grams).

How many times heavier than a baby is an adult?

ID 3493

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

How is the number 999 written in binary code?

ID 3510

ID 3516

If 2 salesmen can sell three luxury cars in 4 days, how many luxury cars can five salesmen sell to six clients in 7 days?

ID 3531

ID 3540

If the probability of an accident occuring in 4 years is 0.9999, what is the probability of an accident occuring in 1 year?

ID 3565

ID 3606

Alex(A), Beatrice (B), and Craig (C) work on a project.

(1) Together, A and B can complete it in 10 days.

(2) Together, B and C can complete it in 12 days.

(3) Together, C and A can complete it in 15 days.

If Alex does it alone, how many days will it take?

ID 3745

I ask you to pick a number from 1 to 100.

I then ask you, “Is the number greater than X?”

You must truly answer yes or no until I tell you the number.

What is the maximum number of questions I ask you if I choose the optimal strategy?

Here X is the number of my choice.

ID 3772

Guesstimation

A man can jump up to four times the length of his own body.

Frogs can jump up to fifty times their length.

A flea can jump 350 times the length of its own body.

What is the average length of these three jumps?

ID 3780

Alex must match three different numbers chosen from the integers 1 to 33 in any order to win a lottery.

He bought 333 tickets, each with a unique combination of numbers.

What is the probability of winning?

ID 3827

In the United States, the average life span is 65 years and the average female gives birth to 2.6 children.

The average age when a female bears children is less than 30.

How many descendants would the female have at the end of her life?

ID 3944

ID 3961

ID 3974

ID 4037

After a test of a code, John detected 2 errors and Mary discovered 3 errors in the same code.

There is one error in common.

Estimate the number of errors that are still undetected.

ID 4082

ID 4095

After a 20% discount and 8% tax, a set of tin solders costs $540.

What was the original price of the set?

ID 4240

ID 4351

One bag contains two white marbles, another bag contains two black marbles, and a third bag contains one white marble and one black marble.

I pick a random bag and take out a black marble.

What is the probability that the remaining marble from the same bag is also black?

ID 4372

A school offers the following dinner choices:

First course: soup or small salad;

Main course: vegetarian, chicken, pizza, cheeseburger or fish;

Dessert: apple cake, doughnut, fruit salad, ice cream or milkshake.

How many school dinners will I have eaten before I have to choose a combination that I have already eaten?

ID 4419

The average IQ of 100 students is 101.

If the first ninety-nine students each have an IQ of 100, what is the IQ of the last student?

ID 4442

Anna spent 120 Swiss francs in a Swiss souvenir shop. She was charged an extra 2% for paying with her credit card.

How much did she spend in USD?

Use an exchange rate of $1 = 0.96 Swiss Franc

ID 4476

ID 4477

ID 4486

If the first President of the USA George Washington took office in 1789 and the fortieth President Roland Reagan completed his duty in 2004 what is average duration of the term for the American Presidents?

ID 4499

Javier Sotomayor (Cuba) is the men's record holder with a jump of 2.45 m set in 1993, the longest standing record in the history of the men's high jump.

Javier is 1.95 m tall.

What percentage of his height did he jump?

Data source : Wikipedia

ID 4510

Bob used to weigh 100kg.

His new stressful job causes him to lose 10% every month.

How much does he weigh after 3 months of work?

ID 4566

How many 9s are there in the result of the multiplication:

12345 x 99999 ?

Don't use the calculator.

ID 4570

John's family tree includes 10 generations.

What is the minimum number of people on his family tree if there were no intermarriages?

ID 4584

A line containing 9 keyboard letters on Gerry's laptop does not work.

If his password consists of 2 letters, 4 numbers, and 1 special symbol, what is the probability that he will be able to log in?

ID 4766

Gerry estimates that two angles of a triangles have a measure between 50 and 70 degrees each.

If this is true, what would be estimate for the third angle?

ID 4770

What is the difference between 11 in decimal (normal) and binary systems?

A binary number is made up of only 0s and 1s.

ID 4808

ID 4839

There are 800 students in a school.

The students' average age is 12 years and 60% of them are girls.

What is the difference between the sums of girls and boys ages?

ID 4849

ID 4950

If you toss a dime five times and it lands heads up three times, what are the chances it will land heads up if you toss it again?

ID 4970

ID 4984

The masses of sugar and water in my 200 g tea cup are in the ratio 1 : 9.

If I drop two 25 g cubes of sugar into the cup, what will be the new percentage of sugar?

(We assume that the cup does not overflow in the process!)

ID 4988

ID 4990

ID 5024

The cost of living increases uniformly by 44% in a period of two years.

What is the annual percent increase?

ID 5031

ID 5056

You are rolling two dice and adding the numbers on the top faces.

What sum is better to bet on if you have no other choices?

ID 5087

ID 5121

Gerry and Jane like to look at registration plates of cars that pass by.

They add the three digits and bet on a result.

Among the values below, what is the best sum of three digits to bet on?

ID 5133

If I put these balls in a bag and take two balls without looking, what is the probability that the two balls are white?

ID 5147

I roll two dice, one with the left hand and one with the right.

If the left hand die gives an odd number, the overall score is zero.

If the right hand die gives an even number, I roll it again and again until it is odd.

The score is the sum of the two numbers, except for the previously mentioned case.

There are exactly 6 possible scores: 0, 3, 5, 7, 9, and 11.

What is the probability of a score of 3?

The problem was suggested by Leslie Green

ID 5157

**Buy 2 for the price of 3 and get 50% off!**

What is the final rebate do you get?

'Buy, buy, says the sign in the shop window; Why, why, says the junk in the yard.' - Paul McCartney

ID 5193

The pie chart shows the number of men, women and kids in a county.

What is the ratio of children to women?

ID 5244

Gerry tosses a coin and Jane tosses 2 coins.

What is the probability that Jane has more heads than Gerry does?

ID 5251

Martin has ten thousand dollars in a bank account. The interest rate for his account is 10% every year.

How much money will Martin have in his bank account after three years?

ID 5258

Jane and Gerry compete in a best-of-three match.

If Gerry plays so that his girl-friend has a 60% chance of winning any particular game, what is the likelihood that she will win the match?

ID 5278

Cletus is absolutely, definitely, the worst student the driving school has ever seen. When asked to drive at a steady speed he constantly accelerates too hard, overshoots the target speed, and then brakes too heavily. He has what the instructors call a "heavy foot".

By some miracle he manages to always hit the same top speed of 20 mph before braking in a continuing non-repeating pattern like the one shown.

What is his average speed?

Author: Leslie Green