ID 805

Statistics, Data Analysis and Probability K10The slice that has been eaten had 11 mushrooms on it.

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



ID 806

Statistics, Data Analysis and Probability K10The population of Funnytown increased from 9,999 people in 1999 to 11,111 in 2001.

What was the percentage increase?



ID 816

Statistics, Data Analysis and Probability K10Bob is rolling two dice and adding the numbers on the top faces.

What sum is Bob most likely to roll?



ID 823

Statistics, Data Analysis and Probability K10The 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

Statistics, Data Analysis and Probability K10Fifteen 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

Statistics, Data Analysis and Probability K10What is the probability that the x-coordinate of a point randomly selected within the triangle is less than the y-coordinate?



ID 831

Statistics, Data Analysis and Probability K10The 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

Statistics, Data Analysis and Probability K10The 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

Statistics, Data Analysis and Probability K10In 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

Statistics, Data Analysis and Probability K10Three 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

Statistics, Data Analysis and Probability K10Everyone 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

Statistics, Data Analysis and Probability K10John 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

Statistics, Data Analysis and Probability K10By 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

Statistics, Data Analysis and Probability K10What is the difference between the sums of numbers in the sixth and third columns?



ID 1311

Statistics, Data Analysis and Probability K10Statistics 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

Statistics, Data Analysis and Probability K10The 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

Statistics, Data Analysis and Probability K10How many different lines can you draw through N points that are evenly spaced on a circle?



ID 1424

Statistics, Data Analysis and Probability K10In how many different ways or orders can four people line up?



ID 1425

Statistics, Data Analysis and Probability K10A pass code must comprise four different numbers from 0 to 9.

How many different pass codes can you use?



ID 1503

Statistics, Data Analysis and Probability K10There 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

Statistics, Data Analysis and Probability K10How many times in a 12-hour period does the sum of the digits on a digital clock equal 5?



ID 1777

Statistics, Data Analysis and Probability K10One person is chosen at random from the list.
What is the probability that his/her name contains the letter 'a'?



ID 1828

Statistics, Data Analysis and Probability K10Two cards are randomly chosen.
Two numbers are added.

What sum of numbers is best to bet on?



ID 1886

Statistics, Data Analysis and Probability K10Bob 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

Statistics, Data Analysis and Probability K10A 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

Statistics, Data Analysis and Probability K10Henry 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

Statistics, Data Analysis and Probability K10The 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

Statistics, Data Analysis and Probability K10I 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

Statistics, Data Analysis and Probability K10This 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

Statistics, Data Analysis and Probability K10Place 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

Statistics, Data Analysis and Probability K10The 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

Statistics, Data Analysis and Probability K10John 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

Statistics, Data Analysis and Probability K10There 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

Statistics, Data Analysis and Probability K10There 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

Statistics, Data Analysis and Probability K10I 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

Statistics, Data Analysis and Probability K10I 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

Statistics, Data Analysis and Probability K10In 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

Statistics, Data Analysis and Probability K10There 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

Statistics, Data Analysis and Probability K10How many times heavier than a rabbit is an elephant?



ID 2251

Statistics, Data Analysis and Probability K10The binary numeral system represents numeric values using two symbols: 0 and 1.

How is the number 999 written in binary code?



ID 2257

Statistics, Data Analysis and Probability K10I plan to roll a die 10 times.

Which of these results is more likely?



ID 2289

Statistics, Data Analysis and Probability K10Bob shaves himself 4 minutes per day.

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



ID 2291

Statistics, Data Analysis and Probability K10There 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

Statistics, Data Analysis and Probability K10The 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

Statistics, Data Analysis and Probability K1080% of IT projects fail, and 20% of managers are female.

What fraction of male managers succeed?



ID 2304

Statistics, Data Analysis and Probability K10I 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

Statistics, Data Analysis and Probability K10What is the logic behind?

What is correct answer?



ID 2309

Statistics, Data Analysis and Probability K10A two-digit integer is 4.5 times is larger than the same number read from right to left.

Find the number.



ID 3119

Statistics, Data Analysis and Probability K10The slice that has been eaten had 16 mushrooms on it.

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



ID 3145

Statistics, Data Analysis and Probability K10Five 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

Statistics, Data Analysis and Probability K10A 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

Statistics, Data Analysis and Probability K10If two dice are rolled 72 times, how many times is the sum of the two top numbers expected to be 10?



ID 3154

Statistics, Data Analysis and Probability K10Which number could be added to the set without changing the average (arithmetic mean of all the numbers)?



ID 3156

Statistics, Data Analysis and Probability K10The 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

Statistics, Data Analysis and Probability K10Four 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

Statistics, Data Analysis and Probability K10Alex 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, Data Analysis and Probability K10Statistics 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

Statistics, Data Analysis and Probability K10As 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

Statistics, Data Analysis and Probability K10One person is chosen at random from the list.
What is the probability that his/her name contains the letter "n"?



ID 3327

Statistics, Data Analysis and Probability K10John 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

Statistics, Data Analysis and Probability K1099 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

Statistics, Data Analysis and Probability K10The 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

Statistics, Data Analysis and Probability K10Eugenia 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

Statistics, Data Analysis and Probability K10I 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

Statistics, Data Analysis and Probability K10A 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

Statistics, Data Analysis and Probability K10John 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

Statistics, Data Analysis and Probability K10There 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

Statistics, Data Analysis and Probability K10Three apples were weighed in pairs and the weights were 200, 212, and 224 grams.

What is the weight of the lightest apple?



ID 3512

Statistics, Data Analysis and Probability K10Four 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

Statistics, Data Analysis and Probability K10How many coins must you move to form two lines, each with five coins?



ID 3523

Statistics, Data Analysis and Probability K10Order the shape by weight from lightest to heaviest.



ID 3557

Statistics, Data Analysis and Probability K10There are 21 cubes in the 6-cube tower.

What is the height of a tower made of 250 cubes?



ID 4052

Statistics, Data Analysis and Probability K10Successive discounts of 1% and 2% are equivalent to a single discount that is



ID 4053

Statistics, Data Analysis and Probability K10Successive discounts of 50% and 50% are equivalent to a single discount that is



ID 4215

Statistics, Data Analysis and Probability K10What is the average (arithmetic mean) of all the multiples of ten from 10 to 1000 inclusive?

This is typical SAT question.



ID 4233

Statistics, Data Analysis and Probability K10How many three digit numbers are evenly divisible by 17 (no remainder)?



ID 4307

Statistics, Data Analysis and Probability K10The 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

Statistics, Data Analysis and Probability K10Seven 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

Statistics, Data Analysis and Probability K10The 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

Statistics, Data Analysis and Probability K10John 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

Statistics, Data Analysis and Probability K10In 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

Statistics, Data Analysis and Probability K10When 4 coins are tossed, what is the probability that exactly one is a head?



ID 4565

Statistics, Data Analysis and Probability K10Jane 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

Statistics, Data Analysis and Probability K10How many 1s are there in the result of the multiplication:

12345 x 99999?

Don't use a calculator.



ID 4578

Statistics, Data Analysis and Probability K10According 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

Statistics, Data Analysis and Probability K10If 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

Statistics, Data Analysis and Probability K10How many different bracelets can you make from four beads?



ID 4805

Statistics, Data Analysis and Probability K10Gerry 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

Statistics, Data Analysis and Probability K10The sum of 55 consecutive integer numbers is 5555.

What is the largest number?



ID 4923

Statistics, Data Analysis and Probability K10The letters A, E, I, O, and U are vowels.

Which word includes the larger percentage of vowels?



ID 4951

Statistics, Data Analysis and Probability K10If you toss eight dimes and three of them land heads up, what are the chances the ninth dime will land heads up?



ID 5032

Statistics, Data Analysis and Probability K10If I roll three dice, what is the probability of rolling a six on at least one of them?



ID 5048

Statistics, Data Analysis and Probability K10A 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

Statistics, Data Analysis and Probability K10There 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

Statistics, Data Analysis and Probability K10Jane 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