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Moving only up or to the right along the grid lines, how many different paths go from A to B?
The sum of four consecutive even integers is 236. What is the least of the four integers?
How many positive factors does 144 have?
Two trains leave stations A and B at the same time, heading toward each other. The stations are 300 miles apart. After how many hours will the trains meet?
Today is Wednesday. What day of the week will it be 100 days from today?
Ms. Lee has 48 pencils and 72 erasers. She wants to make identical supply kits that use all of the pencils and erasers with none left over. What is the greatest number of kits she can make?
The pattern of squares below is made of toothpicks. If the pattern continues, how many toothpicks are needed to build Figure 25?
Ana is three times as old as her brother. In 8 years, she will be twice as old as her brother will be then. How old is Ana now?
Rectangle ABCD has width 9 and diagonal 15, as shown. What is the area of the rectangle?
In an election with three candidates, Candidate A received 45% of the votes, Candidate B received 35%, and Candidate C received the remaining 340 votes. How many votes did Candidate A receive?
Jen runs the first 3 miles of a 6-mile loop at 6 mph and the last 3 miles at 4 mph. What is her average speed for the whole loop, in miles per hour? Express your answer as a decimal.
The greatest common factor of two numbers is 6 and their least common multiple is 180. If one of the numbers is 36, what is the other number?
At a school store, 2 pens cost the same as 6 pencils, and 3 pencils cost the same as 4 erasers. How many erasers cost the same as 10 pens?
A 3 × 3 × 3 cube is painted on all six faces and then cut into 27 unit cubes. How many of the unit cubes have paint on exactly two faces?
The sum of two numbers is 48 and their difference is 14. What is the product of the two numbers?
Seven points are equally spaced on a circle. How many different triangles have all three vertices among these points?
A line passes through the points (1, 2) and (4, 11). What is the y-intercept of the line?
What is the area of the right triangle shown? Express your answer in simplest radical form.
What is the least positive integer that has exactly 10 positive factors?
The cylinder shown has a diameter of 6 cm and a height of 8 cm. What is its volume, in cubic centimeters? Express your answer in terms of π.
A 4-by-4-by-4 cube is painted on all six faces and then cut into 64 unit cubes. How many of the unit cubes have exactly two painted faces?
An isosceles trapezoid has bases of length 8 and 20 units and legs of length 10 units. What is the area of the trapezoid?
The radius of a circle is increased from 5 cm to 7 cm. By how many square centimeters does the area of the circle increase? Express your answer in terms of π.
What is the distance between the points (- 2, 3) and (4, 11) in a coordinate plane?
A triangle has vertices at (0, 0), (8, 0) and (3, 5). What is the area of the triangle?
What is the sum of the interior angles of a convex heptagon?
A 3-by-3-by-3 cube is painted on all six faces and then cut into 27 unit cubes. How many of the unit cubes have exactly one painted face?
Two concentric circles have radii 10 cm and 6 cm. What is the area of the region between the circles? Express your answer in terms of π.
How many squares of any size are there in a 4-by-4 grid of unit squares?
A rectangular box measures 3 inches by 4 inches by 12 inches. What is the length of the longest line segment that can be drawn between two corners of the box?
A 10-by-8 rectangle has a 3-by-4 rectangle cut out of one corner, leaving an L-shaped figure. What is the perimeter of the figure?
The length of a rectangle is increased by 20% and its width is decreased by 10%. By what percent does the area of the rectangle increase?
The diagonals of a rhombus are 16 cm and 30 cm. What is the area of the rhombus?
A right triangle has a hypotenuse of length 17 units and one leg of length 8 units. What is the area of the triangle?
What is the area of an equilateral triangle with side length 8 units? Express your answer in simplest radical form.
A triangle has side lengths 10, 10 and 12 inches. What is the area of the triangle?
A circle is inscribed in a square with side length 10 units. What is the area of the region inside the square but outside the circle? Express your answer in terms of π.
A room is 12 feet by 15 feet and has 8-foot-high walls. The room has two windows, each 3 feet by 4 feet, and no other openings. How many square feet of wall (not including the windows) need to be painted?
An angle measures 10° more than 4 times its supplement. What is the number of degrees in the angle?
A cone has a base radius of 5 cm and a slant height of 13 cm. What is the volume of the cone? Express your answer in terms of π.
Two fair 4-sided dice, each numbered 1 through 4, are rolled. What is the probability that the sum of the two numbers is a multiple of 3? Express your answer as a common fraction.
An integer is chosen at random from 1 to 100, inclusive. What is the probability that it is neither a perfect square nor a perfect cube? Express your answer as a common fraction.
A 3-digit code is formed by choosing each digit at random from 0 through 9 (digits may repeat). What is the probability that all three digits are different? Express your answer as a common fraction.
Two teams of equal ability play a best-of-5 series. The first team to win 3 games wins the series. What is the probability that the series ends after exactly 4 games? Express your answer as a common fraction.
A positive integer less than 100 is chosen at random. What is the probability that it is a perfect cube? Express your answer as a common fraction.
Two fair 6-sided dice are rolled. What is the probability that the sum is 7 or 11? Express your answer as a common fraction.
An integer is chosen at random from 1 to 100, inclusive. What is the probability that it is a multiple of 7 but not a multiple of 2? Express your answer as a common fraction.
Three fair 6-sided dice are rolled. What is the probability that at least one of them shows a 6? Express your answer as a common fraction.
Three boys and five girls line up in a random order. What is the probability that the three boys are standing next to each other? Express your answer as a common fraction.
Three marbles are drawn at random, without replacement, from a bag with 4 red marbles and 4 blue marbles. What is the probability that all three marbles are the same color? Express your answer as a common fraction.
A club has 5 boys and 4 girls. Three members are chosen at random for a committee. What is the probability that the committee has exactly two boys? Express your answer as a common fraction.
A fair coin is flipped until it lands heads. What is the probability that it takes exactly 3 flips? Express your answer as a common fraction.
A fair 6-sided die is rolled. If the result is 1 or 2, you win 9 dollars. If the result is 3 or 4, you win 3 dollars. If the result is 5 or 6, you lose 6 dollars. What is your expected win, in dollars?
An integer is chosen at random from 1 to 20, inclusive. What is the probability that it is prime? Express your answer as a common fraction.
A positive divisor of 100 is chosen at random. What is the probability that it is a multiple of 5? Express your answer as a common fraction.
A fair 6-sided die is rolled twice. What is the probability that the second number rolled is greater than the first? Express your answer as a common fraction.
Three fair coins are flipped and one fair 6-sided die is rolled. What is the probability that all three coins show heads and the die shows a 6? Express your answer as a common fraction.
A bag contains 5 red marbles, 3 blue marbles and 2 green marbles. Two marbles are drawn at random without replacement. What is the probability that both are red? Express your answer as a common fraction.
What is the expected value of the number rolled on a fair 6-sided die? Express your answer as a decimal.
One letter of the alphabet is chosen at random. What is the probability that it is one of the letters in the word PROBABILITY? Express your answer as a common fraction.
The first four terms of a sequence are 4, 9, 14, 19. If the pattern continues, what is the 10th term?
What is the value of 1 + 2 + 3 + ... + 30?
What is the sum of the first 10 positive odd integers?
An arithmetic sequence has first term 7 and common difference 6. Which term of the sequence is equal to 109?
What is the sum of the first 20 positive even integers?
What is the value of 5 + 10 + 15 + ... + 100?
The triangular numbers are 1, 3, 6, 10, 15, ..., where each term adds one more than the last number added. What is the 20th triangular number?
How many integers from 1 through 500 are multiples of 3 or multiples of 5?
An arithmetic sequence begins 12, 19, 26, ... What is the first term of the sequence that is greater than 500?
How many three-digit whole numbers have digits whose sum is 4?
What is the units digit of 2 to the 100th power?
The first term of an arithmetic sequence is 4, and the sum of its first 10 terms is 220. What is the common difference?
In the list 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, ..., each positive integer n appears exactly n times. What is the 50th number in the list?
What is the smallest positive integer n for which 1 + 2 + 3 + ... + n is greater than 500?
The sum of 100 consecutive positive integers is 7,050. What is the largest of these integers?
What is the sum of the first 50 terms of the sequence 1, -2, 3, -4, 5, -6, ...?
How many terms of the sequence 4, 9, 14, 19, ... are less than 500?
The first term of a sequence is 1. Each term after the first is equal to the sum of all the terms before it. What is the 12th term?
The first term of an arithmetic sequence is 2, and the 5th term is 3 times the 2nd term. What is the sum of the first 10 terms?
The whole numbers are written in order with no spaces: 123456789101112131415... What is the 100th digit?
In a class of 30 students, 18 play soccer, 14 play basketball, and 5 play both sports. How many students play neither sport?
Each of the 40 students in a class likes pizza, tacos, or both. If 25 students like pizza and 20 students like tacos, how many students like both?
In a club of 50 students, 30 take French, 25 take Spanish, and 8 take neither language. How many students take both languages?
Of 60 people surveyed, 36 like tea, 28 like coffee, and 10 like both. How many of the people like exactly one of the two drinks?
At a school, 60% of the students have a dog, 50% have a cat, and 20% have neither. What percent of the students have both a dog and a cat?
The Venn diagram shows how many students in a class play soccer (S) and chess (C). How many students play chess?
The Venn diagram shows the 35 students in a class who are in chess club (C) and band (B). What is the value of x?
Each of the 90 people in a group speaks English, Spanish, or both. If 70 people speak English and 50 people speak Spanish, how many people speak only Spanish?
Of 31 students, 17 play basketball, 12 play baseball, and 9 play neither sport. How many students play both sports?
Of 100 students, 45 are in the music club, 38 are in the art club, and 30 are in the drama club. Also, 15 are in both music and art, 12 are in both art and drama, 10 are in both music and drama, and 5 are in all three clubs. How many students are in at least one of the three clubs?
How many integers from 1 through 100 are divisible by neither 3 nor 5?
The Venn diagram shows the numbers of students in the art (A), band (B), and chess (C) clubs. How many students are in exactly two of the clubs?
Of 36 students, 8 play only golf and 4 play neither golf nor tennis. The number of students who play only tennis is twice the number who play both sports. How many students play both sports?
Every member of a 45-member club likes hiking, biking, or both. Exactly 25 members like biking, and the number who like hiking is 3 times the number who like both. How many members like both hiking and biking?
At a party, 80% of the guests like cake, 70% like ice cream, and 60% like pie. What is the smallest possible percent of the guests who like all three desserts?
Of 40 students, 28 have a phone and 22 have a tablet. What is the difference between the largest and the smallest possible numbers of students who have both a phone and a tablet?
How many integers from 1 through 60 are multiples of 4 or multiples of 6, but not multiples of both 4 and 6?
The Venn diagram shows the results of a survey of 55 students about clubs A, B, and C. What is the value of x?
Of the 100 campers at a camp, 55 swim, 45 hike, and 40 canoe. Also, 20 campers swim and hike, 15 hike and canoe, and 18 swim and canoe, while 10 campers do none of the three activities. How many campers do all three activities?
A group of tourists visited Paris, Rome, and London. Of them, 38 visited Paris, 33 visited Rome, and 28 visited London. Also, 17 visited both Paris and Rome, 14 visited both Rome and London, 12 visited both Paris and London, and 6 visited all three cities. How many tourists visited exactly one of the three cities?
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