Digits
What is the mean of all three-digit positive integers whose digits are in the set {2, 0, 1, 9}?
433
A circle with center P is inscribed in isosceles triangle ABC with apex angle A measuring 34 degrees. What is the degree measure of angle APC? Express your answer as a decimal to the nearest tenth.
126.5 degrees
What is the probability that a sequence of five flips of a fair coin will not land heads up twice in a row? Express your answer as a common fraction.
13/32
How many positive integer divisors of 23,328 are perfect cubes?
6
What is the greatest common divisor of 2563 and 4147?
11
While working on a history project, Erika writes down a list of years starting with 1809 and ending with 2019. How many times did Erika write the digit 1?
242 times
What is the smallest possible area of an isosceles triangle with side lengths 5 inches and 6 inches? Express your answer as a decimal to the nearest tenth.
12.0 inches squared
Cayley has a fair six-sided die whose faces are numbered −2, −1, 0, 0, 1 and 2. She rolls the die three times. What is the probability that the sum of the three numbers she rolls is 0? Express your answer as a common fraction.
19/108
If we define the binary operation as a b = ab + b for all numbers a and b, what positive value of x satisfies the equation x (4 x) = 550?
10
The dimensions of a packing box are 15 inches by 13 inches by 10 inches. Every edge of the box is to be secured with packing tape. If the length of tape along each edge is equal to the edge length, how many feet of tape are needed? Express your answer as a mixed number.
12 and 2/3 feet
What is the geometric mean of the median and mode of the set {23, 25, 3, 25, 20, 22, 21, 2, 1, 14, 12}? Express your answer in simplest radical form.
10 square root 5
If A(0, 0, 0) and B(2, 2, 2) are points in coordinate space, how many paths are there from A to B that move from one lattice point to another in the positive x-, y- or z-direction?
90 paths
Burt has a set of tiles spelling BANANAS. Ernie randomly chooses a set of five tiles from Burt’s set. What is the probability that Ernie can create a palindrome using all five tiles? Express your answer as a common fraction.
1/3
What is the sum of the two values of x for which |x − 3| + |x − 7| = 6?
10
Paul and his friends play a version of tag football in which a team earns 5 points for every touchdown and 3 points for every field goal. If Paul’s team has a total of 25 points, how many different sequences of field goals and touchdowns could the team have scored?
22 sequences
Alvin plays mini-golf with four friends. The median and unique mode of all their scores are both 10, and the range of their scores is 16. If the mean of all their scores is 15, what is the sum of all possible values of the lowest score?
27
Regular pentagon ABCDE has diagonal BE. If P is the midpoint of side ED, what is the degree measure of angle EBP?
18 degrees
Jenny has a bag that contains equal numbers of red, green, yellow, orange and purple candies. She likes only the red candies. If she randomly selects a candy from her bag and discards any non-red candy she selects, then she is guaranteed to select a red candy within a minimum of 45 random selections. What is the total number of candies in her bag?
55 candies in her bag
If the value of a is 25 and a – b = a/b – 1, what is the sum of all possible values of b?
26
The ten guppies in Vida’s tank are 5, 5, 8, 8, 8, 9, 10, 11, 11 and 33 weeks old. A guppy of age n weeks is added to her tank. The sum of the mean, median and unique mode of the eleven guppies’ ages equals the range. What is the sum of all possible integer values of n?
48
Two race cars travel in opposite directions in separate lanes of a circular track. Car F takes 120 seconds to complete a lap. Car S takes 240 seconds to complete a lap. Once the two cars pass each other, how long does it take for them to pass each other again?
80 seconds
If a rhombus with area 26 cm2 has one diagonal of length 4 cm, what is the length of its other diagonal?
13 cm
Ilana rolls a fair 8-sided die with faces labeled 1 through 8, and Yolanda rolls a fair 12-sided die with faces labeled 1 through 12. What is the probability that Ilana rolls a smaller number than Yolanda? Express your answer as a common fraction.
5/8
If the coefficients c and d of x3 – 19x2 + cx + d = 0 are chosen so that the roots of the equation are positive integers that form a geometric sequence, what is the value of c + d?
-102
Seven points are equally spaced around a unit circle. How many non-congruent convex pentagons can be drawn by using a subset of the points as vertices of the pentagons?
3 non-congruent convex pentagons