Practice (90/1000)
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Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated opposite each other?
Two congruent squares, $ABCD$ and $PQRS$, have side length $15$. They overlap to form the $15$ by $25$ rectangle $AQRD$ shown. What percent of the area of rectangle $AQRD$ is shaded?
How many digits are in the product $4^5 \cdot 5^{10}$?
Let $A$ be the area of the triangle with sides of length $25, 25$, and $30$. Let $B$ be the area of the triangle with sides of length $25, 25,$ and $40$. What is the relationship between $A$ and $B$?
Let $w$, $x$, $y$, and $z$ be whole numbers. If $2^w \cdot 3^x \cdot 5^y \cdot 7^z = 588$, then what does $2w + 3x + 5y + 7z$ equal?
A fair $6$-sided die is rolled twice. What is the probability that the first number that comes up is greater than or equal to the second number?
How many rectangles are in this figure?
Quadrilateral $ABCD$ is a trapezoid, $AD = 15$, $AB = 50$, $BC = 20$, and the altitude is $12$. What is the area of the trapezoid?
Students guess that Norb's age is $24, 28, 30, 32, 36, 38, 41, 44, 47$, and $49$. Norb says, "At least half of you guessed too low, two of you are off by one, and my age is a prime number." How old is Norb?
What is the tens digit of $7^{2019}$?
How many $4$-digit positive integers have four different digits, where the leading digit is not zero, the integer is a multiple of $5$, and $5$ is the largest digit?
In how many ways can $10001$ be written as the sum of two primes?
A circle with radius $1$ is inscribed in a square and circumscribed about another square as shown. Which fraction is closest to the ratio of the circle's shaded area to the area between the two squares?
In the diagram, all angles are right angles and the lengths of the sides are given in centimeters. Note the diagram is not drawn to scale. What is , $X$ in centimeters?
A rectangular photograph is placed in a frame that forms a border two inches wide on all sides of the photograph. The photograph measures 8 inches high and 10 inches wide. What is the area of the border, in square inches?
The Fort Worth Zoo has a number of two-legged birds and a number of four-legged mammals. On one visit to the zoo, Margie counted 200 heads and 522 legs. How many of the animals that Margie counted were two-legged birds?
How many $4$-digit numbers greater than $1000$ are there that use the four digits of $2012$?
What is the units digit of $13^{2019}$?
In the BIG N, a middle school football conference, each team plays every other team exactly once. If a total of $21$ conference games were played during the $2012$ season, how many teams were members of the BIG N conference?
The smallest number greater than $2$ that leaves a remainder of $2$ when divided by $3$, $4$, $5$, or $6$ lies between what numbers?
Each of the digits $0$, $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, and $9$ is used only once to make two five-digit numbers so that they have the largest possible sum. Which of the following could be one of the numbers?
A square with integer side length is cut into 10 squares, all of which have integer side length and at least 8 of which have area 1. What is the smallest possible value of the length of the side of the original square?
What is the smallest positive integer that is neither prime nor square and that has no prime factor less than 50?
Marla has a large white cube that has an edge of 10 feet. She also has enough green paint to cover 300 square feet. Marla uses all the paint to create a white square centered on each face, surrounded by a green border. What is the area of one of the white squares, in square feet?
An equilateral triangle and a regular hexagon have equal perimeters. If the area of the triangle is 4, what is the area of the hexagon?