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?
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?
The Incredible Hulk can double the distance he jumps with each succeeding jump. If his first jump is 1 meter, the second jump is 2 meters, the third jump is 4 meters, and so on, then on which jump will he first be able to jump more than 1 kilometer?
If $3^p + 3^4 = 90$, $2^r + 44 = 76$, and $5^3 + 6^s = 1421$, what is the product of $p$, $r$, and $s$?
The sum of six consecutive positive integers is 2013. What is the largest of these six integers?
A box contains a collection of triangular and square tiles. There are $25$ tiles in the box, containing $84$ edges total. How many square tiles are there in the box?
The sum of two positive numbers is $5$ times their difference. What is the ratio of the larger number to the smaller number?
How many terms are in the arithmetic sequence $13$, $16$, $19$, $\dotsc$, $70$, $73$?
If $y+4 = (x-2)^2, x+4 = (y-2)^2$, and $x \neq y$, what is the value of $x^2+y^2$?
The zeroes of the function $f(x)=x^2-ax+2a$ are integers .What is the sum of the possible values of a?
Five positive consecutive integers starting with $a$ have average $b$. What is the average of $5$ consecutive integers that start with $b$?
Positive integers $a$ and $b$ are such that the graphs of $y=ax+5$ and $y=3x+b$ intersect the $x$-axis at the same point. What is the sum of all possible $x$-coordinates of these points of intersection?
A sequence of natural numbers is constructed by listing the first $4$, then skipping one, listing the next $5$, skipping $2$, listing $6$, skipping $3$, and, on the $n$th iteration, listing $n+3$ and skipping $n$. The sequence begins $1,2,3,4,6,7,8,9,10,13$. What is the $500,\!000$th number in the sequence?
What is $\frac{2^3 + 2^3}{2^{-3} + 2^{-3}}$?
What is the value of $\frac{2^{2014}+2^{2012}}{2^{2014}-2^{2012}} ?$
When counting from $3$ to $201$, $53$ is the $51^{st}$ number counted. When counting backwards from $201$ to $3$, $53$ is the $n^{th}$ number counted. What is $n$?
Real numbers $x$ and $y$ satisfy the equation $x^2 + y^2 = 10x - 6y - 34$. What is $x + y$?
Jo and Blair take turns counting from $1$ to one more than the last number said by the other person. Jo starts by saying $``1"$, so Blair follows by saying $"1, 2"$. Jo then says $"1, 2, 3"$, and so on. What is the $53^{\text{rd}}$ number said?
Define $a\clubsuit b=a^2b-ab^2$. Which of the following describes the set of points $(x, y)$ for which $x\clubsuit y=y\clubsuit x$?
The real numbers $c,b,a$ form an arithmetic sequence with $a\ge b\ge c\ge 0$ The quadratic $ax^2+bx+c$ has exactly one root. What is this root?
Two non-decreasing sequences of nonnegative integers have different first terms. Each sequence has the property that each term beginning with the third is the sum of the previous two terms, and the seventh term of each sequence is $N$. What is the smallest possible value of $N$ ?
The product of two positive numbers is 9. The reciprocal of one of these numbers is 4 times the reciprocal of the other number. What is the sum of the two numbers?
The sums of three whole numbers taken in pairs are 12, 17, and 19. What is the middle number?
Mary divides a circle into 12 sectors. The central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. What is the degree measure of the smallest possible sector angle?
An iterative average of the numbers 1, 2, 3, 4, and 5 is computed the following way. Arrange the five numbers in some order. Find the mean of the first two numbers, then find the mean of that with the third number, then the mean of that with the fourth number, and finally the mean of that with the fifth number. What is the difference between the largest and smallest possible values that can be obtained using this procedure?