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Questions ( 1365 )
  • Andrew has a circular spinner that looks like a pie chart. 72 degrees of the pie are colored red, 60 degrees are colored blue, 108 degrees are colored green, and the rest is colored yellow. If Andrew spins the spinner twice, what is the probability that he gets the same color both times?

  • Regular hexagon $SQUARE$ and regular pentagon $PRISM$ are coplanar. $SQ = 1$. What is the sum of all possible values of $IS$?

  • What is the largest number that can be made by multiplying a set of counting numbers together where the sum of the numbers is 19?

  • Dave's sister baked $3$ dozen pies of which a third contained chocolate, a quarter contained marshmallows, a sixth contained cayenne, and one twelfth contained salted soy nuts. What is the smallest possible number of pies that had none of these ingredients?

  • Simplify: $\frac{-4.9H^2+15.2H+20.1}{H+1}$

  • What is the product of the numerator and the denominator when $0.\overline{009}$ is expressed as a fraction in lowest terms?

  • For some positive integers $p$, there is a quadrilateral $ABCD$ with positive integer side lengths, perimeter $p$, right angles at $B$and $C$, $AB=2$, and $CD=AD$. How many different values of $p<2015$ are possible?

  • How many positive integers not exceeding $2001$ are multiples of $3$ or $4$ but not $5$?

  • If we flip 6 coins, what is the probability of getting at least 2 heads?

  • Do there exist 1,000,000 consecutive composite numbers? Express why?

  • What is the maximum prime gap for prime up to 500?

  • Evaluate: $\sqrt{(4)}\cdot \frac{2}{3}\cdot \sqrt{9} \cdot \sqrt{144} \sqrt{841}$

  • $2x+73y=13$ and y = 3. Find x.

  • Two distinct points are selected at random from the nine point set $S$.

    S = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}.

    What is the probability that their midpoint belongs to $S$?

  • In isosceles trapezoid ABCD, shown here, sides AB and DC are parallel, AB = 10 and CD = 8. Trapezoids APQR and BCQP are both similar to trapezoid ABCD. What is the area of trapezoid ABCD? Express your answer in simplest radical form.

  • 2018 children are sitting in a circle. All at once, each of the children randomly poke either the child on their left, themself, or the child on their right, with equal probability. What is the expected number of children that are not poked by anyone?

  • If r and s are the solutions of x\(^2\) + 6x − 2 = 0, what is the value of r\(^3\) + s\(^3\)?

  • How many ordered pairs of integers (x, y) satisfy x\(^2\) + y\(^2\) = 65\(^2\)?

  • If a positive two-digit integer is c times the sum of its digits, the number formed by interchanging the digits is the sum of the digits multiplied by what expression that involves c?

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