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Questions ( 1365 )
  • A dartboard consists of three concentric circles with radii 10, 5 and 1, respectively, measured in inches. The area between the largest and middle circles is colored green, the area between the middle and smallest circles is colored yellow, and the area within the smallest circle, the bull’s-eye, is colored red. If a thrown dart is guaranteed to hit the board, but its position on the board is uniformly random, what is the probability that it lands in the yellow portion of the board? Express your answer as a common fraction.

  • Maura is 5 years younger than her sister Cara. Seven years ago, Maura was half as old as her sister. How old is Maura now?

  • If y is a number such that y\(^2\) = (y + 2018)\(^2\), what is the value of y?

  • A square with area 8 units\(^2\) is inscribed in a circle. What is the area of the circle? Express your answer in terms of π. 

  • Gerald Scheetz is building a log cabin. If each log is 9 inches in diameter, how many logs must be stacked on top of one another to create a wall that has a height of 12 feet?

  • Dewey buys soda in 12-ounce cans that cost $1.00 each. Peppar buys soda in 20-ounce bottles that cost $1.25 each. If Dewey and Peppar buy the same volume of soda in one week, then Peppar pays P % less than Dewey. What is the value of P ?

  • If the graph of the equation y = mx + b is a line passing through the points (6, 13) and (10, 31), what is the value of m? Express your answer as a common fraction.

  • Two fair six-sided dice, with sides numbered 1 through 6, are rolled. What is the probability
    that the values on the two top faces add to at least 9? Express your answer as a common
    fraction.

     

  • How many distinct positive factors does 2018 have? 

  • What is the value of the expression 12 × 37 + 12 × 7 + 12 × 6? Express your answer in 2 different ways.

  • On a standard 12-hour clock, the minute hand moves continuously, at a constant rate, making one full revolution every hour, and the hour hand moves similarly, making one full revolution every 12 hours. What is the measure of the smaller of the two angles between the minute hand and the hour hand, in degrees, when the clock reads 5:42?

  • On Chris’ birthday in 1992, he was half the age of his brother Joseph. On Chris’ birthday in 1998, he was two-thirds the age of Joseph. How old will Chris be on his birthday in 2018? 

  • Kim is knitting a baby blanket that requires 750 meters of yarn. There are 180 meters of yarn in each ball. How many balls of yarn must Kim buy to ensure she has enough yarn to complete her blanket?

  • In rectangle ABCD, point P lies on side BC and point Q lies in the interior of the rectangle so that triangle APQ is equilateral. If the measure of angle PAB is 17 degrees, what is the measure of angle QPC?

  • If the digits 7, 8, 2, 3 and 0 are used, each exactly once, to form a three-digit positive integer and a two-digit positive integer that differ by exactly 288, what is the sum of the three-digit integer and the two-digit integer?

  • If x ® y is defined as x\(^2\) − y\(^2\), what is the value of 3 ® (2 ® 1)?

  • What is the value of 1 × 2 + 3 ÷ 6 × 5 − 4? Express your answer as a common fraction.

  • The temperature dropped from 13 °F to −5 °F. How many degrees in Celcius is the absolute value of the change in temperature? 

  • What is the value of \(\sqrt{2.3.4.5.6.7.10}\)? Express your answer in simplest radical form.

  • A standard 52-card deck of playing cards includes four aces. What is the probability that two cards selected randomly, without replacement, will both be aces? Express your answer as a common fraction.

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