Algebra/Number Theory
The number of cupcakes Cagney and Lacey can frost together in 5 minutes if Cagney can frost a cupcake every 20 seconds and Lacey can frost a cupcake every 30 seconds.
What is 25?
The largest number of solid 2 by 2 by 1 blocks that can fit in a 3 by 2 by 3 box.
What is 4?
At a gathering of 30 people, there are 20 people who all know each other and 10 people who know no one. People who know each other hug, and people who do not know each other shake hands. How many handshakes occur within the group?
What is 245?
The number of amphibians that are frogs in a magical swamp where there are two species of talking amphibians: toads, whose statements are always true, and frogs, whose statements are always false, if four amphibians, Brian, Chris, LeRoy, and Mike, who live together in this swamp, make the following statements.
Brian: "Mike and I are different species."
Chris: "LeRoy is a frog."
LeRoy: "Chris is a frog."
Mike: "Of the four of us, at least two are toads."
What is 3?
The greatest number of consecutive integers whose sum is 45.
What is 90?
The area of a circle with a chord of length 10, and a distance from the center of the circle to the chord of 5.
What is 50pi?
The probability that the number of heads obtained from flipping coin A three times and Coin B four times is the same.
What is 35/128?
The day when Yasin's unit of blood expires if a unit of blood expires after 10! seconds and Yasin donates a unit of blood at noon of January 1.
What is February 12?
The minimum value of n, if halfway through a 100-shot archery tournament, Chelsea leads by 50 points and for each shot a bullseye scores 10 points, with other possible scores being 8, 4, 2, and 0 points. Chelsea always scores at least 4 points on each shot, and n is the number of Chelsea's next shots that need to be bullseye to be guaranteed for victory.
What is 42?
The length of one of the two congruent sides of one of the three congruent isosceles triangles that are constructed with their bases on the sides of an equilateral triangle of side length 1 if the sum of the areas of the three isosceles triangles is the same as the area of the equilateral triangle.
What is sqrt3/3?
The number of students that have two acts if each of the 100 students in a certain summer camp can either sing, dance, or act, and some students have more than one talent, but no student has all three talents. There are 42 students who cannot sing, 65 students who cannot dance, and 29 students who cannot act.
What is 64?
The value of log37*log59*log711*log913*...*log2125*log2327.
What is 6?
The sum of all possible x-coordinates of the point of intersection of y=ax+5, y=3x+b, and y=0 where a and b are positive integers.
What is -8?
The degree measure of ∠AMD if point M is chosen on side AB of a rectangle ABCD that has AB=6 and BC=3 so that ∠AMD=∠CMD.
What is 75?
n, if when 7 fair standard 6-sided die are thrown, the probability that the sum of the numbers on the top faces is 10 can be written as n/(67), where n is a positive integer.
What is 84?
a9 if the two geometric sequences a1,a2,a3... and b1,b2,b3... have the same common ratio, with a1 = 27, b1 = 99, and a15 = b11.
What is 363?
The value of n when an = 1 + cosx for a geometric sequence (an) that has a1=sinx, a2=cosx, and a3=tanx for some real number x.
What is 8?
m+n if two different points, C and D, lie on the same side of line AB so that triangle ABC and triangle BAD are congruent with AB=9, BC=AD=10, and CA=DB=17, and the intersection of these two triangular regions has area m/n, where m and n are relatively prime positive integers.
What is 59?
The probability that the point (a,b) lies above the parabola y=ax2-bx if a and b are single-digit positive integers chosen independently and at random.
What is 19/81?
The total number of points scored in the second half of a high school basketball game between the Raiders and Wildcats which was tied at the end of the first quarter if the number of points scored by the Raiders in each of the four quarters formed an increasing geometric sequence, and the number of points scored by the Wildcats in each of the four quarters formed an increasing arithmetic sequence. At the end of the fourth quarter, the Raiders had won by one point. Neither team scored more than 100 points.
What is 34?