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Algebra
Geometry
Combinatorics
Number Theory
Logic / Number Sense
100
This is the value of 20x + 15y if 4x + 3y = 5.
What is 25?
100
A rectangle with integer side lengths has a length of 5 and a width twice its length. What is the difference between its perimeter and its area?
What is 20?
100
Suppose that an elevator travels between 10 floors of a building. For the first and last floors, it travels at only 1/5 the rate as it does through the middle eight. This is the fraction of the total time it spends in transit that it spends traveling between floors 2 through 6.
What is 5/18?
100
This is the second-lowest integer divisible by all positive integers 1 through 5, inclusive.
What is 120?
100
These are the possible values of x^x for x = x^x.
What are 1 and -1?
200
3/(x+y) = 1, 6/(x+z) = 3, and 12/(y+z) = 3. This is the sum of x, y, and z.
What is 9/2?
200
This is the area of a circle whose radius is 10 units shorter than its diameter.
What is 100pi?
200
This is the probability of flipping an equal number of heads and tails with a fair coin that never lands on its edges over 6 flips.
What is 5/16?
200
This is the value of the expression (3 + 6 + 9 + … + 6045) / (4 + 8 + 12 + … + 8060).
What is 3/4?
200
Let there be a function $ such that a$b = 20a + 15b. This is the minimum positive integer value of a$b, for all integral ordered pairs (a, b).
What is 5?
300
This is the ordered pair (x, y) satisfying the following condition: The unsimplified fraction x/y is equivalent to the quantity (x+y)%.
What is (5, 20)? [Pronounced "5, comma 20"]
300
This is the slope of a line perpendicular to the line passing through the point (5, 6) and the lowermost endpoint of the line segment with endpoints both in the first quadrant with a midpoint of (4, 5), all of its three points of the midpoint and the two endpoints lattice points, and a slope of -1/3.
What is 1?
300
Jack can cook 100 batches of recipe A in 3 hours and 30 minutes. Kyle can cook 140 batches of recipe B in 2 hours and 27 minutes. Recipe B requires 3/5 as many ingredients as does Recipe A. This is the ratio of Jack’s cooking efficiency to that of Kyle’s.
What is 5/6?
300
Which of the following values is the smallest: 2015^8060, 4030^2015, 8060^1007, or 16120^1001?
What is 8060^1007?
300
If A holds true when B holds true, C holds true when A is false, D is false when C is false, and D is true, all of these must be true.
What are C, D?
400
This is the sum of all terms of the geometric sequence with first term 1/4, and fifth term 1/324.
What is 3/8?
400
An annulus of two circles is the area between the two circles, or the area remaining if the inner circle were to be cut out from the larger one. This is the area of the annulus of two circles of radius 2016 and 2015.
What is 4031pi?
400
The probability that event A happens, then event B, is 1/4. The probability that event B happens, then not C, is 6/25. Events B and C are equally likely to occur. This is the probability that event A does not happen, then event B happens, then event C happens.
What is 3/50?
400
This is the smallest positive integer with exactly 2015 positive factors.
What is 5^4 * 3^12 * 2^30?
400
David, Hikmet, Jack, Marta, Rand, and Todd were in a 12-person race with 6 other people. Rand finished 6 places ahead of Hikmet. Marta finished 1 place behind Jack. David finished 2 places behind Hikmet. Jack finished 2 places behind Todd. Todd finished 1 place behind Rand. Marta finished in 6th place. This person finished in 8th place. (Source: 2015 AMC 10/12 B)
Who is Hikmet?
500
This is the number of possible integral values for b such that the quadratic equation y = 6x^2 - bx + 15 has no real roots.
What is 37?
500
This is the area of a regular hexagon which has one of its points at (3, 4) and another one of its points at the origin.
What is 75√3 / 2?
500
Suppose that a robot is programmed to draw a pair of socks without replacement from a drawer containing 2 individual socks of four colors. This is the probability that it does not draw any same-colored pairs after two drawings.
What is 26/35?
500
This is the sum of the first 100 triangular numbers.
What is 171,700?
500
Three different models of spaceships designed by the Northern Nevada Aeronautics and Space Administration launch from Earth at different speeds. The first spaceship, spaceship A, launches at a speed of 35,000 feet/second. The second, spaceship B, launches at 25,000 miles per hour. The third and final spaceship, spaceship C, launches at 0.00115 kilometers/millisecond. Assuming that the escape velocity is exactly 7 miles/second, these spaceship(s) will successfully be able to launch into space.
What is (spaceship) C?