(from National Sprint Round, 1993)
What is the remainder when 5 to the 999,999th power is divided by 7?
Go here for the MathCounts solutions.
(from 1992)
Five test scores have a mean (average score) of 90, a median (middle score) of 91, and a mode (most frequent score) of 94. What is the sum of the two lowest test scores?
Go here for the AJHSME solutions.
(from 1989)
A child has a set of 96 distinct blocks. Each block is one of 2 materials (plastic, wood), 3 sizes (small, medium, large), 4 colors (blue, green, red, yellow), and 4 shapes (circle, hexagon, square, triangle). How many blocks in the set are different from the "plastic medium red circle" in exactly two ways? (The "wood medium red square" is such a block.)
(from 1992)
The increasing sequence of positive integers a1, a2, a3, . . . has the property that an+2 = an + an+1 for all n greater than or equal to 1. If a7 = 120, then compute a8.
Go here for the AHSME solutions.
(from 1993)
How many even integers between 4000 and 7000 have four different digits?
Go here for the AIME solutions.
(from 1993)
For each integer n > 1, determine which of the two positive real numbers a and b satisfying equations an = a + 1, b2n = b + 3a is larger.
Go here for the USAMO solutions.
(from 1985 Individual Round)
The graphs of y = x3 - 3x + 2 and x + 4y = 4 intersect in the points (x1,y1), (x2,y2), and (x3,y3). If x1 + x2 + x3 = A and y1 + y2 + y3 = B, compute the ordered pair (A,B).
Go here for the ARML solutions.
Return to the main page.