MAΘ Problem Set 2
August 28, 2003
1. Both 4ABF and 4BCD are equilateral, and quadrilateral BDEF is a
rectangle. Find the degree measure of 6 ABC.
C
S
S
S
B
SD
A
Z
Z
Z
Z
F
E
2. Jack and Jill are at the starting line of a 400 meter track, facing opposite
directions. Jack runs a lap in 2:10, and Jill runs a lap in two minutes even.
How many times will they have passed each other when they are next at
the starting line at the same time (not counting the start or the finish)?
3. Find the next term in the sequence:
1, 2, 3, 7, 46...
4. How many fractions
numbers?
a
b
are less than 1, where a and b are two-digit whole
5. How many of the roots of f (x) = x101 + x99 − 1 are real? (A root of a
function is a number x that makes f (x) = 0).
6. If a is prime, b is the product of two primes, and c is the product of three
primes, how many of the integer values between 1 and 25 inclusive can
ac
take on?
the expression a+b