MAΘ Problem Set 1

MAΘ Problem Set 1
August 21, 2003
1. Of the three-digit multiples of 11, how many are even?
2. If a certain cashier has only three pennies, three dimes, three quarters,
and two nickels, how many of the change values between one cent and 99
cents can she not pay?
3. Maria walks to school every morning by going seven miles due east, eight
miles due north, and one mile due west. How many miles of walking could
she save if she could walk a straight line to school?
4. The product of two primes p and q is equal to the product of two integers
other than p and q. How many different possibilities are there for these
two integers?
5. Let
f (x) = x2 − 7x + 12,
g(x) = ax2 + bx + c, where a, b, and c are constants, and
h(x) = f (x) + g(x).
If the graph of h(x) is a straight line, what are the conditions on the
ordered triple (a,b,c)?
6. For positive rational k, find the rational solution x that satisfies
x + 1 + x − 1 = k.