**Sample
Problems**

1.
Alexis, Emma and Li play in the school band. One plays the flute. One plays the
saxophone. One plays the drums. Alexis is the 6^{th} grader. Alexis and
the saxophone player practice together after school. Emma and the flute player
are 5^{th} graders. Who plays the drums.

2.
The four digit number A7A8 is divisible by 9. What digit does A
represent?

3. Kayla has N
marbles. She groups them by threes and has one left over. She groups them by
sevens and has four left over. Kayla has more than
five marbles. What is the smallest number of marbles Kayla could have.

4. The ages of Amanda,
Britney, and Carly are each prime numbers. Amanda is
the youngest. The sum of the ages of Amanda and Britney is equal to Carly’s age. How old is Amanda?

5. I climb half the
steps in a staircase. Next I climb one-third of the remaining steps. Then I
climb one-eighth of the rest and stop to catch my breath. What is the smallest
possible number of steps in the staircase?