WASHINGTON STATE MATHEMATICS COUNCIL - 1997 MIDDLE SCHOOL MATH OLYMPIAD

8TH GRADE NUMBER SENSE - SCHOOL ___________________________ TEAM_______

1. How many of the first 160 positive whole numbers are divisible (leaving a remainder of 0) by all of the three smallest prime numbers?

Answer:__________________

2. The evil warlord, Grossout, locked Princess Stunning in the dungeon. Before he lets her out, she must find the first perfect square number larger than 100 where the sum of the digits is not a perfect square. Help the princess by finding the number.

Answer:__________________

3. What number must be added to both the numerator and denominator of ^{1}/_{4} to make the resulting fraction ^{7}/_{8}?

Answer:__________________

4. Six numbers between 3 and 30 are either squares or cubes – 4, 8, 16, 25, 27. How many numbers between 30 and 350 are either squares or cubes? Note: If a number is both a square and a cube, it should only be counted once.

5. A five digit number: 6a47b is divisible by 18. What is the smallest possible value of a-b?