WASHINGTON STATE MATHEMATICS COUNCIL 2000 MIDDLE SCHOOL MATH OLYMPIAD Session II: SEVENTH GRADE NUMBER SENSE Make sure you include proper units in your answer!

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1. What is the mean of 4 consecutive odd numbers, whose product is 156,009?

2. Find the 50^th term in this sequence: -4, -1, 2, 5, 8, ...

(Note: -4 is the 1^st term, and 8 is the 5^th term.)

3. What is the unit's digit of 3⁴⁹?

4. Sir Dwayne is in charge of dragon designs at the King's Toy Factory. He hopes that his new designs will please the king. "Your Highness," he says, "I have the plans for the toy dragons. If it pleases you, every 3rd dragon shall billow clouds of smoke through its nostrils, every 4th dragon shall breathe fire, every 6th dragon shall have glowing eyes, and every 8th dragon shall have a tail with spikes on it. I shall make 100 dragons." The king asks, "Sir Dwayne, how many dragons shall have more than one of these characteristics?" Sir Dwayne doesn't have the answer. Can you help him answer the king before he is thrown into the dungeon?

5. A man spent of his money and then lost remainder. He was left with $12.00. How much did he start with?