PROBLEM # 1

For the final step in a calculation, Paul accidentally divided by 1000 instead of multiplying by 1000. What should he do to his final answer to correct it?

PROBLEM # 2

For what number b>0 is it true that b divided by b% of b equals b.

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SOLUTIONS TO PROBLEMS ON 7/17/03

PROBLEM # 1

How many positive integers less than 100 have a remainder of 3 when dvided by 7?

SOLUTION

To have a remainder of 3 when divided by 7, an integer must be 3 more than a multiple of 7. For example when 73 is divided by 7, the quotient is 10 and the remainder is 3. Counting all the multiples of 7 below 100 and adding 3 to it so the sum is still below 100 – there are 14 positive integers.

Winner

Sanjay Yengul is a mechanical engineer who lives and works in Framingham, MA.

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