Monthly Archives: November 2012

Sum of Two Reciprocals

The sum of two numbers is nine. The product of the same two numbers is thirty-eight. Find the sum of the reciprocals of these two numbers. Source: mathcontest.olemiss.edu 11/26/2012 SOLUTION Let and represent the two numbers. Answer:

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Lucas Sequence

Consider the so-called Lucas sequence: , in which every number after the second is the sum of the two preceding numbers. Prove that not a single member of this sequence is divisible by . Source: NCTM Mathematics Teacher SOLUTION The … Continue reading

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Areas in Rectangle

Given rectangle , find the ratio of the area of region to the area of region . Source: NCTM Mathematics Teacher SOLUTION Area of region Area of region Since the diagonals of a rectangle bisect each other, the area of region … Continue reading

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Change For a Quarter

How many ways can you make change for a quarter? Source: NCTM Mathematics Teacher SOLUTION G. Polya in his book “How to Solve It” has a formula that calculates the number of ways to make change for a quarter equals . … Continue reading

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November Sequence Two

Determine the next three numbers in the above pattern. Source: mathcontest.olemiss.edu 11/12/2012 SOLUTION Consider the consecutive powers of If we string the numbers together and separate the digits by commas, they reveal the following sequence Hence, the next three numbers in the pattern … Continue reading

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1200

Let set represent whole numbers greater than zero yet less than . Let set represent the elements in set that are multiples of or , or both. Find the sum of the elements in set . Source: mathcontest.olemiss.edu 11/5/2012 SOLUTION … Continue reading

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