Author Archives: mvtrinh

About mvtrinh

Retired high school math teacher.

Values of Integers

If and are integers such that , what are the possible values of ? (a) only (b) only (c) only multiples of (d) any integer (e) none of these Source: NCTM Mathematics Teacher, September 2006 Solution Let be an integer … Continue reading

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Length of Side of Square

If the numerical value of the area of a square plus two times the numerical value of its perimeter is equal to , what is the length of one side of the square? Source: NCTM Mathematics Teacher, September 2006 Solution … Continue reading

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Lemonade Stand

John has a lemonade stand. He sells a small lemonade for cents and a large lemonade for . A small serving contains cup of lemonade; a large contains cups. At the end of the day, John has made and sold … Continue reading

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Red and Yellow Plums

One store sold red plums at for and yellow plums at for . A second store sold red plums at for and yellow plums at for . You bought red plums and yellow plums from each store, spending a total … Continue reading

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Value of Sum

What is the value of the following sum? Source: NCTM Mathematics Teacher, September 2006 Solution The square bracket in the sum expression contains 1003 pairs of consecutive powers which pairwise sum to zero Answer:

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Biggest Pizza Slice

An 8-inch pizza is cut into equal slices. A 10-inch pizza is cut into equal slices. A 12-inch pizza is cut into equal slices. A 14-inch pizza is cut into equal slices. From which pizza would you take a slice … Continue reading

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Bowling Pins

After rolling the first ball of a frame in a game of 10-pin bowling, how many different pin configurations can remain (assuming all configurations are physically possible)? Source: NCTM Mathematics Teacher, September 2006 Solution A pin configuration is made up … Continue reading

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Spring Garden

Each spring, a meter by meter garden has its length increased by meters but its with decreased by centimeters. What will be the maximum attainable area of the garden? Source: NCTM Mathematics Teacher, October 2006 Solution Area in square meters … Continue reading

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Divided by 5

Find the reminder when is divided by ? Source: NCTM Mathematics Teacher, October 2006 Solution is such a large number that it is impractical to use modulo arithmetic to find the remainder. So we are going to find the remainders … Continue reading

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Clean Your Room

Each day Chris is chided for not cleaning up his room, so he picks up approximately percent of the items on the floor in the morning. (He always rounds off to the nearest whole number if his calculations result in … Continue reading

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