More Practice for National

May 2, 2016
 

In a matter of days, the top scoring MATHCOUNTS competitors from each state will be in Washington, D.C. to compete in the 2016 Raytheon MATHCOUNTS National Competition. They will attempt to solve problems like these selected from the 2015 National Competition. Give them a try!

 

What integer value of n makes the equation 1 + 3n + 32n = 757 true?

[Sprint #3]

 

As Kyle walked along a street at a constant speed, he noticed that every 12 minutes, a bus passed him traveling in the same direction, and every 4 minutes, a bus passed him traveling in the opposite direction as Kyle. If all of the buses travel at a constant speed and leave the terminals at each end of the street at equally spaced intervals, how many minutes long is that interval?

[Target #6]

 

Alec and Beau race to compute 1 + 2 + 3 + ••• + n. Alec skips two numbers and gets a sum of 92. Beau double-counts two numbers and gets a sum of 145. What is the value of n?

[Team #4]

 

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