Problem 4 · 2009 Math Kangaroo
Easy
Algebra & Patterns
arithmetic-sequenceoff-by-one
Harry delivers newspapers in Long Street. He must deliver a paper to every house with an odd house number. If the first house is number 15 and the last is number 53, to how many houses does Harry deliver?
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Answer: B — 20
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Hint 1 of 2
List only the odd numbers from 15 to 53; they rise in steps of 2.
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Hint 2 of 2
Use (last - first)/step + 1, and don't forget the +1.
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Approach: count terms of an arithmetic list
- The odd house numbers are 15, 17, 19, ..., 53, increasing by 2.
- Number of houses = (53 - 15)/2 + 1 = 19 + 1 = 20.
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