2002 AMC 12B Problems/Problem 13
Problem
The sum of consecutive positive integers is a perfect square. The smallest possible value of this sum is
Solution
Solution 1
Let be the consecutive positive integers. Their sum,
, is a perfect square. Since
is a perfect square, it follows that
is a perfect square. The smallest possible such perfect square is
when
, and the sum is
.
Solution 2
Notice that all five choices given are perfect squares.
Let be the smallest number, we have
Subtract 153 from each of the choices and then check its divisibility by 18, we have 225 as the smallest possible sum.
~ Nafer
See also
2002 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 12 |
Followed by Problem 14 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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