2015 AMC 8 Problems/Problem 14

Which of the following integers cannot be written as the sum of four consecutive odd integers?

$\textbf{(A)}\text{ 16}\quad\textbf{(B)}\text{ 40}\quad\textbf{(C)}\text{ 72}\quad\textbf{(D)}\text{ 100}\quad\textbf{(E)}\text{ 200}$

Solution

Let our $4$ numbers be $n, n+2, n+4, n+6$ , where $n$ is odd. Then our sum is $4n+12$ . The only answer choice that cannot be written as $4n+12$ , where $n$ is odd, is $\boxed{\textbf{(D)}\text{ 100}}$ .

2015 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 13	Followed by Problem 15
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All AJHSME/AMC 8 Problems and Solutions

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2015 AMC 8 Problems/Problem 14

Solution

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