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2019 AMC 10A Problems/Problem 5

Revision as of 15:32, 9 February 2019 by Billyqq (talk | contribs) (Created page with "==Problem 5== What is the greatest number of consecutive integers whose sum is <math>45 ?</math> <math>\textbf{(A) } 9 \qquad\textbf{(B) } 25 \qquad\textbf{(C) } 45 \qquad\te...")
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Problem 5

What is the greatest number of consecutive integers whose sum is $45 ?$

$\textbf{(A) } 9 \qquad\textbf{(B) } 25 \qquad\textbf{(C) } 45 \qquad\textbf{(D) } 90 \qquad\textbf{(E) } 120$

Solution

Note that every term in the sequence $-44, -43..., 44, 45$ cancels out except $45$. This results in $\boxed{\textbf{(D) } 90 }$ integers.

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