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1997 AHSME Problems/Problem 7

Revision as of 19:16, 8 August 2011 by Talkinaway (talk | contribs) (Created page with "==Problem== The sum of seven integers is <math>-1</math>. What is the maximum number of the seven integers that can be larger than <math>13</math>? <math> \textbf{(A)}\ 1\qqua...")
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Problem

The sum of seven integers is $-1$. What is the maximum number of the seven integers that can be larger than $13$?

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7$

Solution

If the first six integers are $14$, the last number can be $(-14\cdot 6) - 1 = -85$. The sum of all seven integers will be $-1$.

However, if all seven integers are over $13$, the smallest possible sum is $14\cdot 7 = 98$.

Thus, the answer is $6$, which is option $\boxed{D}$.

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