1997 AHSME Problems/Problem 7

Problem

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

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

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 $\boxed{D}$ .

1997 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 6	Followed by Problem 8
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