1997 AHSME Problems/Problem 7

Revision as of 13:12, 5 July 2013 by Nathan wailes (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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 $\boxed{D}$.

See also

1997 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
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 26 27 28 29 30
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Invalid username
Login to AoPS