Difference between revisions of "1997 AHSME Problems/Problem 7"

Revision as of 09:30, 9 August 2011

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
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

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 Thus, the answer is <math>6</math>, which is option <math>\boxed{D}</math>.
+== See also ==
+{{AHSME box|year=1997|num-b=6|num-a=8}}