1997 AMC 12 Problem 7

Attempt Problem 7 of the 1997 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1997 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

The sum of seven integers is

-1.

What is the maximum number of the seven integers that can be larger than

13?

1

4

5

6

7

All seven cannot exceed

13

because their sum would be positive

There is no lower bound on the remaining integer

If all seven integers exceeded

13,

their sum would be at least

98.

Six can exceed

13

: take six copies of

14

and a seventh integer of

-85.

Thus the maximum is

6,

and the correct answer is D.

Problem 7 in other years