1989 AMC 8 Problem 17

Attempt Problem 17 of the 1989 AMC 8 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 1989 AMC 8 solutions, or check the answer key.

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

17.

The number NN is between 99 and 17.17. Which of the following could be the average of 6,6, 10,10, and N?N?
88
1010
1212
1414
1616
Answer: B
Concepts:meaninequality
Small hint:
The average is 6+10+N3;\frac{6 + 10 + N}{3}; find its value at each end of the range for NN
Big hint:
As NN runs from 99 to 17,17, the average runs from 253\frac{25}{3} to 1111
Solution:
The average is 6+10+N3=16+N3.\frac{6 + 10 + N}{3} = \frac{16 + N}{3}. When N=9N = 9 this is 253≈8.3,\frac{25}{3} \approx 8.3, and when N=17N = 17 it is 11.11.
So the average lies strictly between about 8.38.3 and 11.11. Among the choices, only 1010 falls in this range.
Thus, the correct answer is B .
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