Difference between revisions of "1999 AHSME Problems/Problem 3"
m |
|||
Line 28: | Line 28: | ||
{{AHSME box|year=1999|num-b=2|num-a=4}} | {{AHSME box|year=1999|num-b=2|num-a=4}} | ||
+ | {{MAA Notice}} |
Revision as of 13:34, 5 July 2013
Contents
[hide]Problem
The number halfway between and is
Solution
Solution 1
To find the number halfway between and , simply take the arithmetic mean, which is
Thus the answer is choice
Solution 2
Note that and . Thus, the answer must be greater than .
Answers , , and are all less than , so they can be eliminated.
Answer is equivalent to , which is away from , and is away from . These distances are not equal, eliminating .
Thus, must be the answer. Computing as a check, we see that it is away from , and similarly it is away from .
See Also
1999 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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.