Difference between revisions of "2003 AMC 12A Problems/Problem 6"
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<math> x \heartsuit 0 = |x-0| = |x| </math> | <math> x \heartsuit 0 = |x-0| = |x| </math> |
Latest revision as of 14:38, 19 August 2023
- The following problem is from both the 2003 AMC 12A #6 and 2003 AMC 10A #6, so both problems redirect to this page.
Contents
[hide]Problem
Define to be for all real numbers and . Which of the following statements is not true?
for all and
for all and
for all
for all
if
Solution
We start by looking at the answers. Examining statement C, we notice:
when , but statement C says that it does for all .
Therefore the statement that is not true is
Video Solution
https://www.youtube.com/watch?v=d-IRsaIUdDA ~David
See Also
2003 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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 | ||
All AMC 10 Problems and Solutions |
2003 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 5 |
Followed by Problem 7 |
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 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.