Difference between revisions of "2003 AMC 12A Problems/Problem 6"
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== Solution == | == Solution == | ||
− | Examining statement C: | + | We start by looking at the answers. Examining statement C, we notice: |
<math> x \heartsuit 0 = |x-0| = |x| </math> | <math> x \heartsuit 0 = |x-0| = |x| </math> | ||
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Therefore the statement that is not true is <math>\boxed{\mathrm{(C)}\ x\heartsuit 0=x\ \text{for all}\ x}</math> | Therefore the statement that is not true is <math>\boxed{\mathrm{(C)}\ x\heartsuit 0=x\ \text{for all}\ x}</math> | ||
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+ | == Video Solution == | ||
+ | |||
+ | https://www.youtube.com/watch?v=d-IRsaIUdDA ~David | ||
== See Also == | == See Also == | ||
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[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
+ | {{MAA Notice}} |
Latest revision as of 15:38, 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
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.