Difference between revisions of "2021 Fall AMC 12A Problems/Problem 4"
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~savannahsolver | ~savannahsolver | ||
+ | ==Video Solution by TheBeautyofMath== | ||
+ | for AMC 10: https://youtu.be/o98vGHAUYjM?t=623 | ||
+ | |||
+ | for AMC 12: https://youtu.be/jY-17W6dA3c?t=392 | ||
+ | |||
+ | ~IceMatrix | ||
==See Also== | ==See Also== |
Revision as of 19:43, 7 April 2022
- The following problem is from both the 2021 Fall AMC 10A #5 and 2021 Fall AMC 12A #4, so both problems redirect to this page.
Contents
Problem
The six-digit number is prime for only one digit
What is
Solution
First, modulo or
,
.
Hence,
.
Second modulo ,
.
Hence,
.
Third, modulo ,
.
Hence,
.
Therefore, the answer is .
~NH14
~Steven Chen (www.professorchenedu.com)
Solution 2
divisible by
.
divisible by
.
divisible by
.
divisible by
.
divisible by
.
divisible by
.
divisible by
.
divisible by
.
divisible by
.
This leaves only .
~wamofan
Video Solution
~savannahsolver
Video Solution by TheBeautyofMath
for AMC 10: https://youtu.be/o98vGHAUYjM?t=623
for AMC 12: https://youtu.be/jY-17W6dA3c?t=392
~IceMatrix
See Also
2021 Fall AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 3 |
Followed by Problem 5 |
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 |
2021 Fall AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.