Difference between revisions of "2021 AMC 10A Problems/Problem 11"
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==Solution 2== | ==Solution 2== | ||
− | Vertically subtracting <cmath>2021_b - </cmath> | + | Vertically subtracting <cmath>2021_b - 221_b</cmath> we see that the ones place becomes 0, the b^1 place becomes 0 as well. Now, at the <cmath>b^2</cmath> place, we must perform a carry, but instead of incrementing the place's value by 10 like we normally would in base 10, we do so by <math>b</math>, and make the <cmath>b^3</cmath> place in <cmath>2021_b</cmath> equal to 1. Thus, we have our final number as <math></math>1100_b. |
==Video Solution (Simple and Quick)== | ==Video Solution (Simple and Quick)== |
Revision as of 14:30, 5 May 2021
Contents
Problem
For which of the following integers is the base-
number
not divisible by
?
Solution 1
We have This expression is divisible by
unless
The only choice congruent to
modulo
is
~MRENTHUSIASM
Solution 2
Vertically subtracting we see that the ones place becomes 0, the b^1 place becomes 0 as well. Now, at the
place, we must perform a carry, but instead of incrementing the place's value by 10 like we normally would in base 10, we do so by
, and make the
place in
equal to 1. Thus, we have our final number as $$ (Error compiling LaTeX. Unknown error_msg)1100_b.
Video Solution (Simple and Quick)
~ Education, the Study of Everything
Video Solution
https://www.youtube.com/watch?v=XBfRVYx64dA&list=PLexHyfQ8DMuKqltG3cHT7Di4jhVl6L4YJ&index=10
~North America Math Contest Go Go Go
Video Solution 3
~savannahsolver
Video Solution by TheBeautyofMath
~IceMatrix
See Also
2021 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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.