Difference between revisions of "2022 AMC 10B Problems/Problem 17"
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Revision as of 06:50, 28 November 2022
Contents
Problem
One of the following numbers is not divisible by any prime number less than Which is it?
Solution
For modulo
Thus, is divisible by
For modulo
Thus, is divisible by
For modulo
Thus, is divisible by
For modulo
Thus, is divisible by
Therefore, the answer is
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
~MrThinker (LaTeX Error)
Solution 2 (Factoring)
. A is divisible by 3.
. B is divisible by 5.
. D is divisible by 3.
. E is divisible by 5.
Since all of the other choices have been eliminated, we are left with .
~not_slay
Solution 3 (Elimination)
Mersenne Primes are primes of the form , where
is prime. Using the process of elimination, we can eliminate every option except for
and
. Clearly,
isn't prime, so the answer must be
.
Video Solution
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
Video Solution by OmegaLearn Using Digit Cycles
~ pi_is_3.14
See Also
2022 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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 |
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions.