2022 AMC 10B Problems/Problem 17
Contents
Problem
One of the following numbers is not divisible by any prime number less than 10. Which is it?
Solution
For A, modulo 3,
Thus, is divisible by 3.
For B, modulo 5,
Thus, is divisible by 5.
For D, modulo 3,
Thus, is divisible by 3.
For E, module 5,
Thus, is divisible by 5.
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 2 (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)
See Also
2022 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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All AMC 10 Problems and Solutions |
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