2003 AMC 10A Problems/Problem 15
Problem
What is the probability that an integer in the set is divisible by and not divisible by ?
Solution
There are integers in the set.
Since every integer is divisible by , there are integers divisible by in the set.
To be divisible by both and , a number must be divisible by .
Since every integer is divisible by , there are integers divisible by both and in the set.
So there are integers in this set that are divisible by and not divisible by .
Therefore, the desired probability is
Video Solution by WhyMath
~savannahsolver
Video Solution
https://www.youtube.com/watch?v=4IlfkRW660E ~David
Controversy
Due to the wording of the question, it may be taken as "Find the probability that an integer in said set is divisible by 2 and not 3 EXISTS". One example would be 2, which is not a multiple of 3, thus the probability is 1. But because 1 is not an option, we can assume that it was not meant like that.
See Also
2003 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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.