2003 AMC 10A Problems/Problem 15
Contents
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
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 | |
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All AMC 10 Problems and Solutions |
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