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 2nd 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 6th 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.
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 |