2007 iTest Problems/Problem 34

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Problem

Let $a/b$ be the probability that a randomly selected divisor of $2007$ is a multiple of $3$. If $a$ and $b$ are relatively prime positive integers, find $a+b$.

Solution

The prime factorization of $2007$ is $3^2 \cdot 223$, so $2007$ has $6$ positive divisors. Of the six positive divisors, four of them are divisible by $3$. Thus, the probability that a divisor is a multiple of $3$ is $\frac{4}{6} = \frac{2}{3}$, so $a + b = \boxed{5}$.

See Also

2007 iTest (Problems)
Preceded by:
Problem 33
Followed by:
Problem 35
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