three positive integers are selected at random from 9 consecutive positive integers.what us the probability that there average is also an integer? a.1/28 b 9/29 c.9)28 d.1/3 e.5/14 Related: Foil & Reverse-Foil, Algebra for GMAT?

Question

three positive integers are selected at random from 9 consecutive positive integers.what us the probability that there average is also an integer?   a.1/28 b 9/29 c.9)28 d.1/3 e.5/14 Related:  Foil & Reverse-Foil, Algebra for GMAT?

Answer

Let the consecutive integers be $n-4$, $n-3$, $\ldots$, $n+4$, where $n$ is an integer. Notice that the sum of these integers is $5n$. For the average to be an integer, the sum must be divisible by $3$, so $n$ must be divisible by $3$. There are $3$ possible values of $n$ out of $9$ consecutive integers, so the probability is $\boxed{	extbf{(D)}\ \frac{1}{3}}$.

Answer

1/3

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