SW4 wrote:

If r is an integer, is s an integer?

(1) The average (arithmetic mean) of r, s, and 2s + 3 is not an integer.

(2) The average (arithmetic mean) of r, s, and s + 1 is r.

It should be

B1- Let us calculate Arithmetic mean.

\(\frac{r+s+2s}{3}\)

Simplifying further.

\(\frac{r+3s}{3}\)

or \(\frac{r}{3}+s\) is not an integer. This does not give us much about \(s\) being an integer. \(\frac{r}{3}\) could be an integer if \(r\) is a multiple of 3, or may not be an integer which makes it impossible to accurately determine whether \(s\) is an integer.

2- Creating an expression for the Arithmetic mean.

\(\frac{r+s+s+1}{3} = r\)

\(r+2s+1 = 3r\)

\(2s = 2r - 1\)

\(s = 2r - \frac{1}{2}\)

We know \(r\) (and consequently \(2r\)) is an integer so \(s\) being \(\frac{1}{2}\) less than \(2r\) is not an integer.

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