Question

If the average (arithmetic mean) of $t$ and $(t+2)$ is $x$ and if the average of $t$ and $(t-2)$ is $y$, what is the average of $x$ and $y$?

• A. $1$
• B. $\frac{t}{2}$
• C. $t$
• D. $t+\frac{1}{2}$

Answer 1

The correct option is C $t$

Given, the average (arithmetic mean) of $t$ and $t+2$ is $x$ and the average of $t$ and $t-2$ is $y$

Then $x=\frac{t+(t+1)}{2}=\frac{2t+1}{2}$

And $y=$ $y=\frac{t+(t-1)}{2}=\frac{2t-1}{2}$

Then average $x$ and $y=$ $\frac{x+y}{2}=\frac{\frac{2t+1}{2}+\frac{2t-1}{2}}{2}=\frac{2t+1+2t-1}{2\times 2}=\frac{4t}{4}=t$