Suppose that Jackie had played $n$ games before her last game.
Since she scored an average of 20 points per game over these $n$ games, then she scored $20 n$ points over these $n$ games.
In her last game, she scored 36 points and so she has now scored $20 n+36$ points in total. But, after her last game, she has now played $n+1$ games and has an average of 21 points scored per game.
Therefore, we can also say that her total number of points scored is $21(n+1)$.
Thus, $21(n+1)=20 n+36$ or $21 n+21=20 n+36$ and so $n=15$.
This tells us that after 16 games, Jackie has scored $20(15)+36=336$ points.
For her average to be 22 points per game after 17 games, she must have scored a total of $17 \cdot 22=374$ points.
This would mean that she must score $374-336=38$ points in her next game.
ANSWER: (A)
