jmc

Define $x_i=2y_i-1$. Then $2\left({\sum }_{i=1}^4{y}_i\right)-4=98$, so ${\sum }_{i=1}^4{y}_i=51$. So we want to find four natural numbers that sum up to 51; we can imagine this as trying to split up 51 on the number line into 4 ranges. This is equivalent to trying to place 3 markers on the numbers 1 through 50; thus the answer is $n=\left(\genfrac{}{}{0ex}{}{50}{3}\right)=\frac{50\ast 49\ast 48}{3\ast 2}=19600$, and $\frac{n}{100}=\boxed{196}$.