case $1:$

a resistance $r(\text { say })$ is connected in parallel to the group, its new equivalent resistance $R1$ is

$R_{1}=\frac{R r}{R+r}$

hence, $R_{1} < R$

case $2:$

a resistance $r$ is connected in series to the group, its new equivalent resistance $\mathrm{R} 2$ is

$R_{2}=R+r$

hence, $R_{2}>R$