When are Kp and Kc values equal?
Disclaimer: The following information has been extracted from my own Chemistry lecture notes which was built on contributions from many other general chemistry textbooks.  It is a stereotypical example of relating $K_c$ and $K_p$.

$K_c$ and $K_p$ relationship

For a simple reaction involving gas phase substances

$$\ce{aA(g) &lt;=&gt; bB(g)}$$

The equilibrium constant can be written in terms of molar concentrations or partial pressures as

$$K_c = \frac{[\ce{B}]^b}{[\ce{A}]^a} \qquad\text{or}\qquad K_p = \frac{(P_\ce{B})^b}{(P_\ce{A})^a}$$

Assuming that the gas behaves ideally (a common and convenient assumption for general cases), we can write the ideal gas law for each gas such that

$$ PV = nRT \quad\to\quad P_\ce{A}V = n_\ce{A}RT \quad\to\quad P_\ce{A} = \left(\frac{n_\ce{A}}{V}\right)RT$$

$$ PV = nRT \quad\to\quad P_\ce{B}V = n_\ce{B}RT \quad\to\quad P_\ce{B} = \left(\frac{n_\ce{B}}{V}\right)RT$$

We note that
$$ \frac{n_A}{V} \equiv M $$

where $M$ is simply molarity (moles/unit volume).  Since $[\ce{X}] = M_x$, we get

$$P_\ce{A} = [\ce{A}]RT \qquad\text{and}\qquad P_\ce{B} = [\ce{B}]RT$$

Substitute these terms into the $K_p$ equation to give

$$K_p = \frac{(P_\ce{B})^b}{(P_\ce{A})^a} = \frac{([\ce{B}]RT)^b}{([\ce{A}]RT)^a}$$

and recognize that 

$$\frac{[\ce{B}]^b}{[\ce{A}]^a} = K_c$$

Plug this relationship into the $K_p$ expression to give

$$K_p = K_c (RT)^{b-a} \quad\to\quad K_p = K_c (RT)^{\Delta n}$$

Where $\Delta n$ is simply the difference of the sum of the stoichiometric coefficients of the products and reactants from a balanced chemical equation like so

$$\Delta n = \sum (\mathrm{products}) - \sum (\mathrm{reactants})$$

It should be clear from this that the only way $K_c = K_p$ within the context of an ideal gas is when $\Delta n = 0$.

$$\begin{align*} 
K_p = K_c(RT)^{\Delta n} \quad\to\quad K_p &amp;= K_c(RT)^{0} \\
&amp;= K_c (1) \\
&amp;= K_c
\end{align*}$$

By visual inspection of your image, it is clear why these are the correct answers based upon the derived relationship offered here.