We are told:

$\mathrm{IE}(\mathrm{Mg})$ is smaller than $\mathrm{IE}(X)$ and $\mathrm{IE}(Y)$.

$\mathrm{IE}(\mathrm{Mg})$ is greater than $\mathrm{IE}(Z)$.

Hence we want:

$ \mathrm{IE}(\mathrm{Mg}) < \mathrm{IE}(X), \quad \mathrm{IE}(\mathrm{Mg}) < \mathrm{IE}(Y), \quad \mathrm{IE}(\mathrm{Mg}) > \mathrm{IE}(Z). $

Approximate first ionization energies (in $\mathrm{kJ\,mol^{-1}}$) of the relevant elements:

$\mathrm{IE}(\mathrm{Ne}) \approx 2080$

$\mathrm{IE}(\mathrm{Na}) \approx 496$

$\mathrm{IE}(\mathrm{Mg}) \approx 738$

$\mathrm{IE}(\mathrm{Al}) \approx 578$ (not listed but for reference)

$\mathrm{IE}(\mathrm{Si}) \approx 787$ (not listed but for reference)

$\mathrm{IE}(\mathrm{P}) \approx 1012$ (not listed but for reference)

$\mathrm{IE}(\mathrm{S}) \approx 1000$ (not listed but for reference)

$\mathrm{IE}(\mathrm{Cl}) \approx 1251$

$\mathrm{IE}(\mathrm{Ar}) \approx 1521$

$\mathrm{IE}(\mathrm{Li}) \approx 520$

We test each option:

(A) neon, sodium, chlorine

$X=\mathrm{Ne}$: $\mathrm{IE}(\mathrm{Ne})=2080 > 738$ ✓

$Y=\mathrm{Na}$: $\mathrm{IE}(\mathrm{Na})=496 < 738$ ✗ (contradicts “$\mathrm{Mg}$ < $Y$”)

$Z=\mathrm{Cl}$: $\mathrm{IE}(\mathrm{Cl})=1251 > 738$ ✗ (contradicts “$\mathrm{Mg}$ > $Z$”)

So (A) does not fit the requirement.

(B) argon, chlorine, sodium

$X=\mathrm{Ar}$: $\mathrm{IE}(\mathrm{Ar})=1521 > 738$ ✓

$Y=\mathrm{Cl}$: $\mathrm{IE}(\mathrm{Cl})=1251 > 738$ ✓

$Z=\mathrm{Na}$: $\mathrm{IE}(\mathrm{Na})=496 < 738$ ✓

Thus $\mathrm{IE}(\mathrm{Mg}) < \mathrm{IE}(\mathrm{Ar}), \,\mathrm{IE}(\mathrm{Cl})$ and $\mathrm{IE}(\mathrm{Mg}) > \mathrm{IE}(\mathrm{Na})$.

This matches perfectly.

(C) chlorine, lithium, sodium

$X=\mathrm{Cl}$: $\mathrm{IE}(\mathrm{Cl})=1251 > 738$ ✓

$Y=\mathrm{Li}$: $\mathrm{IE}(\mathrm{Li})=520 < 738$ ✗ (contradicts “$\mathrm{Mg}$ < $Y$”)

$Z=\mathrm{Na}$: $\mathrm{IE}(\mathrm{Na})=496 < 738$, but the mismatch in $Y$ is enough to discard it.

(D) argon, lithium, sodium

$X=\mathrm{Ar}$: $\mathrm{IE}(\mathrm{Ar})=1521 > 738$ ✓

$Y=\mathrm{Li}$: $\mathrm{IE}(\mathrm{Li})=520 < 738$ ✗ (contradicts “$\mathrm{Mg}$ < $Y$”)

$Z=\mathrm{Na}$: $\mathrm{IE}(\mathrm{Na})=496 < 738$ is fine for $Z$, but $Y$ fails.

Hence only (B) satisfies all conditions:

$ \boxed{\text{(B) argon, chlorine, and sodium.}} $