Step 1: Concept
Dehydrogenases and reductases require specific nicotinamide adenine dinucleotide coenzymes ($\text{NAD}^{+}$/$\text{NADH}$ or $\text{NADP}^{+}$/$\text{NADPH}$) as electron carriers. Generally, pathways that break down molecules for energy (catabolism) use $\text{NAD}^{+}$, while pathways that build molecules (anabolism) use $\text{NADP}^{+}$.
Step 2: Meaning
An $\text{NAD}^{+}$-dependent enzyme specifically recognizes the non-phosphorylated dinucleotide core to catalyze oxidation-reduction conversions.
Step 3: Analysis
* Statement A (Glyceraldehyde 3-phosphate dehydrogenase): A core catabolic enzyme in glycolysis that converts glyceraldehyde 3-phosphate to 1,3-bisphosphoglycerate, reducing $\text{NAD}^{+}$ to $\text{NADH}$. It is strictly $\text{NAD}^{+}$-dependent.
* Statement B (Lactate dehydrogenase): Catalyzes the reversible anaerobic reduction of pyruvate to lactate using $\text{NADH}$/$\text{NAD}^{+}$. It is strictly $\text{NAD}^{+}$-dependent.
* Statement C (Malic enzyme): Catalyzes the oxidative decarboxylation of malate to pyruvate, preferentially using $\text{NADP}^{+}$ to generate $\text{NADPH}$ for biosynthesis.
* Statement D (HMG CoA reductase): The rate-limiting enzyme in cholesterol biosynthesis that reduces HMG-CoA to mevalonate using $\text{NADPH}$.
Step 4: Conclusion
Thus, only enzymes A and B are dependent on the $\text{NAD}^{+}$ coenzyme system.
Final Answer: (A)