Final answer:
B) Gram-staining test
To distinguish between high-GC and low-GC Gram-positive bacteria, DNA analysis should be used because it provides specific information about the GC content of the bacterial DNA, which is not possible through Gram staining, cell shape analysis, or metabolic pathway analysis.
Step-by-step explanation:
To distinguish between high-GC Gram-positive bacteria and low-GC Gram-positive bacteria, the appropriate experiment is DNA analysis. Gram staining is useful for determining whether bacteria are Gram-positive or Gram-negative, but it does not provide information about the GC content of the bacterial DNA. Since the question specifically asks about distinguishing based on GC content within Gram-positive bacteria, we look to other methods like DNA analysis which can measure the proportion of guanine and cytosine in the bacterial genome. Differences in metabolic pathways, cell shape, or Gram-staining would not directly provide this genetic information.
High-GC Gram-positive bacteria and low-GC Gram-positive bacteria can have similar cellular morphology which makes visual characteristics such as shape and arrangement less useful for differentiation in this context. Observations of endospores can signal certain genera within Gram-positive bacteria, but it is not a distinguishing factor for GC content. Biochemical tests can provide a 'fingerprint' for a species, but again, not specifically for differentiating based on high or low GC content within the DNA of Gram-positive bacteria. Therefore, DNA analysis is the correct answer.