Group-number shortcut: A simple trend for the earlier transition series is that the maximum possible oxidation state often equals the element's group number. Chromium sits in group 6, so its ceiling is +6, seen in chromium trioxide and dichromate. Manganese sits in group 7, so its ceiling is +7, seen in potassium permanganate. That directly gives +6 for chromium and +7 for manganese, option (B), without checking individual compounds one by one.