Yor answer is correct, but your reasoning is not.
For example, the H to "other stuff" ratio in methane is 4:1. The ratio in water is 2:1. Methane has a higher ratio, but I'm sure you'll agree that hydrogen bonding is not a factor in methane, whereas it's extensive in water.
Consider this hydrogen bond,
X H---Y
What are the requirements of X and Y for this hydrogen bond (the dotted one) to be strong?