Understanding the elasticity of demand for a monopoly
From the sounds of the question, the firm isn't operating at optimal efficiency. As you note, this firm is not on the elastic portion of the demand curve because $|e|=|\frac{.05}{.10}|=|0.5|&lt;1$. 

As an employee of this firm, you should suggest that they continue to adjust the price until they transition to the elastic portion of the demand curve. Once they do this, the firm should notice that their marginal revenue becomes positive. 

I think your confusion stems from (1) your ability to think critically and (2) a misunderstanding that its the marginal revenue which monopolies want to be positive. Questions such as these are usually designed to capture a person's basic understanding of a concept, you pulled together multiple concepts..."too smart for the question." As for marginal revenue, this can be negative, but a firm that wants to maximize profit should adjust their business practices if marginal revenue is negative.