Can methoxide ion be used as a base in an E1 elimination reaction?

This one problem given in my textbook is confusing because all I know is we can use a weak base for an E1 Reaction. But the reagent given is a methoxide ion. I thought the answer would B but it is C. Compound C is a result of ring expansion which is a characteristic of an E1 Reaction. I still firmly believe that the pathway should be an E2 reaction.


It's the third problem.


[![enter image description here](https://i.stack.imgur.com/tqAmh.png)](https://i.stack.imgur.com/tqAmh.png)


