The solution will be acidic.
You're dealing with dimethylammonium chloride, which will dissociate in aqueous solution into
This means that the reaction of interest, after dimethylammonium chloride dissociates, will be
The reaction increases the concetration of hydronium ions, which in turn will make the solution acidic.
As a conclusion, look at the cations and anions that form your salt. In this case, you were dealing with an acid salt. Here's a link detailing the acid/base properties of salts