Price Elasticity of Demand - elastic demand and impact of price reductions on total revenue
Like anything derived from calculus, the statement is guaranteed to hold true only for infinitesimal change. Unfortunately, since I don't know the entire demand function, I can't say much more than this.

A clear example of why this wouldn't work: starting at the same point \$100 and Q = 1000, we can decrease price to zero and total revenue would go down.