smc

The well-known area formula for a circle is $A=\pi r^2$, so doubling the radius will result it quadrupling the area (since $A^{\prime }=\pi (2r{)}^2=4\pi r^2=4A$). Statement $\boxed{\text{Doubling the radius of a given circle doubles the area.}}$ is therefore incorrect, and is the correct answer choice. Statements $\text{(A)}$ and $\text{(B)}$ are evidently correct, since in triangles the area is directly proportional to both the base and the height ($A=\frac{1}{2}bh$). Statement $\text{(D)}$ is also correct: let $q=\frac{a}{b}$. Then $q^{\prime }=\frac{a÷2}{2b}=\frac{a}{4b}=\frac{q}{4}$, which is a change from $q$. Finally, statement $\text{(E)}$ is true: $2x<x$ if $x<0$, as doubling a negative number makes it even more negative (and therefore less than it originally was).