The expression 0.35 x represents the result of decreasing a positive quantity x by what percent?

Choice D is correct. Let $n\%$ represent the percent by which the positive quantity $x$ is decreased to result in $0.35x$. The value of $n$ can be found by solving the equation $x-\left(\frac{n}{100}\right)x=0.35x$. Since $x$ is a common factor of each of the terms on the left-hand side of this equation, the equation can be rewritten as $x\left(1-\frac{n}{100}\right)=0.35x$. Dividing each side of this equation by $x$ yields $1-\frac{n}{100}=0.35$. Multiplying each side of this equation by $100$ yields $100-n=35$. Subtracting $100$ from each side of this equation yields $-n=-65$. Dividing each side of this equation by $-1$ yields $n=65$. Therefore, the expression $0.35x$ represents the result of decreasing the positive quantity $x$ by $65\%$.

Choice A is incorrect. Decreasing the quantity $x$ by $3.5\%$ yields $x-0.035x$, or $0.965x$, not $0.35x$.

Choice B is incorrect. Decreasing the quantity $x$ by $35\%$ yields $x-0.35x$, or $0.65x$, not $0.35x$.

Choice C is incorrect. Decreasing the quantity $x$ by $6.5\%$ yields $x-0.065x$, or $0.935x$, not $0.35x$.