Question 162·200 Super-Hard SAT Math Questions·Problem Solving and Data Analysis

Every relationship is a percent comparison, so scaling all four amounts together won't change the percent that $b$ is of $d$. Choose $d=100$ and type $d=100$ in Desmos. Then $k\%$ of $d$ equals $k$, so the value you find for $b$ will also be $k$.

In $0.4\%$ of $d$, $d$ is the amount the percent is taken of. Type $c=0.4\%\operatorname{of}d$ below the first line. Desmos gives $c=0.4$. Keep the percent sign: $0.4$ times $100$ would be $40$, not $0.4$.

The percent increase is measured against $c$. Since $a$ is $60\%$ more than $c$, it contains all of $c$ plus another $60\%$ of $c$. Add the percents:

So $a$ is $160\%$ of $c$, not $60\%$ of $c$. For “percent more than,” start with the original $100\%$.

Type $a=160\%\operatorname{of}c$ below the existing lines. Desmos gives $a=0.64$. That value includes both the original $c$ and the increase.

In $a$ is $25\%$ of $b$, $b$ is the base, so it goes after “of”:

Taking $25\%$ of $a$ instead would reverse the relationship.

Type $25\%\operatorname{of}b_1\sim a$. The subscript and $\sim$ tell Desmos to find $b_1$ rather than make a slider for $b$. Under PARAMETERS, it shows $b_1=2.56$. Since $d=100$, $b=2.56$ means $b$ is $2.56\%$ of $d$. So $k=2.56$. Choice C.