is 62.5% more than , and is 0.32% of . If is 0.13% of , then is % of . Which choice must equal?

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Super-Hard SAT Math Question 21 | Free SAT Prep | Aniko

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Question 21·200 Super-Hard SAT Math Questions·Problem Solving and Data Analysis

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$a$ is 62.5% more than $b$ , and $b$ is 0.32% of $c$ .

If $a$ is 0.13% of $d$ , then $d$ is $k$ % of $c$ . Which choice must $k$ equal?

For chained percent relationships, rewrite each statement as a clean multiplier or decimal ratio (e.g., “ $p\%$ more” $\to 1+\frac{p}{100}$ , and “ $p\%$ of” $\to \frac{p}{100}$ ). If the problem links the same variable (here $a$ ) to two different quantities, set those expressions equal and solve for the needed ratio, then convert to a percent only at the end.

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Translate “62.5% more than”

“ $p\%$ more than” becomes a multiplier of $1+\frac{p}{100}$ , so $a=(1+0.625)b$ .

Translate a percent to a decimal

To turn 0.32% (or 0.13%) into a decimal multiplier, divide by 100.

You may need to divide, not just multiply

After you write $a$ as a multiple of $c$ and also as a multiple of $d$ , set the two expressions for $a$ equal and solve for $\frac{d}{c}$ .

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Compute $a$ as a fraction of $c$

Enter ac = (1+0.625)*(0.32/100) to compute $\frac{a}{c}$ .

Convert 0.13% to a decimal multiplier

Enter ad = 0.13/100 to represent $\frac{a}{d}$ .

Solve for $\frac{d}{c}$ by dividing

Enter dc = ac/ad to compute $\frac{d}{c}$ .

Convert to percent and match a choice

Enter k = 100*dc. The value of k should match exactly one answer choice.

Step-by-step Explanation

Write $a$ in terms of $b$ , and $b$ in terms of $c$

“62.5% more than $b$ ” means

a=b+0.625b=1.625b.

“0.32% of $c$ ” means

b=0.0032c.

Substitute to write $a$ in terms of $c$

Substitute $b=0.0032c$ into $a=1.625b$ :

a=1.625(0.0032)c=0.0052c.

Use the relationship between $a$ and $d$ to find $d$ in terms of $c$

“ $a$ is 0.13% of $d$ ” means

$$a=0.0013d $.$

0.0013d=a=0.0052c \quad\Rightarrow\quad d=\frac{0.0052}{0.0013}c=4c.

Convert $\frac{d}{c}$ to a percent

Since $d=4c$ , we have

$$\frac{d}{c}=4 $.$

That means $d$ is $4\times 100=400\%$ of $c$ , so $k=\mathbf{400}$ .

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