SAT Percentages Practice Question 6 (Hard)

Math · Problem-Solving and Data AnalysisHard

The number $a$ is $40\%$ greater than the number $b$ , and $b$ is $25\%$ less than the positive number $c$ . The value of $a$ is what percent of $c$ ?

$65\%$

$95\%$

$115\%$

$105\%$

Show answer and explanation

Answer: D

Translate each statement: $a = 1.4b$ and $b = 0.75c$ . Substituting gives $a = 1.4(0.75c) = 1.05c$ . So $a$ is $105\%$ of $c$ .

Choice C adds and subtracts the percents ( $100 + 40 - 25 = 115$ ), which ignores that the $40\%$ applies to $b$ , not to $c$ .

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