Question #ad911622 - SAT Suite Question Bank

Modded SAT Question Bank by Abdullah Mallik

The value of a collectible comic book increased by $167 percent sign$ from the end of $2011$ to the end of $2012$ and then decreased by $16 percent sign$ from the end of $2012$ to the end of $2013$ . What was the net percentage increase in the value of the collectible comic book from the end of $2011$ to the end of $2013$ ?

$124.28 percent sign$
$140.28 percent sign$
$151.00 percent sign$
$209.72 percent sign$

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Correct Answer: A

Rationale

Choice A is correct. It’s given that the value of the comic book increased by $167 percent sign$ from the end of $2011$ to the end of $2012$ . Therefore, if the value of the comic book at the end of $2011$ was $x$ dollars, then the value, in dollars, of the comic book at the end of $2012$ was $x + (\frac{167}{100}) x$ , which can be rewritten as $1 x plus 1.67 x$ , or $2.67 x$ . It’s also given that the value of the comic book decreased by $16 percent sign$ from the end of $2012$ to the end of $2013$ . Therefore, the value, in dollars, of the comic book at the end of $2013$ was $2.67 x - 2.67 x (\frac{16}{100})$ , which can be rewritten as $2.67 x minus left parenthesis 2.67 x right parenthesis left parenthesis 0.16 right parenthesis$ , or $2.2428 x$ . Thus, if the value of the comic book at the end of $2011$ was $x$ dollars, and the value of the comic book at the end of $2013$ was $2.2428 x$ dollars, then from the end of $2011$ to the end of $2013$ , the value of the comic book increased by $2.2428 x minus 1 x$ , or $1.2428 x$ , dollars. Therefore, the increase in the value of the comic book from the end of $2011$ to the end of $2013$ is equal to $1.2428$ times the value of the comic book at the end of $2011$ . It follows that from the end of $2011$ to the end of $2013$ , the net percentage increase in the value of the comic book was $left parenthesis 1.2428 right parenthesis left parenthesis 100 right parenthesis percent sign$ , or $124.28 percent sign$ .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This is the difference between the net percentage increase in the value of the comic book from the end of $2011$ to the end of $2012$ and the net percentage decrease in the value of the comic book from the end of $2012$ to the end of $2013$ , not the net percentage increase in the value of the comic book from the end of $2011$ to the end of $2013$ .

Choice D is incorrect. This is the net percentage increase in the value of the comic book from the end of $2011$ to the end of $2013$ , if the value of the comic book increased by $167 percent sign$ from the end of $2011$ to the end of $2012$ and then increased, not decreased, by $16 percent sign$ from the end of $2012$ to the end of $2013$ .

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