Percentages — sat-dog

Hard Math · Problem-Solving and Data Analysis · Percentages · MCQ

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 $2013$ ?

A
$124.28 percent sign$
B
$140.28 percent sign$
C
$151.00 percent sign$
D
$209.72 percent sign$

Correct answer: A

Explanation

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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id cb_question_bank:f65322f4-7b1d-4535-afa3-be7fc37f3a13 · question ad911622 · JSON