The value of a collectible comic book increased by 167 % from the end of 2011 to the end of

Question

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.

$209.72 percent sign$

Accepted Answer

Choice A is correct. It&rsquo;s given that the value of the comic book increased by 167 % 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 + 167 100 x , which can be rewritten as 1 x + 1.67 x , or 2.67 x . It&rsquo;s also given that the value of the comic book decreased by 16 % 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 16 100 , which can be rewritten as 2.67 x - 2.67 x 0.16 , 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 - 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 1.2428 100 % , or 124.28 % . 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 % from the end of 2011 to the end of 2012 and then increased, not decreased, by 16 % from the end of 2012 to the end of 2013 .

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