{"id":"cb_question_bank:f65322f4-7b1d-4535-afa3-be7fc37f3a13","source_id":"cb_question_bank","source_item_id":"f65322f4-7b1d-4535-afa3-be7fc37f3a13","external_id":"02ff4aa9-be78-434c-a64d-d18b83b4e58a","ibn":null,"question_id":"ad911622","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.B.","skill":"Percentages","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"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 ?","stimulus":"","stimulus_html":null,"stem_html":"

The value of a collectible comic book increased by 167% from the end of 2011 to the end of 2012 and then decreased by 16% 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?

","rationale_html":"

Choice A is correct. It’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\n dollars, then the value, in dollars, of the comic book at the end of 2012 was x+167100x, which can be rewritten as 1x+1.67x, or \n\t2.67\n\tx\n\n. It’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 2.67x-2.67x16100, which can be rewritten as 2.67x-2.67x0.16, or 2.2428x. Thus, if the value of the comic book at the end of 2011 was x\n dollars, and the value of the comic book at the end of 2013 was \n\t2.2428\n\tx\n\n dollars, then from the end of 2011 to the end of 2013, the value of the comic book increased by 2.2428x-1x, or \n\t1.2428\n\tx\n\n, 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\n 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 1.2428100%, or 124.28%.

\n

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

\n

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.

\n

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.

","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.832000+00:00","source_updated_at":"2023-08-02T20:25:59.832000+00:00","options":[{"label":"A","content_html":"

124.28%

","ord":0},{"label":"B","content_html":"

140.28%

","ord":1},{"label":"C","content_html":"

151.00%

","ord":2},{"label":"D","content_html":"

209.72%

","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}