{"id":"cb_question_bank:f446937b-00fb-4f60-8d0e-e89e628a1907","source_id":"cb_question_bank","source_item_id":"f446937b-00fb-4f60-8d0e-e89e628a1907","external_id":"252ab91d-897c-4c0d-8d50-e60456359300","ibn":null,"question_id":"51c9d65f","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.A.","skill":"Ratios, rates, proportional relationships, and units","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"For a certain rectangular region, the ratio of its length to its width is 35 to 10 . If the width of the rectangular region increases by 7 units, how must the length change to maintain this ratio?","stimulus":"","stimulus_html":null,"stem_html":"

For a certain rectangular region, the ratio of its length to its width is 35\n to 10\n. If the width of the rectangular region increases by 7\n units, how must the length change to maintain this ratio?

","rationale_html":"

Choice B is correct. It’s given that the ratio of the rectangular region’s length to its width is 35\n to 10\n. This can be written as a proportion: lengthwidth=3510, or lw=3510. This proportion can be rewritten as 10l=35w, or l=3.5w. If the width of the rectangular region increases by 7\n, then the length will increase by some number x\n in order to maintain this ratio. The value of x\n can be found by replacing l with l+x and w\n with \n\tw\n\t+\n\t7\n\n in the equation, which gives l+x=3.5w+7. This equation can be rewritten using the distributive property as l+x=3.5w+24.5. Since l=3.5w, the right-hand side of this equation can be rewritten by substituting l for \n\t3.5\n\tw\n\n, which gives l+x=l+24.5, or \n\tx\n\t=\n\t24.5\n\n. Therefore, if the width of the rectangular region increases by 7\n units, the length must increase by 24.5\n units in order to maintain the given ratio.

\n

Choice A is incorrect. If the width of the rectangular region increases, the length must also increase, not decrease.

\n

Choice C is incorrect. If the width of the rectangular region increases, the length must also increase, not decrease.

\n

Choice D is incorrect. Since the ratio of the length to the width of the rectangular region is 35\n to 10\n, if the width of the rectangular region increases by 7\n units, the length would have to increase by a proportional amount, which would have to be greater than 7\n units.

","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.830000+00:00","source_updated_at":"2023-08-02T20:25:59.830000+00:00","options":[{"label":"A","content_html":"

It must decrease by 24.5\n units.

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

It must increase by 24.5\n units.

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

It must decrease by 7\n units.

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

It must increase by 7\n units.

","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}}