{"id":"cb_question_bank:9c6d3083-e5ee-4c11-a2d6-0e8801f22b3a","source_id":"cb_question_bank","source_item_id":"9c6d3083-e5ee-4c11-a2d6-0e8801f22b3a","external_id":null,"ibn":"03867-DC","question_id":"e8f9e117","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.E.","skill":"Linear inequalities in one or two variables","difficulty":"H","score_band":6,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The formula above is Ohm’s law for an electric circuit with current I , in amperes, potential difference V , in volts, and resistance R , in ohms. A circuit has a resistance of 500 ohms, and its potential difference will be generated by n six-volt batteries that produce a total potential difference of 6 n volts. If the circuit is to have a current of no more than 0.25 ampere, what is the greatest number, n , of six-volt batteries that can be used?","stimulus":"I equals, V over R","stimulus_html":"<div class=\"stimulus_reference \">\n\t<p class=\"standalone_statement style:1 \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/953af04950a1c07414a05ab471467ab43e52b53f9f2917b745721b58c627ed22\" alt=\"I equals, V over R\"></span></span></p>\n</div>\n","stem_html":"<p class=\"stem_paragraph \">The formula above is Ohm’s law for an electric circuit with current <span class=\"italic\">I</span>, in amperes, potential difference <span class=\"italic\">V</span>, in volts, and resistance <span class=\"italic\">R</span>, in ohms. A circuit has a resistance of 500 ohms, and its potential difference will be generated by <span class=\"italic\">n</span> six-volt batteries that produce a total potential difference of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a084193c1da37ba9e745711580be587239fdc7067d6cedd2d173d2e7dc59a32c\" alt=\"6 n\"></span></span> volts. If the circuit is to have a current of no more than 0.25 ampere, what is the greatest number, <span class=\"italic\">n</span>, of six-volt batteries that can be used?</p>\n","rationale_html":"<p>The correct answer is 20. For the given circuit, the resistance <span class=\"italic\">R</span> is 500 ohms, and the total potential difference <span class=\"italic\">V</span> generated by <span class=\"italic\">n</span> batteries is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a084193c1da37ba9e745711580be587239fdc7067d6cedd2d173d2e7dc59a32c\" alt=\"6 n\"></span> volts. It’s also given that the circuit is to have a current of no more than 0.25 ampere, which can be expressed as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fbb3bd997a6f1598c375e6db7e90d9f99854cd888942fb6b0cae038add6de65f\" alt=\"I is less than 0 point 2 5\"></span>. Since Ohm’s law says that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/953af04950a1c07414a05ab471467ab43e52b53f9f2917b745721b58c627ed22\" alt=\"I equals, V over R\"></span>, the given values for <span class=\"italic\">V</span> and <span class=\"italic\">R</span> can be substituted for <span class=\"italic\">I</span> in this inequality, which yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e76d75570ec70e1a08ee4c96aacada734b1a96db3b24a5b561fc3d898e0d9b71\" alt=\"6 n over 500 is less than 0 point 2 5\"></span>. Multiplying both sides of this inequality by 500 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6abe7fa895f3a87a74139f8946a366ff1d5e736083edab8599cbaf602aaa28e4\" alt=\"6 n is less than 125\"></span>, and dividing both sides of this inequality by 6 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4c223181bd93a94f1d400ea33dbc3b1dc61851f2ea5dbd8b4fe593ec781ec181\" alt=\"n is less than 20 point 8 3 3\"></span>. Since the number of batteries must be a whole number less than 20.833, the greatest number of batteries that can be used in this circuit is 20.</p>\n","correct_answer":["20"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.627000+00:00","source_updated_at":"2023-08-02T20:25:59.627000+00:00","options":[],"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}}