{"id":"act_practice_pdf:pt1:math:001","source_id":"act_practice_pdf","source_item_id":"pt1-math-001","external_id":null,"program":"ACT","section":"math","category_code":"IES","category":"Integrating Essential Skills","subcategory_code":null,"subcategory":null,"form_id":"act_practice_pdf:pt1","passage_id":null,"position":1,"scored":true,"layout_warning":null,"stem":"Cameron took 4 tests, and his scores were as follows: 100 , 60 , 80 , and 30 . Cameron took another test that was scored x . The mean score of the 5 tests he took is 72 . What is the value of x ?","stimulus":"","stimulus_html":"<figure><img src=\"/api/assets/93fb1ba050ee7b836d251397719472ff5ddd94977ac39881b8a5c64fcac25971\" alt=\"Question 1 as printed in the Preparing for the ACT — Practice Test 1 booklet\"><figcaption>As printed in the official booklet.</figcaption></figure>","stem_html":"<p>Cameron took 4 tests, and his scores were as follows: 100 , 60 , 80 , and 30 . Cameron took another test that was scored x . The mean score of the 5 tests he took is 72 . What is the value of x ?</p>","rationale_html":null,"correct_answer":["D"],"equiv_key":"edd90b16f4386104494758e1","has_media":true,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>54</p>","ord":0},{"label":"B","content_html":"<p>67.5</p>","ord":1},{"label":"C","content_html":"<p>68.4</p>","ord":2},{"label":"D","content_html":"<p>90</p>","ord":3}],"passage":null,"attribution":{"source_id":"act_practice_pdf","source_name":"Official ACT full-length practice tests (PDF)","rights_holder":"ACT Education Corp.","canonical_url":"https://www.act.org/content/act/en/products-and-services/the-act/test-preparation.html","retrieved_from":"https://www.act.org/content/act/en/products-and-services/the-act/test-preparation.html","attribution":"Full-length ACT practice tests © ACT Education Corp., published free at act.org. Questions are retired items from previous ACT administrations.","disclaimer":"Extracted from a print-layout PDF: equations, figures and charts do not survive as text. Use the original PDF for anything that renders poorly. ACT® is a registered trademark of ACT Education Corp., which is not affiliated with, does not sponsor, and does not endorse this project.","license":"ACT Education Corp. copyright. Published free for personal test preparation; not licensed for redistribution.","redistributable":false,"item_count":342},"equivalents":[{"id":"act_quizme:math:q1:01","source_id":"act_quizme","source_item_id":"math-q1-01","external_id":"c30fc68040d7dc64","program":"ACT","section":"math","category_code":null,"category":null,"subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":1,"scored":true,"layout_warning":null,"stem":"Cameron took 4 tests, and his scores were as follows: 100, 60, 80, and 30. Cameron took another test that was scored x. The mean score of the 5 tests he took is 72. What is the value of x?","stimulus":"","stimulus_html":null,"stem_html":"<div class=\"math-question-wrap\"><p>Cameron took 4 tests, and his scores were as follows: 100, 60, 80, and 30. Cameron took another test that was scored x. The mean score of the 5 tests he took is 72. What is the value of x?</p></div>\n<div><div class=\"math-answer-select-wrap\"></div></div>","rationale_html":"<p><strong>A.</strong> <strong>Incorrect.</strong> Make sure that you include x in the average of the exam scores. You may have only summed the first four exam scores when calculating the exam average: <span style=\"white-space: nowrap;\"><math><mfrac><mrow><mn>100</mn><mo>+</mo><mn>60</mn><mo>+</mo><mn>80</mn><mo>+</mo><mn>30</mn></mrow><mn>5</mn></mfrac><mo>=</mo><mfrac><mn>275</mn><mn>5</mn></mfrac><mo>=</mo><mn>54</mn></math>.</span></p><p><strong>B.</strong> <strong>Incorrect.</strong> Make sure that you include the fifth exam in the average. You may have only averaged the first four exams: <span style=\"white-space: nowrap;\"><math><mfrac><mrow><mn>100</mn><mo>+</mo><mn>60</mn><mo>+</mo><mn>80</mn><mo>+</mo><mn>30</mn></mrow><mn>4</mn></mfrac><mo>=</mo><mfrac><mn>270</mn><mn>4</mn></mfrac><mo>=</mo><mn>67</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>5</mn></math>.</span></p><p><strong>C.</strong> <strong>Incorrect.</strong> Keep in mind that the average should be set equal to 72. You may have included 72 in the exam average: <span style=\"white-space: nowrap;\"><math><mfrac><mrow><mn>100</mn><mo>+</mo><mn>60</mn><mo>+</mo><mn>80</mn><mo>+</mo><mn>30</mn><mo>+</mo><mn>72</mn></mrow><mn>5</mn></mfrac><mo>=</mo><mfrac><mn>342</mn><mn>5</mn></mfrac><mo>=</mo><mn>68</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>4</mn></math>.</span></p><p><strong>D.</strong> <strong>Correct.</strong> To calculate the mean (average) score of the 5 tests, sum the individual scores and divide that sum by the number of tests: <span style=\"white-space: nowrap;\"><math><mfrac><mrow><mn>100</mn><mo>+</mo><mn>60</mn><mo>+</mo><mn>80</mn><mo>+</mo><mn>30</mn><mo>+</mo><mi>x</mi></mrow><mn>5</mn></mfrac><mo>=</mo><mfrac><mrow><mn>270</mn><mo>+</mo><mi>x</mi></mrow><mn>5</mn></mfrac></math>.</span> Set this fraction equal to the given average score, <span style=\"white-space: nowrap;\"><math><mfrac><mrow><mn>270</mn><mo>+</mo><mi>x</mi></mrow><mn>5</mn></mfrac><mo>=</mo><mn>72</mn></math>;</span> then, multiply by 5 and subtract 270 to calculate <span style=\"white-space: nowrap;\"><math><mi>x</mi><mo>=</mo><mn>90</mn></math>.</span></p>","correct_answer":["D"],"equiv_key":"edd90b16f4386104494758e1","has_media":false,"has_mathml":true,"has_table":false,"section_label":"Mathematics","attribution":{"source_id":"act_quizme","source_name":"ACT QuizMe official practice questions","rights_holder":"ACT Education Corp.","canonical_url":"https://quizme.act.org/","retrieved_from":"https://quizme.act.org/","attribution":"Official ACT practice questions © ACT Education Corp., from the QuizMe practice quizzes at quizme.act.org.","disclaimer":"ACT® is a registered trademark of ACT Education Corp., which is not affiliated with, does not sponsor, and does not endorse this project.","license":"ACT Education Corp. copyright. Published free on the public web; not licensed for redistribution.","redistributable":false,"item_count":78}}]}