{"id":"act_quizme:math:q1:03","source_id":"act_quizme","source_item_id":"math-q1-03","external_id":"13aede84ab4becff","program":"ACT","section":"math","category_code":null,"category":null,"subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":3,"scored":true,"layout_warning":null,"stem":"Marco designs a spinner wheel that has exactly 4 sections: red, blue, green, and yellow. He wants the spinner wheel to have a 25% chance of landing on each section. He spins the wheel 500 times. The results of the spins are shown in this table. Spinner wheel section Number of times the spinner lands in each section Red 80 Blue 165 Green 130 Yellow 125 Based on the results in this table, one of the following changes would be the best fix. Which one?","stimulus":"","stimulus_html":null,"stem_html":"<div class=\"math-question-wrap\"> <p>Marco designs a spinner wheel that has exactly 4 sections: red, blue, green, and yellow. He wants the spinner wheel to have a 25% chance of landing on each section. He spins the wheel 500 times. The results of the spins are shown in this table.</p> <table style=\"width: 300px; border-collapse: collapse; border-spacing: 0px; border-style: solid; border-width: 1px;\" cellspacing=\"0\"> <thead> <tr> <th style=\"width: 127.4px; text-align: center; vertical-align: bottom; font-weight: normal; border-style: solid; border-width: 1px; padding: 3px;\"> Spinner wheel section</th> <th style=\"width: 124.6px; text-align: center; vertical-align: bottom; font-weight: normal; border-style: solid; border-width: 1px; padding: 3px;\"> Number of times the spinner lands in each section</th> </tr> </thead> <tbody> <tr> <td style=\"text-align: left; vertical-align: middle; width: 127.4px; border-style: solid; border-width: 1px; padding: 3px;\"> Red</td> <td style=\"text-align: left; vertical-align: middle; width: 124.6px; border-style: solid; border-width: 1px; padding: 3px;\"> 80</td> </tr> <tr> <td style=\"text-align: left; vertical-align: middle; width: 127.4px; border-style: solid; border-width: 1px; padding: 3px;\"> Blue</td> <td style=\"text-align: left; vertical-align: middle; width: 124.6px; border-style: solid; border-width: 1px; padding: 3px;\"> 165</td> </tr> <tr> <td style=\"text-align: left; vertical-align: middle; width: 127.4px; border-style: solid; border-width: 1px; padding: 3px;\"> Green</td> <td style=\"text-align: left; vertical-align: middle; width: 124.6px; border-style: solid; border-width: 1px; padding: 3px;\"> 130</td> </tr> <tr> <td style=\"text-align: left; vertical-align: middle; width: 127.4px; border-style: solid; border-width: 1px; padding: 3px;\"> Yellow</td> <td style=\"text-align: left; vertical-align: middle; width: 124.6px; border-style: solid; border-width: 1px; padding: 3px;\"> 125</td> </tr> </tbody> </table> <p>Based on the results in this table, one of the following changes would be the best fix. Which one?</p> </div> <div> <div class=\"math-answer-select-wrap\"> </div></div>","rationale_html":"<p><strong>A.</strong> <strong>Incorrect.</strong> Marco wants the spinner wheel to have a <span style=\"white-space: nowrap;\"><math><mn>25</mn><mo>%</mo></math>&nbsp;chance</span> of landing on each section. For <span style=\"white-space: nowrap;\"><math><mn>500</mn></math>&nbsp;spins,</span> this means the spinner should land on each section approximately <span style=\"white-space: nowrap;\"><math><mn>0</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>25</mn><mo>(</mo><mn>500</mn><mo>)</mo><mo>=</mo><mn>125</mn></math>&nbsp;times.</span> Be careful when reading values from the table. You may have switched the numbers for the red and blue sections.&nbsp;</p><p><strong>B.</strong> <strong>Correct.</strong> Marco wants the spinner wheel to have a <span style=\"white-space: nowrap;\"><math><mn>25</mn><mo>%</mo></math>&nbsp;chance</span> of landing on each section. For <span style=\"white-space: nowrap;\"><math><mn>500</mn></math>&nbsp;spins,</span> this means the spinner should land on each section approximately <span style=\"white-space: nowrap;\"><math><mn>0</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>25</mn><mo>(</mo><mn>500</mn><mo>)</mo><mo>=</mo><mn>125</mn></math>&nbsp;times.</span> The number of times the spinner landed on the green section and the yellow section are both close to this number already, but the number of times the spinner landed on the red section is too small and the number of times the spinner landed on the blue section is too large. Therefore, Marco should increase the area of the red section by decreasing the area of the blue section.</p><p><strong>C.</strong> <strong>Incorrect.</strong> You may have correctly noticed that the number of times that the spinner lands in the red section is less than the number of times it lands in green, yellow, or blue, so the red area needs to be increased. However, it <strong>does</strong> matter which area gets decreased because the number of times the spinner lands on yellow and green areas are already close to the desired value of&nbsp;<math><mn>25</mn><mo>%</mo></math>&nbsp;of <span style=\"white-space: nowrap;\"><math><mn>500</mn></math>&nbsp;spins,</span> or <span style=\"white-space: nowrap;\"><math><mn>0</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>25</mn><mo>(</mo><mn>500</mn><mo>)</mo><mo>=</mo><mn>125</mn></math>.</span></p><p><strong>D.</strong> <strong>Incorrect.</strong> You may have correctly noticed that the number of times that the spinner lands in the blue section is greater than the number of times it lands in green, yellow, or red, so the blue area needs to be decreased. However, it <strong>does</strong> matter which area gets increased because the number of times the spinner lands on yellow and green areas are already close to the desired value of&nbsp;<math><mn>25</mn><mo>%</mo></math>&nbsp;of <span style=\"white-space: nowrap;\"><math><mn>500</mn></math>&nbsp;spins,</span> or <span style=\"white-space: nowrap;\"><math><mn>0</mn><mo lspace=\"0\" rspace=\"0\">.</mo><mn>25</mn><mo>(</mo><mn>500</mn><mo>)</mo><mo>=</mo><mn>125</mn></math>.</span></p>","correct_answer":["B"],"equiv_key":"4ee27470d6dd25e395a55e5a","has_media":false,"has_mathml":true,"has_table":true,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>He should decrease the area of the red section by increasing the area of the blue section.</p>","ord":0},{"label":"B","content_html":"<p>He should increase the area of the red section by decreasing the area of the blue section.</p>","ord":1},{"label":"C","content_html":"<p>He should increase the area of the red section by decreasing the area of any of the other three sections.</p>","ord":2},{"label":"D","content_html":"<p><span>He should decrease the area of the blue section, and then it does <strong>not</strong> matter which section’s area is increased.</span></p>","ord":3}],"passage":null,"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},"equivalents":[{"id":"act_practice_pdf:pt1:math:003","source_id":"act_practice_pdf","source_item_id":"pt1-math-003","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":3,"scored":true,"layout_warning":null,"stem":"Marco designs a spinner wheel that has exactly 4 sections: red, blue, green, and yellow. He wants the spinner wheel to have a 25% chance of landing on each section. He spins the wheel 500 times. The results of the spins are shown in this table. Spinner Number of times wheel the spinner lands section in each section Red 80 Blue 165 Green 130 Yellow 125 Based on the results in this table, one of the following changes would be the best fix. Which one?","stimulus":"","stimulus_html":"<figure><img src=\"/api/assets/9c97b66960a271bea7b5ff76c1a56a6d4e205616c2d399c2378c2cbff9e9f141\" alt=\"Question 3 as printed in the Preparing for the ACT — Practice Test 1 booklet\"><figcaption>As printed in the official booklet.</figcaption></figure>","stem_html":"<p>Marco designs a spinner wheel that has exactly 4 sections: red, blue, green, and yellow. He wants the spinner wheel to have a 25% chance of landing on each section. He spins the wheel 500 times. The results of the spins are shown in this table. Spinner Number of times wheel the spinner lands section in each section Red 80 Blue 165 Green 130 Yellow 125 Based on the results in this table, one of the following changes would be the best fix. Which one?</p>","rationale_html":null,"correct_answer":["B"],"equiv_key":"4ee27470d6dd25e395a55e5a","has_media":true,"has_mathml":false,"has_table":false,"section_label":"Mathematics","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}}]}