{"id":"aqua_rat:6fe0c1e0fdaf4e04e923224a337d6ba1","source_id":"aqua_rat","source_item_id":"6fe0c1e0fdaf4e04e923224a337d6ba1","external_id":null,"program":null,"section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":null,"scored":true,"layout_warning":null,"stem":"Two numbers are said to be relatively prime if they share no common positive factors other than 1. Set S contains the set of integers from 1 to 1,000, inclusive. What is the probability that a number chosen from S is relatively prime to 1,000?","stimulus":"","stimulus_html":null,"stem_html":"<p>Two numbers are said to be relatively prime if they share no common positive factors other than 1. Set S contains the set of integers from 1 to 1,000, inclusive. What is the probability that a number chosen from S is relatively prime to 1,000?</p>","rationale_html":"<p>We need all numbers between 1 and 1000 that are co-prime.</p><p>Between 1 to 10 there are 4 : 1,3,7,9</p><p>Take the period of 10&#x27;s , we have 100 periods of 10&#x27;s between 1 to 1000</p><p>So the total number of co-primes = 400</p><p>Now, the simple part ...</p><p>Probability = 400/1000 (i.e picking a co-prime from the first 1000 numbers )</p><p>Ans: 2/5 D</p>","correct_answer":["D"],"equiv_key":"ddcfd694ea03f2e5446f45a9","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>5/7</p>","ord":0},{"label":"B","content_html":"<p>3/5</p>","ord":1},{"label":"C","content_html":"<p>4/7</p>","ord":2},{"label":"D","content_html":"<p>2/5</p>","ord":3},{"label":"E","content_html":"<p>2/7</p>","ord":4}],"passage":null,"attribution":{"source_id":"aqua_rat","source_name":"AQuA-RAT algebra word problems with rationales","rights_holder":"Google DeepMind and the AQuA-RAT contributors","canonical_url":"https://github.com/google-deepmind/AQuA","retrieved_from":"https://raw.githubusercontent.com/google-deepmind/AQuA/master/","attribution":"Algebra word problems from the AQuA-RAT dataset (Ling et al., 2017), published by Google DeepMind under the Apache License 2.0.","disclaimer":"AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.","license":"Apache License 2.0. Crowdsourced by DeepMind and published for free use, including commercially.","redistributable":true,"item_count":508},"equivalents":[]}