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abdulhakeem 2025-01-30 23:44:12 -06:00
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{
"question": "In a 60-item quiz, 40% of the questions are easy, and the rest are equally divided as average and difficult questions. If Aries is sure to get 75% of the easy questions, and half of the average and difficult questions correctly, how many points is she sure to get?",
"answer": "The average and difficult questions comprises 100% - 40% = 60% of the quiz.\nThere are 60 questions x 40/100 = <<60*40/100=24>>24 easy questions.\nThere are a total of 60 questions x 60/100 = <<60*60/100=36>>36 average and difficult questions.\nIf Aries is sure to get 75% of the easy questions, then this means she is sure of her 24 questions x 75/100 = <<24*75/100=18>>18 points.\nFrom the average and difficult questions, she is sure to get half of it correctly so that is 36 questions / 2 = <<36/2=18>>18 points.\nThus, she is sure of getting 18 points + 18 points = <<18+18=36>>36 points in her quiz.\n#### 36",
"id_orig": 1021,
"id_shuffled": 19,
"question_annotated": "In a {n,60}-item quiz, {p1,40}% of the questions are {s1,easy}, and the rest are equally divided as {s2,average} and {s3,difficult} questions. If {name,Aries} is sure to get {r1,75}% of the {s1,easy} questions, and {frac,half} of the {s2,average} and {s3,difficult} questions correctly, how many points is she sure to get?\n\n#init:\n- s1, s2, s3 = sample([\"history\", \"geography\", \"biology\", \"chemistry\", \"physics\", \"economics\", \"literature\", \"algebra\", \"geometry\" ], 3)\n- name = sample(names_female)\n- $frac = sample(fractions)\n- $p1 = range(5, 71, 5)\n- $r1 = range(5, 101, 5)\n- $n = range(10, 151, 10)\n\n#conditions:\n- is_int(n * (p1/100))\n- is_int(n * (p1/100) * (r1/100))\n- is_int(n*(1-(p1/100))*frac)\n\n#answer: int(n * (p1/100) * (r1/100)) + int(n*(1-(p1/100))*frac)",
"answer_annotated": "The {s2} and {s3} questions comprises 100% - {p1}% = {100-p1}% of the quiz.\nThere are {n} questions x {p1}/100 = <<{n}*{p1}/100={int(n * (p1/100))}>>{int(n * (p1/100))} {s1} questions.\nThere are a total of {n} questions x {100-p1}/100 = <<{n}*{100-p1}/100={int(n*(1-(p1/100)))}>>{int(n*(1-(p1/100)))} {s2} and {s3} questions.\nIf {name} is sure to get {r1}% of the {s1} questions, then this means she is sure of her {int(n * (p1/100))} questions x {r1}/100 = <<{int(n * (p1/100))}*{r1}/100={int(n * (p1/100) * (r1/100))}>>{int(n * (p1/100) * (r1/100))} points.\nFrom the {s2} and {s3} questions, she is sure to get {frac} of it correctly so that is {int(n*(1-(p1/100)))} questions * {frac} = <<{int(n*(1-(p1/100)))}*{frac}={int(n*(1-(p1/100))*frac)}>>{int(n*(1-(p1/100))*frac)} points.\nThus, she is sure of getting {int(n * (p1/100) * (r1/100))} points + {int(n*(1-(p1/100))*frac)} points = <<{int(n * (p1/100) * (r1/100))}+{int(n*(1-(p1/100))*frac)}={int(n * (p1/100) * (r1/100)) + int(n*(1-(p1/100))*frac)}>>{int(n * (p1/100) * (r1/100)) + int(n*(1-(p1/100))*frac)} points in her quiz.\n#### {int(n * (p1/100) * (r1/100)) + int(n*(1-(p1/100))*frac)}"
}