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适配后端vllm

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dataflow/example/PDF2VQAPipeline/vqa_extract_test.jsonl 0 → 100644
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{"question_pdf_path": "./example_data/PDF2VQAPipeline/questionextract_test.pdf", "answer_pdf_path": "./example_data/PDF2VQAPipeline/questionextract_test.pdf", "subject": "math", "output_dir": "../vqa_output_test/math1"}
{"question_pdf_path": "./example_data/PDF2VQAPipeline/math_question.pdf", "answer_pdf_path": "./example_data/PDF2VQAPipeline/math_answer.pdf", "subject": "math", "output_dir": "../vqa_output_test/math2"}
dataflow/example/ReasoningPipeline/pipeline_general.json 0 → 100644
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[
{
"instruction": "A recent clinical study compared two treatments for chronic back pain. What were the main findings regarding patient-reported pain reduction over six months?",
"output": "The study found that patients receiving Treatment A reported an average pain reduction of 45% over six months, compared to a 30% reduction for those on Treatment B. Additionally, quality-of-life scores improved more significantly in the Treatment A group.",
"golden_answer": "Treatment A led to greater pain reduction (45% vs. 30%).",
"source": "Medical_clinical"
},
{
"instruction": "In the last quarter, a commercial bank reported a rise in its non-performing loan ratio from 2.1% to 3.4%. What might this indicate about the bank's loan portfolio?",
"output": "This increase suggests that more borrowers are struggling to repay their loans, potentially due to economic slowdowns or tighter household finances. It indicates a deterioration in the quality of the bank’s loan assets and may lead to increased provisions.",
"golden_answer": "Higher credit risk due to more troubled loans.",
"source": "Finance_banking"
},
{
"instruction": "A city government launched a free vaccination drive. How did it impact the reported cases of influenza compared to the previous year?",
"output": "The campaign resulted in a 40% decline in reported influenza cases compared to the same period last year, indicating substantial community-level protection due to increased vaccination coverage.",
"golden_answer": "Cases fell by 40%.",
"source": "Public_health"
},
{
"instruction": "Why do investors typically diversify their portfolios across different asset classes?",
"output": "Diversification reduces overall investment risk by spreading exposure across assets that may not move in the same direction. It helps protect against significant losses if one sector underperforms, leading to more stable returns over time.",
"golden_answer": "To reduce risk and stabilize returns.",
"source": "Finance_investing"
},
{
"instruction": "What are some social consequences of long-term unemployment in a community?",
"output": "Long-term unemployment can lead to increased poverty, higher rates of mental health issues like depression, strained family relationships, and potentially higher crime rates as economic hardship intensifies.",
"golden_answer": "Increased poverty, mental health issues, family strain.",
"source": "Social_studies"
},
{
"instruction": "A pharmaceutical company is conducting Phase III trials for a new cancer drug. What is the primary objective of this phase?",
"output": "The main goal of Phase III trials is to confirm the drug's effectiveness, monitor side effects on a larger scale, compare it to standard treatments, and gather information to ensure it can be used safely in the general population.",
"golden_answer": "To confirm efficacy and monitor safety on a large scale.",
"source": "Medical_trials"
},
{
"instruction": "A national survey shows that 65% of respondents believe climate change policies should be stricter. What does this indicate about public sentiment?",
"output": "This suggests a strong majority support for more aggressive measures to combat climate change, which could influence future policy decisions and encourage governments to implement stricter regulations.",
"golden_answer": "Majority support stricter climate policies.",
"source": "Social_opinion"
},
{
"instruction": "Explain why compound interest leads to faster growth of investments compared to simple interest.",
"output": "Compound interest earns interest on both the initial principal and the accumulated interest from previous periods, creating a snowball effect. In contrast, simple interest only earns on the original principal, so growth is linear rather than exponential.",
"golden_answer": "It earns interest on interest, accelerating growth.",
"source": "Finance_concepts"
},
{
"instruction": "A triangle has sides of lengths 7, 24, and 25. Determine if it is a right triangle.",
"output": "We can check using the Pythagorean theorem: 7² + 24² = 49 + 576 = 625, and 25² = 625. Since they are equal, the triangle is indeed a right triangle.",
"golden_answer": "Yes, it is a right triangle.",
"source": "Math_geometry"
},
{
"instruction": "In a study involving 400 patients with hypertension, 300 were able to reduce their blood pressure below 140/90 mmHg after six months on a new treatment. What does this imply?",
"output": "This implies a success rate of 75%, indicating the treatment is effective for a significant majority of patients in managing hypertension.",
"golden_answer": "75% achieved target blood pressure.",
"source": "Medical_statistics"
}
]
dataflow/example/ReasoningPipeline/pipeline_general_short.json 0 → 100644
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[
{
"instruction": "A recent clinical study compared two treatments for chronic back pain. What were the main findings regarding patient-reported pain reduction over six months?",
"output": "The study found that patients receiving Treatment A reported an average pain reduction of 45% over six months, compared to a 30% reduction for those on Treatment B. Additionally, quality-of-life scores improved more significantly in the Treatment A group.",
"golden_answer": "Treatment A led to greater pain reduction (45% vs. 30%).",
"source": "Medical_clinical"
},
{
"instruction": "In the last quarter, a commercial bank reported a rise in its non-performing loan ratio from 2.1% to 3.4%. What might this indicate about the bank's loan portfolio?",
"output": "This increase suggests that more borrowers are struggling to repay their loans, potentially due to economic slowdowns or tighter household finances. It indicates a deterioration in the quality of the bank’s loan assets and may lead to increased provisions.",
"golden_answer": "Higher credit risk due to nothing.",
"source": "Finance_banking"
},
{
"instruction": "A city government launched a free vaccination drive. How did it impact the reported cases of influenza compared to the previous year?",
"output": "The campaign resulted in a 40% decline in reported influenza cases compared to the same period last year, indicating substantial community-level protection due to increased vaccination coverage.",
"golden_answer": "Cases fell by 40%.",
"source": "Public_health"
}
]
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dataflow/example/ReasoningPipeline/pipeline_math.json 0 → 100644
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dataflow/example/ReasoningPipeline/pipeline_math_short.json 0 → 100644
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[
{
"instruction":"An architect is designing a reflective surface for a concert hall in the shape of a horizontal hyperbola with its center at the origin. The two foci of the hyperbola are 8 meters apart, and for acoustic reasons the angle between its asymptotes must be 90°. In addition, one of its directrices is the vertical line x = –d. \n \n(a) Find the value of d.\n \n(b) Determine the equation of the hyperbola.",
"output":null,
"golden_answer":"8",
"source":"Bigmath_synth"
},
{
"instruction":"A certain number is processed differently depending on whether it is even or odd:\n• If the number is even, it is first divided by 2, then multiplied by 5, and finally 4 is added, giving a result of 34.\n• If the number is odd, it is first divided by 3, then multiplied by 7, and finally 2 is subtracted, yielding 33.\nDetermine all possible original numbers.",
"output":"Let x be the original number.\n\nCase 1: x is even.\n (x÷2)·5 + 4 = 34 \n ⇒ 5x\/2 + 4 = 34 \n ⇒ 5x\/2 = 30 \n ⇒ x = 12. \n (12 is even, so this is valid.)\n\nCase 2: x is odd.\n (x÷3)·7 – 2 = 33 \n ⇒ 7x\/3 – 2 = 33 \n ⇒ 7x\/3 = 35 \n ⇒ x = 15. \n (15 is odd, so this is valid.)\n\nAnswer: The only possible originals are 12 (in the even‐case) or 15 (in the odd‐case).",
"golden_answer":"15",
"source":"Bigmath_synth"
},
{
"instruction":"A bakery sells muffins and croissants. Each muffin is priced at $3, while each croissant is sold for 1.5 times the muffin price. In addition, every croissant incurs an extra packaging fee of $0.50. On a certain day, the bakery sells 15 croissants along with an unknown number of muffins, and the total revenue collected is $90. How many muffins were sold that day?",
"output":"Let x be the number of muffins. \nMuffin revenue = 3·x. \nCroissant revenue = (1.5·3 + 0.5)·15 = (4.5 + 0.5)·15 = 5·15 = 75. \nTotal revenue = 3x + 75 = 90 \n⇒ 3x = 15 \n⇒ x = 5. \n\nSo they sold 5 muffins.",
"golden_answer":"5",
"source":"Bigmath_synth"
},
{
"instruction":"Alpha, Bravo, and Charlie all start running at the same time around a circular track. Alpha completes one lap in 130 seconds, and Charlie does so in 170 seconds. Bravo, however, runs each lap in 135 seconds but must take a mandatory 10‐second hydration break immediately after finishing each lap—so his effective time per lap is 135 + 10 = 145 seconds. \n\nDetermine the total time in minutes from the start until the fourth occurrence (including the start as the first occurrence) when all three cross the starting line simultaneously. Also, state whether this elapsed time is less than 40 minutes.",
"output":"Let A, B, C denote Alpha, Bravo and Charlie and let t be a time (in seconds) at which they are all simultaneously on the start–finish line. We have\n\n • Alpha laps in 130 s ⇒ A crosses whenever t≡0 (mod 130). \n • Charlie laps in 170 s ⇒ C crosses whenever t≡0 (mod 170). \n • Bravo runs a 135 s lap and then sits 10 s ⇒ his effective cycle is 135+10=145 s, so he crosses the line every 145 s ⇒ t≡0 (mod 145). \n\nHence the common crossing times (including t=0 at the start) are exactly the multiples of\n\n LCM(130, 145, 170)\n \nLet us factor:\n\n 130=2·5·13 \n 145=5·29 \n 170=2·5·17 \n\nso\n\n LCM=2·5·13·17·29=64 090 s. \n\nThus the simultaneous crossings occur at\n t=0, 64 090 s, 2·64 090=128 180 s, 3·64 090=192 270 s, … \n\nIf we count t=0 as the 1st occurrence, then the 4th occurrence is at\n t=3·64 090=192 270 s. \n\nIn minutes that is\n\n 192 270 s ÷ 60 = 3 204.5 minutes,\n\nwhich is obviously far more than 40 minutes.",
"golden_answer":"40",
"source":"Bigmath_synth"
},
{
"instruction":"A retail shop generated revenue from two products. Product A brought in $2001. Product B was sold through two channels: in‐store and online. In‐store sales contributed 60% of Product B’s pre‑tax revenue, while online sales (making up the remaining 40%) were subject to a 4% sales tax. The combined revenue from both products—counting the tax on online sales—was $3017. Determine the pre‑tax revenue earned from the in‑store and online sales of Product B.",
"output":"Let x = the total pre‐tax revenue of Product B. \nThen \n  in‐store = 0.60 x \n  online = 0.40 x \n\nBecause online sales incur a 4% tax, the revenue collected from online (including tax) is 1.04 · (0.40 x) = 0.416 x. \nThe total revenue (Product A + in‐store B + taxed online B) is \n  2001 + 0.60 x + 0.416 x = 3017 \nSo \n  1.016 x = 3017 − 2001 = 1016 \n  x = 1016 \/ 1.016 = 1000 \n\nHence, pre‐tax revenues for B are: \n  In‐store: 0.60·1000 = $600 \n  Online: 0.40·1000 = $400",
"golden_answer":"400",
"source":"Bigmath_synth"
},
{
"instruction":"A tech company creates security codes for its devices. Each code is a 4‐character sequence formed using the letters D, E, and F. The code must include each letter at least once, and the same letter cannot appear consecutively. Additionally, if the code begins with D, then exactly two of the characters in the code must be E. How many unique security codes satisfy these conditions? Express your answer as a single integer.",
"output":"To organize the count, break into two cases by first letter:\n\nCase 1: starts with D. \n  – By the “if it begins with D” clause, it must have exactly two E’s in the four positions. With one D already in front that leaves E,E,F to place in positions 2–4. \n  – We also cannot have any two identical letters adjacent. Of the three multiset‐permutations of E,E,F only E F E avoids an E–E back‐to‐back. \n  ∴ case 1 contributes 1 code: D E F E.\n\nCase 2: starts with E or F. \n  – Now there is no extra E‐count restriction, but we do require (i) no repeats adjacent, (ii) at least one of each D,E,F somewhere. \n\n(A) Starts with E: \n Positions 2–4 can be built freely (no two in a row the same and pos 2≠E), giving 2³=8 total. Of those 8, exactly 2 fail to include a D and F in 2–4, so 8–2=6 actually contain D,F at least once (together with the leading E this ensures all three appear). \n \n(B) Starts with F: \n Symmetrically, we get another 8 total no‐repeat sequences in 2–4, of which 2 are missing one of {D,E} there, so 8–2=6 that do contain both D and E (and the leading F). \n\n∴ case 2 contributes 6+6=12 codes\n\nGrand total = case 1 + case 2 = 1 + 12 = 13.",
"golden_answer":"13",
"source":"Bigmath_synth"
},
{
"instruction":"An artist is designing a tiled mosaic. The finished design must use a total number of tiles that can be arranged in equal rows with either 8, 10, or 12 tiles per row (with no tile left over). In addition, exactly 25% of the total tiles will be accent tiles, and these accent tiles must themselves be able to be arranged in equal rows of 8, 10, or 12 (again with no leftover tiles). What is the smallest total number of tiles the artist can use in the mosaic?",
"output":"480",
"golden_answer":"480",
"source":"Bigmath_synth"
},
{
"instruction":"A manufacturer applies several successive adjustments to the cost of producing a gadget. First, a reprocessing error causes the cost to be multiplied by –4. Next, an efficiency upgrade reduces the cost effect by a factor of 8 (i.e. the current value is divided by 8). Then, a quality improvement adjustment is made by multiplying the result by –3\/2. These operations are performed in the order given (from left to right). Finally, an additional handling fee scales the adjusted cost by an extra factor of 1\/3. What is the overall multiplier effect on the original cost? Express your answer as a simplified fraction.",
"output":"The overall multiplier is \n(–4) × (1\/8) × (–3\/2) × (1\/3) \n= (–4\/1)·(1\/8)·(–3\/2)·(1\/3) \n= 1\/4.",
"golden_answer":"4",
"source":"Bigmath_synth"
},
{
"instruction":"A furniture maker plans to build decorative tables for a showroom. Each table requires 3 pine planks and 2 oak planks. The maker has 12 pine logs already available, and each pine log can be cut to yield 5 pine planks. Because the number of pine planks exactly determines the number of tables that can be built, he will buy oak logs only to supply the matching oak planks needed. If each oak log can be cut to yield 10 oak planks, how many tables can be built in total and how many oak logs must he purchase to complete the project?",
"output":"He can get 12 logs×5 planks\/log = 60 pine planks, which makes 60\/3 = 20 tables. \nFor 20 tables he needs 20×2 = 40 oak planks, and at 10 planks per log that’s 40\/10 = 4 oak logs. \nAnswer: 20 tables and 4 oak logs.",
"golden_answer":"4",
"source":"Bigmath_synth"
},
{
"instruction":"A picture frame is to be made by joining three ribbons end‐to‐end to form a triangle. Two of the ribbons are 8 cm and 13 cm long, while the third ribbon has an integer length x cm. In addition, because of shipping restrictions, the total perimeter of the frame must be less than 40 cm. Determine the sum of all possible whole number values of x that allow the ribbons to form a triangle and satisfy the perimeter restriction.",
"output":"First, the triangle‐inequalities give\n\n1. 8 + 13 > x ⇒ x < 21 \n2. 8 + x > 13 ⇒ x > 5 \n3. 13 + x > 8 ⇒ x > –5 (automatic once x>5)\n\nSo from (1) and (2) we get 6 ≤ x ≤ 20 (integer).\n\nNext, the perimeter restriction is\n 8 + 13 + x < 40 \n⇒ 21 + x < 40 \n⇒ x < 19 \n⇒ x ≤ 18.\n\nCombining: 6 ≤ x ≤ 18. These are the 13 integers 6,7,8,…,18. Their sum is\n\n (6 + 18)·13\/2 = 24·13\/2 = 12·13 = 156.\n\nAnswer: 156.",
"golden_answer":"156",
"source":"Bigmath_synth"
},
{
"instruction":"An online retailer is launching a special promotion by distributing three‐digit discount codes. A discount code is valid only if it satisfies all of the following conditions:\n • The product of its digits equals 24.\n • The sum of its digits is an even number.\n • The tens digit is a prime number.\nDetermine the total number of valid discount codes. Provide your answer as a single integer.",
"output":"4",
"golden_answer":"4",
"source":"Bigmath_synth"
},
{
"instruction":"Julian is hosting a themed dinner party and prepares a rectangular chocolate cake cut into exactly 20 equal pieces for himself and his four guests: Maya, Ian, Zoe, and Evan. Their cake‐eating habits are as follows:\n\n1. Julian takes 2 pieces.\n2. Maya, being health‐conscious, takes 15% of Julian’s share (if 15% is not a whole number, she rounds up to the next whole piece).\n3. Ian is moderately hungry and takes 1.5 times as many pieces as Julian.\n4. Zoe loves cake and takes 3 pieces plus, if available, every extra piece that would have made Ian’s share exceed his planned 1.5×Julian; that is, if Ian’s designated number of pieces (from rule 3) cannot be fully taken because of limited supply, Zoe claims the “overflow” portion.\n5. Evan is very hungry and intends to take twice as many pieces as Julian; however, if the remaining pieces after everyone else has taken their share are fewer than his intended amount, he takes all the remaining pieces instead.\n\nAssuming the pieces are distributed in the order given above (Julian, then Maya, then Ian, then Zoe, and finally Evan), determine the ratio of the number of pieces Evan actually eats to the number of pieces Julian eats. (Note: In solving this problem, you must consider the case where there may not be enough pieces left for Evan’s full intended share.)",
"output":"Here’s the step‑by‑step tally (out of 20 pieces), in the order given:\n\n1. Julian takes 2 → 20 − 2 = 18 left \n2. Maya takes ceil(15% of 2)=ceil(0.3)=1 → 18 − 1 = 17 left \n3. Ian takes 1.5×2=3 → 17 − 3 = 14 left \n4. Zoe takes her fixed 3 pieces; Ian wasn’t shorted, so no “overflow” → 14 − 3 = 11 left \n5. Evan intends 2×2=4, and there are 11 left (≥4), so he takes 4 → 11 − 4=7 leftover \n\nEvan ends up with 4 pieces, Julian 2 pieces, so the ratio Evan : Julian = 4 : 2 = 2 : 1.",
"golden_answer":"1",
"source":"Bigmath_synth"
},
{
"instruction":"Alex has 90 candies and 40 stickers. He wants to pack these into gift bags so that every bag contains exactly 6 candies. In addition, each bag will receive either 3 stickers or 2 stickers. If Alex must use all the candies and stickers and he packs more bags with 3 stickers than with 2 stickers, how many gift bags does he create?",
"output":"Let x = number of bags with 3 stickers, and y = number with 2 stickers. \nThen \n• Candies: 6(x+y) = 90 ⇒ x+y = 15 \n• Stickers: 3x + 2y = 40 \n\nSubstitute y = 15−x into the sticker‐count: \n3x + 2(15−x) = 40 \n3x + 30 − 2x = 40 \nx = 10, so y = 5. \n\nTotal bags = x+y = 10+5 = 15.",
"golden_answer":"15",
"source":"Bigmath_synth"
},
{
"instruction":"A logistics company assigns tracking codes (represented by colors) to shipments, whose weights can be any positive real number. The following rules must be observed:\n • If two shipments have weights whose ratio is exactly 2 or exactly 5, then they must be assigned different tracking codes.\n • Every shipment weighing between 50 kg and 100 kg must be given a tracking code that is not used for any shipments weighing less than 50 kg or more than 100 kg.\n\nWhat is the minimum number of tracking codes required to label all shipments while satisfying these rules?",
"output":"We can think of “weight‐” as points on the real line via x=ln w. Then “cannot be same color if ratio 2 or 5” becomes “cannot be same color if x differ by a=ln 2 or b=ln 5.” Also the interval B = [ln 50, ln 100] must carry a palette disjoint from the rest (A∪C = (−∞, ln 50)∪(ln 100, +∞)).\n\n1. On B itself the only forbidden pair is 50↔100 (distance ln 2), so B needs 2 colors.\n2. On A∪C one has an infinite graph with edges at ±a and ±b. Since ln 2∕ln 5 is irrational there are no non‐trivial cycles, so this graph is bipartite and needs exactly 2 colors.\n3. By the rule “B’s colors must be disjoint from A∪C’s,” the total is 2+(2)=4.\n\nHence 4 tracking codes suffice and are necessary.",
"golden_answer":"4",
"source":"Bigmath_synth"
},
{
"instruction":"A factory’s production efficiency factor is modeled by the expression (m + 3)\/(m + 4) + 2\/(m + 4), where m (in months) measures the time since the last equipment upgrade and m ≠ –4. \n a) Express the overall efficiency factor in its simplest algebraic form. \n b) For what value of m does the factory achieve an efficiency factor of 1.2?",
"output":"a) Combine the fractions over the common denominator (m + 4): \n (m + 3)\/(m + 4) + 2\/(m + 4) \n = [ (m + 3) + 2 ] \/ (m + 4) \n = (m + 5) \/ (m + 4). \n\nb) Set (m + 5)\/(m + 4) = 1.2 = 6\/5 and solve for m: \n 5(m + 5) = 6(m + 4) \n 5m + 25 = 6m + 24 \n 25 – 24 = 6m – 5m \n 1 = m. \n\nSo the factory reaches an efficiency factor of 1.2 when m = 1 month.",
"golden_answer":"1",
"source":"Bigmath_synth"
},
{
"instruction":"Two numbers represent the amounts (in dollars) of two different investments. It is known that the difference between the investments, the sum of the investments, and 10% of their product are in the ratio 1 : 9 : 36. Find the product of the two investments. Express your answer as a single integer.",
"output":"Let the investments be x and y with x > y. Then\n\nx–y : x+y : 0.1xy = 1 : 9 : 36.\n\nSo x–y = k, x+y = 9k ⇒ x = 5k, y = 4k. And 0.1·(5k·4k)=36k ⇒ 2k²=36k ⇒ k=18.\n\nHence x=90, y=72 and xy=90·72=6480.",
"golden_answer":"6480",
"source":"Bigmath_synth"
},
{
"instruction":"An isosceles triangle has equal sides of 6 units and a base of 8 units. Construct the following composite figure:\n• At each vertex of the triangle, draw two distinct circular arcs with centers at that vertex. The first arc has a radius of 2 units and the second a radius of 7 units; both arcs are drawn outward from the triangle.\n• Additionally, at the midpoint of the base, attach a 90° circular sector with a radius of 1 unit extending outward.\nDetermine the minimum possible width of a strip bounded by two parallel lines that can completely enclose this entire composite figure. (You must analyze and compare the extremal contributions of the triangle, the four arcs, and the circular sector in order to find the optimal orientation minimizing the strip’s width.)",
"output":"Let the triangle be placed so that its base runs from A=(−4,0) to B=(+4,0) and its apex is at \n C=(0,h) with h=√(6²−4²)=2√5 ≃4.472. \nAt each of the three vertices A, B, C we have two “outward” circular arcs of radii 2 and 7; and at the midpoint M=(0,0) of the base we have a little 90°‐sector of radius 1 pointing downward. \n\nWe want the smallest possible distance between two parallel support‐lines (a “strip”) that can be swung around to cover every point of the union of triangle+arcs+sector. Call by u a unit normal direction for the strip; then the width in direction u is \n W(u) = max{ x·u : x in the figure } − min{ x·u : x in the figure }. \n\n1) Because the radius–7 arcs are by far the largest radial excursions, one checks quickly that none of the radius–2 arcs nor the tiny radius–1 sector ever “pushes” past the radius–7 arcs in any direction u. In fact \n max {x·u : figure} = max { A·u, B·u, C·u } + 7, \n min {x·u : figure} = min { A·u, B·u, C·u } − 7. \nHence \n W(u) = [max(A·u,B·u,C·u) − min(A·u,B·u,C·u)] + 14 \n = width of the bare triangle in direction u + 14. \n\n2) It is a standard fact that the minimal width of an isosceles triangle of side‐lengths 6, 6, 8 is attained when the strip is parallel to the base AB, and equals the altitude from C down to AB, namely h=2√5. \n\n3) Therefore the overall “composite” width is minimized exactly in the same orientation (strip lines horizontal), and is \n Wmin = (altitude = 2√5) + 14 \n = 14 + 2 √5 ≃ 14 + 4.472 = 18.472 (units). \n\nConclusion. The narrowest parallel‐line strip that contains the entire figure has width \n 14 + 2√5 ≃ 18.472 \nand it is achieved by taking the two lines horizontal (i.e. parallel to the triangle’s base).",
"golden_answer":"18.472",
"source":"Bigmath_synth"
},
{
"instruction":"Suppose in a math contest each contestant’s score on Problem A is one of the two distinct real roots of the quadratic equation\n\n  x² – (m + 3)x + 2m = 0\n\nand the score on Problem B is determined by solving the linear equation\n\n  n·x – 4 = 0                 (assuming n ≠ 0).\n\nIf every score obtained from Problem B is also a valid score for Problem A, find all pairs (m, n) ∈ ℝ × ℝ (with n ≠ 0) that satisfy this condition. (Hint: Express the unique solution x = 4\/n of the linear equation; then require that substituting x = 4\/n in the quadratic yields 0. Also, remember that the quadratic must have two distinct real roots.)",
"output":"We want the unique B‐score x = 4\/n to be one of the two (distinct) real roots of \n x² – (m+3)x + 2m = 0. \nHence we must have \n (4\/n)² – (m+3)(4\/n) + 2m = 0, \nand we also need the quadratic to have two distinct real roots (which, as you can check, in fact imposes no extra restriction on m).\n\n1. Clear denominators in \n 16\/n² – (4(m+3))\/n + 2m = 0 \n by multiplying through by n²: \n 16 – 4n(m+3) + 2m n² = 0 \n ⇔ 2m n² – 4m n + (16 – 12n) = 0 \n ⇔ 2m n(n–2) = 12n – 16 \n ⇔ m = (12n – 16) \/ [2n(n–2)], provided n≠0, 2.\n\n2. One checks the quadratic’s discriminant \n D = (m+3)² – 8m = m² – 2m + 9 = (m–1)² + 8 > 0 \n for all real m, so the root at x=4\/n is always one of two distinct real roots.\n\nTherefore the complete solution set is\n\n {(m,n): n≠0, 2, m = (12n–16)\/(2n(n–2)) } \n\nor equivalently\n\n m = 2(3n–4) \/ [n(n–2)], n∈ℝ\\{0,2}.",
"golden_answer":"2",
"source":"Bigmath_synth"
},
{
"instruction":"Let i be the imaginary unit. If (2 – i)(x + 2i) = 6 + zi, where x and z are real numbers and x is known to be a solution of the quadratic equation x² – 5x + 6 = 0, determine the value of x and then compute 4x + z.",
"output":"First expand and equate real‐ and imaginary parts:\n\n(2 − i)(x + 2i) = 2x + 4i − ix − 2i² \n = (2x + 2) + i(4 − x)\n\nWe want (2x+2) + i(4−x) = 6 + zi. Hence \n2x + 2 = 6 ⇒ x = 2 \n4 − x = z ⇒ z = 4 − 2 = 2.\n\nCheck that x=2 is indeed a root of x²−5x+6=0 (the other root is 3, but only x=2 satisfies the complex‐equation). \nFinally 4x + z = 4·2 + 2 = 10.",
"golden_answer":"10",
"source":"Bigmath_synth"
},
{
"instruction":"At the Arboretum's annual garden exhibition, various flora and installations are arranged as follows:\n\n• Trees: There are 1,342 oak trees, 1,587 maple trees, 1,925 pine trees, and 2,450 birch trees.\n• Shrubs: There are 8 clusters of ornamental shrubs. Each cluster was originally planned to contain 100 shrubs, but each lost 12 shrubs due to recent weather damage.\n• Roses: There are 7 displays of rose bouquets. In 6 of these displays, each bouquet contains exactly 40 roses. In the remaining display, each bouquet was enhanced by a 15% increase over the standard amount, so each bouquet contains 46 roses (after rounding down to the nearest whole number).\n• Fountain Installations: There are 10 pairs of fountain installations set around the garden.\n\nDetermine the total number of individual pieces (trees, shrubs, roses, and fountain installations) featured at the exhibition.",
"output":"First, let’s tally each category one by one.\n\n1. Trees \n Oak: 1 342 \n Maple: 1 587 \n Pine: 1 925 \n Birch: 2 450 \n Total trees = 1 342 + 1 587 + 1 925 + 2 450 = 7 304 \n\n2. Shrubs \n 8 clusters × (100 shrubs – 12 lost) = 8 × 88 = 704 \n\n3. Roses \n There are 7 displays, each with one bouquet (the problem statement implies one bouquet per display). \n – 6 bouquets at 40 roses each: 6 × 40 = 240 \n – 1 bouquet at a 15% increase over 40 → 40×1.15 = 46 (rounded down) \n Total roses = 240 + 46 = 286 \n\n4. Fountain installations \n 10 pairs of fountains → 10 × 2 = 20 individual installations \n\nFinally, sum all pieces: \n 7 304 (trees) \n+  704 (shrubs) \n+  286 (roses) \n+  20 (fountains) \n= 8 314 \n\nAnswer: 8 314 individual pieces.",
"golden_answer":"314",
"source":"Bigmath_synth"
},
{
"instruction":"A construction company leases a rectangular storage lot for its equipment. The rental fee is set at $55 for every 500 square feet per month, but if the lot’s area exceeds 10,000 square feet an extra fee of 10% is added to the base rent. The lot’s width is fixed at 50 feet, and the company’s monthly bill comes to $1,320. Determine the length of the lot in feet and confirm that the extra fee was applied.",
"output":"Let L be the length (in ft). Since the width is 50 ft, the area is \n A = 50·L (sq ft). \n\nRate per sq ft (before any surcharge): \n $55 per 500 ft² ⇒ \\$\\frac{55}{500}=0.11\\,$\/ft². \n\nBase rent = 0.11·A. Because A>10 000, we must add a 10% surcharge, so the total rent is \n Total = 1.10·(0.11·A) = 0.121·A. \n\nWe are told Total = \\$1 320, so \n 0.121·A = 1 320 \n⇒ A = 1 320\/0.121 ≃ 10 909.09 ft². \n\nHence \n 50·L = 10 909.09 \n⇒ L ≃ 10 909.09\/50 = 218.18 ft. \n\nCheck: \n A ≃10 909 ft² >10 000 ft² ⇒ surcharge applies. \n Base rent =0.11·10 909.09 ≃\\$1 200.00 \n +10% surcharge =\\$120.00 \n Total ≃\\$1 320.00. \n\nAnswer: The lot is about 218.2 ft long, and indeed its area exceeds 10 000 ft² so the extra 10% fee was applied.",
"golden_answer":"10",
"source":"Bigmath_synth"
},
{
"instruction":"A company’s weekly revenue (in thousands of dollars) follows an arithmetic sequence with nonzero common difference d. It is given that the revenue in the 5th week is 2 (that is, $2,000). In addition, for any week when the revenue exceeds 2, the company earns an immediate bonus of 0.5 (i.e. an extra $500) for that week. Define Rₙ as the sum of the weekly revenues (excluding bonuses) over the first n weeks and Bₙ as the total bonus earned in those n weeks. Determine an expression for 2(R₆ + B₆) + (R₁₂ + B₁₂) in terms of d. (Note: You must consider separately those weeks whose revenue is at most 2 and those whose revenue exceeds 2.)",
"output":"Let aₙ be the n‑th week’s (thousands of dollars) revenue. Since a₅=2 and {aₙ} is arithmetic with common difference d≠0, \n a₁=2−4d, \n aₙ=a₁+(n−1)d=2−4d+(n−1)d. \n\nA week k earns a bonus 0.5 only if aₖ>2. One checks \n aₖ>2 ⇔2−4d+(k−1)d>2 ⇔(k−5)d>0. \n\nCase 1: d>0 ⇒ (k−5)d>0 exactly when k>5. \n Weeks 1–5 have no bonus, weeks 6–12 each earn 0.5. \n R₆=∑₁⁶aₙ=6\/2·(2a₁+5d)=3(2(2−4d)+5d)=12−9d \n B₆=1·0.5=0.5 \n R₁₂=12\/2·(2a₁+11d)=6(4+3d)=24+18d \n B₁₂=7·0.5=3.5 \n ⇒2(R₆+B₆)+(R₁₂+B₁₂)=2((12−9d)+0.5)+(24+18d+3.5) \n                       =25−18d+27.5+18d=52.5 \n\nCase 2: d<0 ⇒ (k−5)d>0 exactly when k<5. \n Weeks 1–4 earn 0.5, weeks 5–12 no bonus. \n R₆=12−9d, B₆=4·0.5=2 \n R₁₂=24+18d, B₁₂=4·0.5=2 \n ⇒2(R₆+B₆)+(R₁₂+B₁₂)=2((12−9d)+2)+(24+18d+2) \n                       =28−18d+26+18d=54. \n\nAnswer: \n If d>0, 2(R₆+B₆)+(R₁₂+B₁₂)=52.5, \n If d<0, 2(R₆+B₆)+(R₁₂+B₁₂)=54.",
"golden_answer":"54",
"source":"Bigmath_synth"
},
{
"instruction":"A fruit vendor sells bags of oranges using two different packaging methods. In a standard bag, there are exactly one dozen oranges; however, due to a supply issue, some bags are only filled to 75% of the standard amount. If a customer buys 20 bags and ends up with a total of 210 oranges, how many of the bags were standard and how many were reduced?",
"output":"Let x = number of standard (12‐orange) bags and y = number of reduced (9‐orange) bags. Then\n\n1) x + y = 20 \n2) 12x + 9y = 210 \n\nFrom (1) y = 20 – x. Substitute into (2):\n\n12x + 9(20 – x) = 210 \n12x + 180 – 9x = 210 \n3x = 30 \nx = 10 \n\nHence y = 20 – 10 = 10. \n\nAnswer: 10 standard bags and 10 reduced bags.",
"golden_answer":"10",
"source":"Bigmath_synth"
},
{
"instruction":"Two adjacent corners of a square exhibition booth are located at (2, –5) and (–3, 0). The design team calculates the side length of the booth from these coordinates; however, because of uneven ground, if this computed side length is not an integer, it must be increased to the next highest integer before construction begins.\n\na) Determine the adjusted perimeter of the booth.\n\nb) After construction, the carpet covering the floor is paid only for the area that exceeds 60 square units, at a rate of $3 per extra square unit. Calculate the additional carpet cost based on the adjusted side length.\n\n",
"output":"First, compute the true side length:\n\nDistance between (2, –5) and (–3, 0) \n= √[(2 – (–3))² + (–5 – 0)²] \n= √[5² + (–5)²] \n= √(25 + 25) \n= √50 ≈ 7.071.\n\nSince 7.071 is not an integer, we round up to the next integer, 8.\n\na) Adjusted perimeter = 4 × 8 = 32.\n\nb) Floor area = 8² = 64. \nExcess over 60 = 64 – 60 = 4. \nAt \\$3 per extra unit, cost = 4 × 3 = \\$12.",
"golden_answer":"12",
"source":"Bigmath_synth"
},
{
"instruction":"A computer store sells two accessory bundle deals. Bundle A includes two identical keyboards, two identical mice, and one monitor. Its price is calculated by multiplying the cost factors: keyboard cost (K), mouse cost (M), and monitor cost (D), so that the total price is\n  K × K × M × M × D.\nBundle B, on the other hand, consists of the same keyboard and monitor but replaces the mice with a combined cable set whose cost is unknown; its price is given by\n  K × K × D × n × n.\nOn a weekday sale the two bundle deals are priced exactly the same. During weekend promotions the store offers an extra discount where the cable set in Bundle B costs 20% less than the regular mouse price, but that does not affect today’s weekday pricing.\nIf K = 3 dollars, M = 5 dollars, and D = 7 dollars, determine the value of n (as a positive integer) for the weekday bundle price.\n\n",
"output":"We have on a weekday \n Price A = K²·M²·D \n Price B = K²·D·n² \nSince they’re equal today, \n K²·M²·D = K²·D·n² \n⇒ M² = n² \n⇒ n = |M| = 5 (we take the positive root) \nHence n = 5.",
"golden_answer":"5",
"source":"Bigmath_synth"
},
{
"instruction":"Samuel has a decorative fountain that he refills using a 100‑ounce jug. To bring the fountain exactly to his preferred display level, he follows a two‐step refill procedure: first he pours the jug 16 times (thereby “overfilling” the fountain) and then he drains off exactly the equivalent of 2 full jugfuls. (In other words, on any day without loss his planned net water addition per “refill cycle” is 16·100 – 2·100 = 1,400 ounces.) However, on days when the temperature exceeds 85°F (the weekdays), evaporation causes a loss of 8% during each cycle; to end up with the desired net 1,400 ounces, Samuel must pour extra water so that only 92% of what he pours remains. On cooler days (the weekend) no extra water is needed because there is no significant evaporation loss.\n\nSamuel follows a schedule in which on each weekend day he completes exactly twice as many refill cycles as on any given weekday. (For example, if he performs x cycles on a weekday then on each weekend day he performs 2x cycles.) In one week he uses exactly 13,208.7 ounces of water to run these refill cycles.\n\n(a) Let x be the number of cycles Samuel performs on each weekday. Write an expression in terms of x for the total water used during the week, taking into account the increased requirement on hot days.\n\n(b) Find the value of x that makes the total water used equal 13,208.7 ounces, and then state how many refill cycles Samuel completes on all weekdays and on all weekend days combined.\n\nRemember: On a weekday each cycle requires extra water so that\n  (actual water poured per cycle) = 1,400\/0.92 ounces,\nwhile on a weekend cycle the water poured is exactly 1,400 ounces.\n\nSolve the problem step by step.",
"output":"a) Let x = number of refill‐cycles on each weekday. \nThere are 5 weekdays and 2 weekend days. On a weekday each cycle uses (1400 oz)\/0.92 of water, on a weekend cycle exactly 1400 oz. \nSo the total water used in one week is \n Total(x) = (number of weekday cycles)·(per‐cycle weekday use) \n    + (number of weekend cycles)·(per‐cycle weekend use) \n = (5x)·(1400\/0.92) + (2 days·2x cycles\/day)·1400 \n = 5x·(1400\/0.92) + 4x·1400. \n\nb) Set this equal to 13 208.7 and solve for x: \n 5x·(1400\/0.92) + 4x·1400 = 13 208.7. \nCompute the coefficient of x: \n 5·1400\/0.92 ≈ 7000\/0.92 ≈ 7608.69565; 4·1400 = 5600 \nso \n x·(7608.69565 + 5600) ≈ x·13 208.69565 = 13 208.7 \n⇒ x ≈ 13 208.7\/13 208.69565 ≈ 1.0000003 ≈ 1. \n\nHence x = 1 cycle per weekday. \nTotal weekday cycles = 5·x = 5·1 = 5. \nTotal weekend cycles = 2 days·(2x) = 2·2·1 = 4.",
"golden_answer":"4",
"source":"Bigmath_synth"
},
{
"instruction":"A square has vertices that lie on four distinct horizontal lines in the coordinate plane with y‐coordinates 1, 3, 7, and 9. Although the square is rotated relative to the axes, its vertically “projected” span is 9 – 1 = 8. It is given that the ratio of this vertical span to the side length equals the ratio of the square’s area to its perimeter. Find the area of the square.\n\n",
"output":"Label the side‐length of the square by s and let θ be its angle of rotation above the horizontal. One checks (e.g. by writing out the four vertices) that its vertical span is\n\n V = s (sin θ + cos θ).\n\nWe are told V = 9 − 1 = 8, so\n\n s (sin θ + cos θ) = 8. (1)\n\nOn the other hand the ratio of its vertical span to its side length is\n\n V\/s = sin θ + cos θ,\n\nand the ratio of its area to its perimeter is\n\n s²\/(4s) = s\/4.\n\nThe problem asserts these two ratios are equal, so\n\n sin θ + cos θ = s\/4. (2)\n\nCompare (1) and (2): from (1) we get sin θ + cos θ = 8\/s, so (2) gives\n\n 8\/s = s\/4 ⇒ s² = 32.\n\nHence the area s² = 32.",
"golden_answer":"32",
"source":"Bigmath_synth"
},
{
"instruction":"A company manufactures rectangular storage containers with integer side lengths. One of its containers measures 2 cm, 6 cm, and 18 cm. To create a new product line, the container is to be sliced along one of its dimensions into two congruent smaller boxes—but with the design requirement that the side length in the chosen cutting direction must be exactly halved (i.e. the cut is made exactly through the middle of that side). \n\nFor each valid cutting direction, a smaller box will have dimensions as follows:\n • If cut along the 2‐cm side, the smaller box measures 1 cm, 6 cm, and 18 cm.\n • If cut along the 6‐cm side, the smaller box measures 2 cm, 3 cm, and 18 cm.\n • If cut along the 18‐cm side, the smaller box measures 2 cm, 6 cm, and 9 cm.\n\nDetermine, after analyzing these three cases, the square of the largest possible length of the space diagonal of one of the resulting smaller boxes.",
"output":"For the three possible halving‐cuts you get smaller boxes with dimensions\n\n1) (1, 6, 18) → diagonal² = 1² + 6² + 18² = 1 + 36 + 324 = 361 \n2) (2, 3, 18) → diagonal² = 4 + 9 + 324 = 337 \n3) (2, 6, 9)   → diagonal² = 4 + 36 + 81 = 121 \n\nThe maximum of these is 361.",
"golden_answer":"361",
"source":"Bigmath_synth"
},
{
"instruction":"A combination lock uses a six‐digit code that begins with 5 and is divisible by 15. (Recall that being divisible by 15 means the code must also be divisible by both 3 and 5.) In addition, if the code ends in 0 then the sum of its six digits must be divisible by 7, but if the code ends in 5 then the product of its hundreds digit (the fourth digit) and its tens digit (the fifth digit) must be even. How many distinct valid codes are possible?",
"output":"Let d₁…d₆ be the six‐digit code. Since it must begin with 5 and be a multiple of 15, we have\n\n• d₁=5, \n• d₆∈{0,5} (to be multiple of 5), \n• d₁+…+d₆≡0 mod 3 (to be multiple of 3).\n\nWe split into two cases:\n\nCase 1: d₆=0. \nThen the sum S=d₁+…+d₆=5+(d₂+…+d₅)+0 must be ≡0 mod 3 (for divisibility by 3) and also ≡0 mod 7 (by the extra “if ends in 0” condition). Hence S≡0 mod 21. But 5≤S≤5+4·9=41, so the only possibility is S=21. Thus\n d₂+ d₃+ d₄+ d₅ =21−5=16,\nwith 0≤each≤9. The number of nonnegative solutions x₂+…+x₅=16 with xi≤9 is\n C(16+4−1,3) −4·C(6+4−1,3)\n = C(19,3) −4·C(9,3)\n = 969 −4·84\n = 969 −336\n = 633.\n\nCase 2: d₆=5. \nWe still need d₁+…+d₆≡0 mod 3, i.e. 5+5+(d₂+…+d₅)≡0 mod 3 ⇒ d₂+…+d₅≡2 mod 3. \nAlso the extra “if ends in 5” condition says the 4th and 5th digits (d₄,d₅) have an even product, i.e. at least one of d₄,d₅ is even. \n• There are in all 10⁴=10,000 choices for (d₂,d₃,d₄,d₅). Exactly one third of those have sum ≡2 mod 3, i.e. 10,000\/3 rounded down = 3,333. \n• We must remove from those the cases in which both d₄,d₅ are odd. There are 100 choices for (d₂,d₃)×25 choices for (d₄,d₅ both odd) =2,500 total, and exactly one third of these (833) have sum≡2 mod 3. \nSo Case 2 contributes 3,333−833=2,500 codes.\n\nTotal = 633 + 2,500 = 3,133.",
"golden_answer":"3133",
"source":"Bigmath_synth"
},
{
"instruction":"At the local community center, a shed is used to store various wheeled devices for activities. Inside, there are 3 bicycles (normally 2 wheels each), 3 tricycles (normally 3 wheels each), 5 skateboards (normally 4 wheels each), and 2 scooters (normally 2 wheels each). However, note the following adjustments:\n• One of the bicycles is missing 1 wheel.\n• 40% of the tricycles (rounding to the nearest whole number) have an extra spare wheel attached.\n• Two of the skateboards have lost 2 wheels each.\n• One of the scooters has been modified by adding an extra wheel.\nDetermine the total number of wheels present in the shed.",
"output":"Here’s a quick breakdown:\n\n1. Bicycles \n – Normally 3 × 2 = 6 wheels \n – One is missing 1 wheel ⇒ 6 − 1 = 5 wheels\n\n2. Tricycles \n – Normally 3 × 3 = 9 wheels \n – 40% of 3 tricycles = 1.2 ⇒ rounds to 1 trike with an extra wheel \n – Extra wheel adds +1 ⇒ 9 + 1 = 10 wheels\n\n3. Skateboards \n – Normally 5 × 4 = 20 wheels \n – Two boards lost 2 wheels each ⇒ 4 wheels lost ⇒ 20 − 4 = 16 wheels\n\n4. Scooters \n – Normally 2 × 2 = 4 wheels \n – One has +1 wheel ⇒ 4 + 1 = 5 wheels\n\nTotal wheels = 5 + 10 + 16 + 5 = 36 wheels.",
"golden_answer":"36",
"source":"Bigmath_synth"
},
{
"instruction":"A manufacturing plant operates 3 identical machines that produce gadgets. On weekdays (Monday through Friday), each machine produces 12 gadgets per hour and runs for 4 hours each day. However, on weekends (Saturday and Sunday), each machine runs for an unknown number of hours per day, and due to a temporary slowdown in the production line, each machine produces only 10 gadgets per hour. Over a period of 4 weeks, the plant produced exactly 3,360 gadgets. Determine the number of hours each machine operates on Saturdays and Sundays during this period.",
"output":"Let hSat and hSun be the (constant) hours that each machine runs on a Saturday and on a Sunday, respectively, in any given week. Then over 4 weeks:\n\n1. Weekday output \n – Each machine makes 12 gadgets\/hour \n – Runs 4 hours\/day, 5 days\/week ⇒ per machine per week = 12·4·5 = 240 gadgets \n – 3 machines ⇒ 3·240 = 720 gadgets\/week \n – Over 4 weeks ⇒ 4·720 = 2880 gadgets\n\n2. Weekend output \n – Each machine makes 10 gadgets\/hour \n – Runs hSat on Saturday and hSun on Sunday ⇒ per machine per weekend = 10·(hSat + hSun) \n – 3 machines ⇒ 3·10·(hSat + hSun) = 30·(hSat + hSun) gadgets per weekend \n – Over 4 weekends ⇒ 4·30·(hSat + hSun) = 120·(hSat + hSun)\n\nTotal over 4 weeks is given as 3360 gadgets, so \n Weekdays + Weekends = 3360 \n 2880 + 120·(hSat + hSun) = 3360 \n 120·(hSat + hSun) = 480 \n hSat + hSun = 4\n\nIn the absence of any other distinction, the most natural assumption is that Saturday and Sunday schedules are the same, so \n hSat = hSun = 4\/2 = 2 hours.\n\nAnswer: Each machine runs 2 hours on Saturdays and 2 hours on Sundays.",
"golden_answer":"2",
"source":"Bigmath_synth"
},
{
"instruction":"A rectangular storage container has a base area of 6 square meters. The base is a rectangle whose length and width are in the ratio 2 : 3, and the container has a fixed height of 4 meters. To protect the goods during shipping, the container is to be completely enclosed by a spherical safety cover. In order to allow for insulation, the cover must have a volume that is at least 20% larger than the minimum volume just needed to enclose the container. If the cost to produce the spherical cover is determined by its surface area at a rate of $15 per square meter, what is the minimum production cost? Express your answer in terms of π and simplify any exponents.\n\nConsider that for any rectangular prism with length L, width W, and height H the smallest sphere that can contain it must have a radius equal to half the length of the space diagonal, that is, r₀ = (1\/2)·√(L² + W² + H²). Note that the extra 20% in volume means that the actual sphere must have a radius r satisfying\n\n  (4⁄3)π·r³ = 1.2·(4⁄3)π·(r₀)³     (1)\n\nYour answer will be expressed in terms of known quantities.",
"output":"First, since the base area is 6 m² and the sides are in the ratio 2 : 3, write \n L=2x, W=3x, (2x)(3x)=6 ⇒6x²=6⇒x=1. \nThus L=2 m, W=3 m, and H=4 m.\n\nThe minimal‐enclosing sphere has radius \n r₀=½√(L²+W²+H²)=½√(4+9+16)=½√29. \n\nWe need a 20% larger volume, so by \n (4\/3)π r³=1.2·(4\/3)π r₀³ \nwe get \n r=(1.2)^{1\/3}·r₀=(6\/5)^{1\/3}·(√29\/2). \n\nThe cost is \\$15 per m² of surface, and the sphere’s area is 4πr², so \n Cost=15·4πr²=60π·r² \n  =60π·[(6\/5)^{1\/3}·(√29\/2)]² \n  =60π·(6\/5)^{2\/3}·(29\/4) \n  =(60·29\/4)·(6\/5)^{2\/3}π \n  =15·29·(6\/5)^{2\/3}π \n  =435 π (6\/5)^{2\/3}. \n\nAnswer:  $\\displaystyle 435\\,\\pi\\,(6\/5)^{2\/3}\\,$.",
"golden_answer":"3",
"source":"Bigmath_synth"
},
{
"instruction":"A chef is preparing full-course meals, where each meal consists of a starter, a main course, and a dessert. The starter requires 1 unit of spice mix A; the main course requires 2 units of spice mix A and 1 unit of spice mix B; and the dessert requires 1 unit of spice mix B. The chef has 10 packets of spice mix A, with each packet containing 4 units, and 8 packets of spice mix B, with each packet containing 3 units. However, 2 units of spice mix B must be reserved for emergencies and cannot be used in any meal. Assuming the chef uses the spices without any waste, what is the maximum number of full-course meals that can be prepared?",
"output":"First, calculate the total available units of each spice: \n• Spice A: 10 packets × 4 units = 40 units \n• Spice B: 8 packets × 3 units = 24 units, but 2 units are reserved → 24 – 2 = 22 units usable \n\nEach full‐course meal (starter + main + dessert) consumes: \n• Spice A: 1 + 2 + 0 = 3 units \n• Spice B: 0 + 1 + 1 = 2 units \n\nNow find how many meals each spice stock can support: \n• A‐limited: ⌊40 ÷ 3⌋ = 13 meals \n• B‐limited: ⌊22 ÷ 2⌋ = 11 meals \n\nThe B stock is the bottleneck, so the maximum number of full‐course meals is 11.",
"golden_answer":"11",
"source":"Bigmath_synth"
},
{
"instruction":"A two‐phase experiment measures a force vector M along a specific direction. In Phase I, a calibrated device finds that the projection of M onto a direction represented by the unit vector N is 4 newtons. In Phase II, using another instrument that reports projections differently, the same projection is recorded as 5 newtons; however, this second device is known to overestimate the true projection by 25% whenever the angle between M and N is acute and to underestimate it by 15% when the angle is obtuse. Determine the value of M ⋅ N and indicate whether the angle between M and N is acute or obtuse.",
"output":"Let p = M·N be the true projection. The second instrument reads \n‐ if ∠(M,N) is acute: R = 1.25 p \n‐ if ∠(M,N) is obtuse: R = 0.85 p \n\nSince it reports R = 5 N, we get two candidates: \n acute: p = 5\/1.25 = 4 N \n obtuse: p = 5\/0.85 ≃ 5.88 N \n\nBut Phase I (a calibrated device) told us p = 4 N, so the only consistent case is the acute one. \n\nAnswer: M·N = 4 newtons, and the angle between M and N is acute.",
"golden_answer":"4",
"source":"Bigmath_synth"
},
{
"instruction":"Let k be a real number and consider the quadratic equation \n  x² – 10x + (|2k – 3| + |k + 5|) = 0.\n(a) Determine all values of k for which this equation has two distinct real roots that are both nonnegative.\n(b) Under the condition in part (a), find the set of k for which the product of the roots is at least 16.",
"output":"Let C(k)=|2k–3|+|k+5|. The equation is \n x²–10x+C(k)=0 \nwith sum of roots S=10>0 and product P=C(k). Its discriminant is Δ=100–4C(k), so two distinct real roots ⇐⇒ C(k)<25. Since C(k)≥0 always, the smaller root is 5–√(25–C)≥0 automatically, so the only nonnegativity condition is C(k)<25. \n\n1. Solve |2k–3|+|k+5|<25. Break at k=–5 and k=3\/2: \n • k<–5: |2k–3|=3–2k, |k+5|=–(k+5) ⇒ C=–3k–2<25 ⇒ k>–9 ⇒ –9<k<–5 \n • –5≤k<3\/2: |2k–3|=3–2k, |k+5|=k+5 ⇒ C=8–k<25 is automatic for k≥–5 \n • k≥3\/2: |2k–3|=2k–3, |k+5|=k+5 ⇒ C=3k+2<25 ⇒ k<23\/3 \n\nHence (a) \n –9<k<23\/3. \n\n2. Under this, the product of the roots is P=C(k). We impose C(k)≥16. Again piecewise: \n • k<–5: C=–3k–2≥16 ⇒ –3k≥18 ⇒ k≤–6. Intersect with –9<k<–5 gives –9<k≤–6. \n • –5≤k<3\/2: C=8–k≥16 ⇒ k≤–8, impossible in [–5,3\/2). \n • k≥3\/2: C=3k+2≥16 ⇒ 3k≥14 ⇒ k≥14\/3. Intersect with k<23\/3 gives 14\/3≤k<23\/3. \n\nHence (b) \n k∈(–9,–6]∪[14\/3,23\/3).",
"golden_answer":"3",
"source":"Bigmath_synth"
},
{
"instruction":"At a small bakery, the cost functions for producing cakes and pies are modeled by polynomials. The cost function for cakes, F(x), is a polynomial of degree 100, and the cost function for pies, G(x), is a polynomial of degree 99. Due to recent changes in ingredient prices, the bakery revises its overall cost structure, resulting in two new functions:\n\n  H(x) = F(x) + 5·G(x)               (Overall cost function)\n  I(x) = F(x) – 2·G(x)               (Discounted cost function)\n\nLet m be the degree of H(x) and n be the degree of I(x). (Note: If the formation of I(x) produces cancellation of the leading terms, then the degree of I(x) would decrease by one.) \n\nDetermine the value of the expression:\n  |m – n| + |3m – 100| + |n + 2|\n\nAssume that no cancellation occurs in forming H(x) or I(x).",
"output":"First note \n  deg F = 100,  deg G = 99. \nSince no cancellation occurs \n  deg H = deg(F + 5G) = max(100, 99) = 100 ⇒ m = 100 \n  deg I = deg(F − 2G) = max(100, 99) = 100 ⇒ n = 100 \n\nHence \n  |m − n| + |3m − 100| + |n + 2| \n = |100−100| + |300−100| + |100+2| \n = 0 + 200 + 102 \n = 302",
"golden_answer":"302",
"source":"Bigmath_synth"
},
{
"instruction":"A communications engineer is designing a satellite dish in the xy‐plane. The dish’s cross‐section is modeled by a parabola with its vertex fixed at (1, 1). To ensure optimal signal focusing, the dish’s focus must lie somewhere on the horizontal line y = 1—that is, the parabola is oriented horizontally and can open either to the right (if p > 0) or to the left (if p < 0). In addition, laboratory tests have shown that the point (5, 4) must lie on the surface of the dish. \n\na) Write the standard (vertex form) equation of the parabola in terms of the parameter p.\n\nb) Using the condition that (5, 4) lies on the parabola, determine the value of p. Then, identify which orientation (opening to the right or to the left) yields this value and write the final equation of the dish’s parabola.",
"output":"a) Since the vertex is at (h,k)=(1,1) and the axis is horizontal (y=1), the parabola in vertex‐form is \n  (y−1)² = 4p (x−1) \nwhere p is the signed focal‐parameter (p>0 ⇒ opens right, p<0 ⇒ opens left). \n\nb) Plug in (x,y)=(5,4): \n  (4−1)² = 4p (5−1) \n  9 = 4p·4 =16p \n⇒ p = 9\/16 (>0). \n\nSince p>0 the parabola opens to the right, and 4p=4·(9\/16)=9\/4. Thus the final equation is \n  (y−1)² = (9\/4) (x−1).",
"golden_answer":"1",
"source":"Bigmath_synth"
},
{
"instruction":"At a farmer’s market, a vendor has 384 oranges and 192 lemons. The lemons are bundled evenly into 16 bundles. The oranges are packed in two types of crates: large crates hold 24 oranges each, and small crates hold 12 oranges each. To offer a balanced display, the vendor packs the oranges so that the total number of oranges in all the large crates is exactly three times the total number of oranges in all the small crates. Determine how many large crates and how many small crates were used, and how many lemons are in each bundle.",
"output":"Let L = number of large crates and S = number of small crates. Then\n\n1) Total oranges: 24·L + 12·S = 384 \n2) Balance condition: (oranges in large) = 3×(oranges in small) \n ⇒ 24·L = 3·(12·S) = 36·S \n ⇒ L = (36\/24) S = (3\/2) S \n\nFrom L = (3\/2) S plug into 24·L +12·S =384:\n 24·(3\/2 S) +12·S =36 S +12 S =48 S =384 \n ⇒ S =384\/48 =8 \n ⇒ L =(3\/2)·8 =12 \n\nAnd the lemons, 192 of them, are split evenly into 16 bundles:\n lemons per bundle = 192\/16 =12. \n\nAnswer:\n• Large crates: 12 \n• Small crates: 8 \n• Lemons per bundle: 12",
"golden_answer":"12",
"source":"Bigmath_synth"
},
{
"instruction":"A drone is set to follow a straight-line flight path given by the equation y = 2x + 4. However, due to new airspace restrictions, the flight plan is modified in two stages:\n\n1. The original path is rotated 90° counterclockwise about the fixed control point P(2, 3) to yield a new path L₁.\n2. To ensure safe clearance from obstacles, L₁ is then shifted vertically upward so that its y-intercept increases by exactly 6 units, producing the final flight path L₂.\n\n(a) Find the equation of the final flight path L₂.\n\n(b) Determine whether the x-intercept of L₂ lies to the left or to the right of the point P. Provide a brief explanation to support your conclusion.",
"output":"Here is a step‐by‐step solution.\n\n1. Start with the original line \n y = 2x + 4. \n A direction vector for this line is v = (1, 2).\n\n2. Rotate that line 90° CCW about P(2,3). \n – Rotating the direction vector v=(1,2) by 90° CCW gives \n v′ = (–2, 1). \n – Thus the slope of the rotated line L₁ is m₁ = rise\/run = 1\/(–2) = –½. \n – And L₁ passes through P(2,3), so in point–slope form: \n y–3 = (–½)(x–2) \n ⇒ y = –½ x + 1 + 3 = –½ x + 4. \n\n3. Shift L₁ upward so its y‑intercept goes from 4 to 10 (i.e. +6). \n This yields the final path L₂: \n y = –½ x + 10. \n\n(a) Answer: L₂: y = –½ x + 10. \n\n(b) Its x‑intercept is found by setting y=0: \n 0 = –½ x + 10 ⇒ x = 20, so the intercept is (20,0). \n Since 20 > 2, this point lies to the right of P(2,3).",
"golden_answer":"23",
"source":"Bigmath_synth"
},
{
"instruction":"A science fair assigns project scores using the formula\n  S(x) = x² – 4x + 6,\nwhere x is the project’s difficulty rating. Two students choose individual projects with different difficulty ratings a and b and each earns the same score (that is, S(a) = S(b)). Later, a team project is entered with difficulty rating (a + b) and it earns a score n that is exactly 20% higher than the individual score earned by each student. Find n.\n\n",
"output":"First note that \n S(a)=S(b) \nimplies \n a²−4a+6 = b²−4b+6 \n⇒ a²−b² =4(a−b) \n⇒ (a−b)(a+b−4)=0. \nSince a≠b, we get a+b=4. \nHence the team score is \n n = S(a+b) = S(4) = 4²−4·4+6 = 6. \nCheck: the individual score is S(a)=a²−4a+6; from 6=1.2·S(a) ⇒ S(a)=5, which indeed happens for a=2±√3. \nAnswer: n=6.",
"golden_answer":"6",
"source":"Bigmath_synth"
},
{
"instruction":"Alice and Bob are making deliveries in a city. When driving in urban zones, the speed limit is 20 miles per hour, and when driving in suburban zones, it is 40 miles per hour. Alice’s entire route is in the urban zone, and she drives for 90 minutes at the urban speed limit. Bob’s route covers both suburban and urban areas; he drives for a total of 2 hours, spending 75% of his driving time in suburban areas and 25% in urban areas. However, due to a minor incident, Bob must reduce his suburban driving speed by 25% (relative to the suburban speed limit). Calculate the total distance traveled by Alice and Bob combined.",
"output":"Alice’s distance \n• Speed = 20 mph, Time = 90 min = 1.5 h \n• Distance = 20 mph × 1.5 h = 30 mi \n\nBob’s distance \n• Total time = 2 h \n – Suburban time = 0.75×2 h = 1.5 h \n – Urban time = 0.25×2 h = 0.5 h \n• Suburban speed = 40 mph × (1 – 0.25) = 30 mph \n – Suburban distance = 30 mph × 1.5 h = 45 mi \n• Urban speed = 20 mph \n – Urban distance = 20 mph × 0.5 h = 10 mi \n• Bob’s total = 45 mi + 10 mi = 55 mi \n\nCombined distance = 30 mi + 55 mi = 85 miles.",
"golden_answer":"85",
"source":"Bigmath_synth"
},
{
"instruction":"Three competitors in a contest receive scores a, b, and c that satisfy\n  a² + b² + c² = 52  and  ab + ac + bc = 72.\nTheir preliminary total score is a + b + c. In the contest rules, if the preliminary total is less than 15, an extra 3 points are added as a bonus; if it is 15 or more, 2 points are deducted as a penalty. Find the final adjusted total score.",
"output":"We set S = a+b+c. Then \nS² = (a²+b²+c²) + 2(ab+ac+bc) = 52 + 2·72 = 196 \n⇒ S = ±14. Since scores are (non‐negative) preliminaries we take S=14. \nThen 14<15 so we add 3 ⇒ final total = 14+3 = 17.",
"golden_answer":"17",
"source":"Bigmath_synth"
},
{
"instruction":"At a science museum, an adult admission is $10 and a child ticket is sold at a full price of x dollars. However, if a group has more than 5 children, any child beyond the fifth receives a 50% discount on the ticket. A teacher brings 1 adult along with 7 children. Paying with a $60 bill, the teacher receives $10 in change. What is the full price, in dollars, of a child ticket?",
"output":"Let A be the number of adults (each \\$10) and C=7 the number of children. Since “a teacher brings 1 adult” there are actually 2 adults paying. Children beyond the first 5 get a 50% discount, so\n\nAdult cost = 2·10 = \\$20 \nChild cost = 5·x + 2·(½x) = 5x + x = 6x \n\nTotal spent = \\$20 + 6x. They hand over \\$60 and get \\$10 back, so they’ve actually paid \\$50:\n\n 20 + 6x = 50 \n 6x = 30 \n x = 5.\n\nHence the full‐price child ticket is \\$5.",
"golden_answer":"5",
"source":"Bigmath_synth"
},
{
"instruction":null,
"output":null,
"golden_answer":null,
"source":null
}
]
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{"raw_content": "../example_data/SpeechTranscription/audio/test.wav"}
{"raw_content": "https://raw.githubusercontent.com/FireRedTeam/FireRedASR/main/examples/wav/IT0011W0001.wav"}
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dataflow/example/Text2SQLPipeline/pipeline_refine.jsonl 0 → 100644
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{"db_id": "california_schools", "question": "What is the highest eligible free rate for K-12 students in the schools in Alameda County?", "SQL": "SELECT `Free Meal Count (K-12)` / `Enrollment (K-12)` FROM frpm WHERE `County Name` = 'Alameda' ORDER BY (CAST(`Free Meal Count (K-12)` AS REAL) / `Enrollment (K-12)`) DESC LIMIT 1"}
{"db_id": "california_schools", "question": "Please list the lowest three eligible free rates for students aged 5-17 in continuation schools.", "SQL": "SELECT `Free Meal Count (Ages 5-17)` / `Enrollment (Ages 5-17)` FROM frpm WHERE `Educational Option Type` = 'Continuation School' AND `Free Meal Count (Ages 5-17)` / `Enrollment (Ages 5-17)` IS NOT NULL ORDER BY `Free Meal Count (Ages 5-17)` / `Enrollment (Ages 5-17)` ASC LIMIT 3"}
{"db_id": "california_schools", "question": "Please list the zip code of all the charter schools in Fresno County Office of Education.", "SQL": "SELECT T2.Zip FROM frpm AS T1 INNER JOIN schools AS T2 ON T1.CDSCode = T2.CDSCode WHERE T1.`District Name` = 'Fresno County Office of Education' AND T1.`Charter School (Y/N)` = 1"}
{"db_id": "california_schools", "question": "What is the unabbreviated mailing street address of the school with the highest FRPM count for K-12 students?", "SQL": "SELECT T2.MailStreet FROM frpm AS T1 INNER JOIN schools AS T2 ON T1.CDSCode = T2.CDSCode ORDER BY T1.`FRPM Count (K-12)` DESC LIMIT 1"}
{"db_id": "california_schools", "question": "Please list the phone numbers of the direct charter-funded schools that are opened after 2000/1/1.", "SQL": "SELECT T2.Phone FROM frpm AS T1 INNER JOIN schools AS T2 ON T1.CDSCode = T2.CDSCode WHERE T1.`Charter Funding Type` = 'Directly funded' AND T1.`Charter School (Y/N)` = 1 AND T2.OpenDate > '2000-01-01'"}
{"db_id": "california_schools", "question": "How many schools with an average score in Math greater than 400 in the SAT test are exclusively virtual?", "SQL": "SELECT COUNT(DISTINCT T2.School) FROM satscores AS T1 INNER JOIN schools AS T2 ON T1.cds = T2.CDSCode WHERE T2.Virtual = 'F' AND T1.AvgScrMath > 400"}
{"db_id": "california_schools", "question": "Among the schools with the SAT test takers of over 500, please list the schools that are magnet schools or offer a magnet program.", "SQL": "SELECT T2.School FROM satscores AS T1 INNER JOIN schools AS T2 ON T1.cds = T2.CDSCode WHERE T2.Magnet = 1 AND T1.NumTstTakr > 500"}
{"db_id": "california_schools", "question": "What is the phone number of the school that has the highest number of test takers with an SAT score of over 1500?", "SQL": "SELECT T2.Phone FROM satscores AS T1 INNER JOIN schools AS T2 ON T1.cds = T2.CDSCode ORDER BY T1.NumGE1500 DESC LIMIT 1"}
{"db_id": "california_schools", "question": "What is the number of SAT test takers of the schools with the highest FRPM count for K-12 students?", "SQL": "SELECT NumTstTakr FROM satscores WHERE cds = ( SELECT CDSCode FROM frpm ORDER BY `FRPM Count (K-12)` DESC LIMIT 1 )"}
{"db_id": "california_schools", "question": "Among the schools with the average score in Math over 560 in the SAT test, how many schools are directly charter-funded?", "SQL": "SELECT COUNT(T2.`School Code`) FROM satscores AS T1 INNER JOIN frpm AS T2 ON T1.cds = T2.CDSCode WHERE T1.AvgScrMath > 560 AND T2.`Charter Funding Type` = 'Directly funded'"}
{"db_id": "california_schools", "question": "For the school with the highest average score in Reading in the SAT test, what is its FRPM count for students aged 5-17?", "SQL": "SELECT T2.`FRPM Count (Ages 5-17)` FROM satscores AS T1 INNER JOIN frpm AS T2 ON T1.cds = T2.CDSCode ORDER BY T1.AvgScrRead DESC LIMIT 1"}
{"db_id": "california_schools", "question": "Please list the codes of the schools with a total enrollment of over 500.", "SQL": "SELECT T2.CDSCode FROM schools AS T1 INNER JOIN frpm AS T2 ON T1.CDSCode = T2.CDSCode WHERE T2.`Enrollment (K-12)` + T2.`Enrollment (Ages 5-17)` > 500"}
{"db_id": "california_schools", "question": "Among the schools with an SAT excellence rate of over 0.3, what is the highest eligible free rate for students aged 5-17?", "SQL": "SELECT MAX(CAST(T1.`Free Meal Count (Ages 5-17)` AS REAL) / T1.`Enrollment (Ages 5-17)`) FROM frpm AS T1 INNER JOIN satscores AS T2 ON T1.CDSCode = T2.cds WHERE CAST(T2.NumGE1500 AS REAL) / T2.NumTstTakr > 0.3"}
{"db_id": "california_schools", "question": "Please list the phone numbers of the schools with the top 3 SAT excellence rate.", "SQL": "SELECT T1.Phone FROM schools AS T1 INNER JOIN satscores AS T2 ON T1.CDSCode = T2.cds ORDER BY CAST(T2.NumGE1500 AS REAL) / T2.NumTstTakr DESC LIMIT 3"}
{"db_id": "california_schools", "question": "List the top five schools, by descending order, from the highest to the lowest, the most number of Enrollment (Ages 5-17). Please give their NCES school identification number.", "SQL": "SELECT T1.NCESSchool FROM schools AS T1 INNER JOIN frpm AS T2 ON T1.CDSCode = T2.CDSCode ORDER BY T2.`Enrollment (Ages 5-17)` DESC LIMIT 5"}
{"db_id": "california_schools", "question": "Which active district has the highest average score in Reading?", "SQL": "SELECT T1.District FROM schools AS T1 INNER JOIN satscores AS T2 ON T1.CDSCode = T2.cds WHERE T1.StatusType = 'Active' ORDER BY T2.AvgScrRead DESC LIMIT 1"}
{"db_id": "california_schools", "question": "How many schools in merged Alameda have number of test takers less than 100?", "SQL": "SELECT COUNT(T1.CDSCode) FROM schools AS T1 INNER JOIN satscores AS T2 ON T1.CDSCode = T2.cds WHERE T1.StatusType = 'Merged' AND T2.NumTstTakr < 100 AND T1.County = 'Lake'"}
{"db_id": "california_schools", "question": "Rank schools by their average score in Writing where the score is greater than 499, showing their charter numbers.", "SQL": "SELECT CharterNum, AvgScrWrite, RANK() OVER (ORDER BY AvgScrWrite DESC) AS WritingScoreRank FROM schools AS T1 INNER JOIN satscores AS T2 ON T1.CDSCode = T2.cds WHERE T2.AvgScrWrite > 499 AND CharterNum is not null"}
{"db_id": "california_schools", "question": "How many schools in Fresno (directly funded) have number of test takers not more than 250?", "SQL": "SELECT COUNT(T1.CDSCode) FROM frpm AS T1 INNER JOIN satscores AS T2 ON T1.CDSCode = T2.cds WHERE T1.`Charter Funding Type` = 'Directly funded' AND T1.`County Name` = 'Fresno' AND T2.NumTstTakr <= 250"}
{"db_id": "california_schools", "question": "What is the phone number of the school that has the highest average score in Math?", "SQL": "SELECT T1.Phone FROM schools AS T1 INNER JOIN satscores AS T2 ON T1.CDSCode = T2.cds ORDER BY T2.AvgScrMath DESC LIMIT 1"}
{"db_id": "student_club", "question": "What's Angela Sanders's major?", "SQL": "SELECT T2.major_name FROM member AS T1 INNER JOIN major AS T2 ON T1.link_to_major = T2.major_id WHERE T1.first_name = 'Angela' AND T1.last_name = 'Sanders'"}
{"db_id": "student_club", "question": "How many students in the Student_Club are from the College of Engineering?", "SQL": "SELECT COUNT(T1.member_id) FROM member AS T1 INNER JOIN major AS T2 ON T1.link_to_major = T2.major_id WHERE T2.college = 'College of Engineering'"}
{"db_id": "student_club", "question": "Please list the full names of the students in the Student_Club that come from the Art and Design Department.", "SQL": "SELECT T1.first_name, T1.last_name FROM member AS T1 INNER JOIN major AS T2 ON T1.link_to_major = T2.major_id WHERE T2.department = 'Art and Design Department'"}
{"db_id": "student_club", "question": "How many students of the Student_Club have attended the event \"Women's Soccer\"?", "SQL": "SELECT COUNT(T1.event_id) FROM event AS T1 INNER JOIN attendance AS T2 ON T1.event_id = T2.link_to_event WHERE T1.event_name = 'Women''s Soccer'"}
{"db_id": "student_club", "question": "Please list the phone numbers of the students from the Student_Club that has attended the event \"Women's Soccer\".", "SQL": "SELECT T3.phone FROM event AS T1 INNER JOIN attendance AS T2 ON T1.event_id = T2.link_to_event INNER JOIN member AS T3 ON T2.link_to_member = T3.member_id WHERE T1.event_name = 'Women''s Soccer'"}
{"db_id": "student_club", "question": "Among the students from the Student_Club who attended the event \"Women's Soccer\", how many of them want a T-shirt that's in medium size?", "SQL": "SELECT COUNT(T1.event_id) FROM event AS T1 INNER JOIN attendance AS T2 ON T1.event_id = T2.link_to_event INNER JOIN member AS T3 ON T2.link_to_member = T3.member_id WHERE T1.event_name = 'Women''s Soccer' AND T3.t_shirt_size = 'Medium'"}
{"db_id": "student_club", "question": "What is the event that has the highest attendance of the students from the Student_Club?", "SQL": "SELECT T1.event_name FROM event AS T1 INNER JOIN attendance AS T2 ON T1.event_id = T2.link_to_event GROUP BY T1.event_name ORDER BY COUNT(T2.link_to_event) DESC LIMIT 1"}
{"db_id": "student_club", "question": "Which college is the vice president of the Student_Club from?", "SQL": "SELECT T2.college FROM member AS T1 INNER JOIN major AS T2 ON T1.link_to_major = T2.major_id WHERE T1.position LIKE 'vice president'"}
{"db_id": "student_club", "question": "Please list the event names of all the events attended by Maya Mclean.", "SQL": "SELECT T1.event_name FROM event AS T1 INNER JOIN attendance AS T2 ON T1.event_id = T2.link_to_event INNER JOIN member AS T3 ON T2.link_to_member = T3.member_id WHERE T3.first_name = 'Maya' AND T3.last_name = 'Mclean'"}
{"db_id": "student_club", "question": "How many events of the Student_Club did Sacha Harrison attend in 2019?", "SQL": "SELECT COUNT(T1.event_id) FROM event AS T1 INNER JOIN attendance AS T2 ON T1.event_id = T2.link_to_event INNER JOIN member AS T3 ON T2.link_to_member = T3.member_id WHERE T3.first_name = 'Sacha' AND T3.last_name = 'Harrison' AND SUBSTR(T1.event_date, 1, 4) = '2019'"}
{"db_id": "student_club", "question": "Among the events attended by more than 10 members of the Student_Club, how many of them are meetings?", "SQL": "SELECT T1.event_name FROM event AS T1 INNER JOIN attendance AS T2 ON T1.event_id = T2.link_to_event GROUP BY T1.event_id HAVING COUNT(T2.link_to_event) > 10 EXCEPT SELECT T1.event_name FROM event AS T1 WHERE T1.type = 'Meeting'"}
{"db_id": "student_club", "question": "List all the names of events that had an attendance of over 20 students but were not fundraisers.", "SQL": "SELECT T1.event_name FROM event AS T1 INNER JOIN attendance AS T2 ON T1.event_id = T2.link_to_event GROUP BY T1.event_id HAVING COUNT(T2.link_to_event) > 20 EXCEPT SELECT T1.event_name FROM event AS T1 WHERE T1.type = 'Fundraiser'"}
{"db_id": "student_club", "question": "What is the average attendance of meetings in 2020?", "SQL": "SELECT CAST(COUNT(T2.link_to_event) AS REAL) / COUNT(DISTINCT T2.link_to_event) FROM event AS T1 INNER JOIN attendance AS T2 ON T1.event_id = T2.link_to_event WHERE SUBSTR(T1.event_date, 1, 4) = '2020' AND T1.type = 'Meeting'"}
{"db_id": "student_club", "question": "What is the most expensive item that was spent in support of club events?", "SQL": "SELECT expense_description FROM expense ORDER BY cost DESC LIMIT 1"}
{"db_id": "student_club", "question": "How many members of the Student_Club have majored Environmental Engineering?\n", "SQL": "SELECT COUNT(T1.member_id) FROM member AS T1 INNER JOIN major AS T2 ON T1.link_to_major = T2.major_id WHERE T2.major_name = 'Environmental Engineering'"}
{"db_id": "student_club", "question": "List the full name of all the members of the Student_Club who attended the \"Laugh Out Loud\" event.", "SQL": "SELECT T1.first_name, T1.last_name FROM member AS T1 INNER JOIN attendance AS T2 ON T1.member_id = T2.link_to_member INNER JOIN event AS T3 ON T2.link_to_event = T3.event_id WHERE T3.event_name = 'Laugh Out Loud'"}
{"db_id": "student_club", "question": "List the last name of all the students who majored Law and Constitutional Studies. \n", "SQL": "SELECT T1.last_name FROM member AS T1 INNER JOIN major AS T2 ON T1.link_to_major = T2.major_id WHERE T2.major_name = 'Law and Constitutional Studies'"}
{"db_id": "student_club", "question": "What county did Sherri Ramsey grew up?", "SQL": "SELECT T2.county FROM member AS T1 INNER JOIN zip_code AS T2 ON T1.zip = T2.zip_code WHERE T1.first_name = 'Sherri' AND T1.last_name = 'Ramsey'"}
{"db_id": "student_club", "question": "What college offers the major that Tyler Hewitt took?", "SQL": "SELECT T2.college FROM member AS T1 INNER JOIN major AS T2 ON T1.link_to_major = T2.major_id WHERE T1.first_name = 'Tyler' AND T1.last_name = 'Hewitt'"}
{"db_id": "student_club", "question": "What is the amount of the funds that the Vice President received?", "SQL": "SELECT T2.amount FROM member AS T1 INNER JOIN income AS T2 ON T1.member_id = T2.link_to_member WHERE T1.position = 'Vice President'"}
{"db_id": "thrombosis_prediction", "question": "Are there more in-patient or outpatient who were male? What is the deviation in percentage?", "SQL": "SELECT CAST(SUM(CASE WHEN Admission = '+' THEN 1 ELSE 0 END) AS REAL) * 100 / SUM(CASE WHEN Admission = '-' THEN 1 ELSE 0 END) FROM Patient WHERE SEX = 'M'"}
{"db_id": "thrombosis_prediction", "question": "What is the percentage of female patient were born after 1930?", "SQL": "SELECT CAST(SUM(CASE WHEN STRFTIME('%Y', Birthday) > '1930' THEN 1 ELSE 0 END) AS REAL) * 100 / COUNT(*) FROM Patient WHERE SEX = 'F'"}
{"db_id": "thrombosis_prediction", "question": "For patient born between Year 1930 to 1940, how many percent of them were inpatient?", "SQL": "SELECT CAST(SUM(CASE WHEN Admission = '+' THEN 1 ELSE 0 END) AS REAL) * 100 / COUNT(*) FROM Patient WHERE STRFTIME('%Y', Birthday) BETWEEN '1930' AND '1940'"}
{"db_id": "thrombosis_prediction", "question": "What is the ratio of outpatient to inpatient followed up treatment among all the 'SLE' diagnosed patient?", "SQL": "SELECT SUM(CASE WHEN Admission = '+' THEN 1.0 ELSE 0 END) / SUM(CASE WHEN Admission = '-' THEN 1 ELSE 0 END) FROM Patient WHERE Diagnosis = 'SLE'"}
{"db_id": "thrombosis_prediction", "question": "What is the disease patient '30609' diagnosed with. List all the date of laboratory tests done for this patient.", "SQL": "SELECT T1.Diagnosis, T2.Date FROM Patient AS T1 INNER JOIN Laboratory AS T2 ON T1.ID = T2.ID WHERE T1.ID = 30609"}
{"db_id": "thrombosis_prediction", "question": "State the sex and birthday of patient ID '163109'. When was the examination taken and what symptom does the patient had.", "SQL": "SELECT T1.SEX, T1.Birthday, T2.`Examination Date`, T2.Symptoms FROM Patient AS T1 INNER JOIN Examination AS T2 ON T1.ID = T2.ID WHERE T1.ID = 163109"}
{"db_id": "thrombosis_prediction", "question": "List the patient ID, sex and birthday of patient with LDH beyond normal range.", "SQL": "SELECT DISTINCT T1.ID, T1.SEX, T1.Birthday FROM Patient AS T1 INNER JOIN Laboratory AS T2 ON T1.ID = T2.ID WHERE T2.LDH > 500"}
{"db_id": "thrombosis_prediction", "question": "State the ID and age of patient with positive degree of coagulation.", "SQL": "SELECT DISTINCT T1.ID, STRFTIME('%Y', CURRENT_TIMESTAMP) - STRFTIME('%Y', T1.Birthday) FROM Patient AS T1 INNER JOIN Examination AS T2 ON T1.ID = T2.ID WHERE T2.RVVT = '+'"}
{"db_id": "thrombosis_prediction", "question": "For patients with severe degree of thrombosis, list their ID, sex and disease the patient is diagnosed with.", "SQL": "SELECT DISTINCT T1.ID, T1.SEX, T1.Diagnosis FROM Patient AS T1 INNER JOIN Examination AS T2 ON T1.ID = T2.ID WHERE T2.Thrombosis = 2"}
{"db_id": "thrombosis_prediction", "question": "List all patients who were born in 1937 whose total cholesterol was beyond the normal range.", "SQL": "SELECT DISTINCT T1.ID FROM Patient AS T1 INNER JOIN Laboratory AS T2 ON T1.ID = T2.ID WHERE STRFTIME('%Y', T1.Birthday) = '1937' AND T2.`T-CHO` >= 250"}
{"db_id": "thrombosis_prediction", "question": "For patient with albumin level lower than 3.5, list their ID, sex and diagnosis.", "SQL": "SELECT DISTINCT T1.ID, T1.SEX, T1.Diagnosis FROM Patient AS T1 INNER JOIN Laboratory AS T2 ON T1.ID = T2.ID WHERE T2.ALB < 3.5"}
{"db_id": "thrombosis_prediction", "question": "What is the percentage of female patient had total protein not within the normal range?", "SQL": "SELECT CAST(SUM(CASE WHEN T1.SEX = 'F' AND (T2.TP < 6.0 OR T2.TP > 8.5) THEN 1 ELSE 0 END) AS REAL) * 100 / COUNT(*) FROM Patient AS T1 INNER JOIN Laboratory AS T2 ON T1.ID = T2.ID WHERE T1.SEX = 'F'"}
{"db_id": "thrombosis_prediction", "question": "For in-patient age 50 and above, what is their average anti-cardiolipin antibody (IgG) concentration?", "SQL": "SELECT AVG(T2.`aCL IgG`) FROM Patient AS T1 INNER JOIN Examination AS T2 ON T1.ID = T2.ID WHERE STRFTIME('%Y', CURRENT_TIMESTAMP) - STRFTIME('%Y', T1.Birthday) >= 50 AND T1.Admission = '+'"}
{"db_id": "thrombosis_prediction", "question": "How many female patients who came at the hospital in 1997 was immediately followed at the outpatient clinic?", "SQL": "SELECT COUNT(*) FROM Patient WHERE STRFTIME('%Y', Description) = '1997' AND SEX = 'F' AND Admission = '-'"}
{"db_id": "thrombosis_prediction", "question": "What was the age of the youngest patient when they initially arrived at the hospital?", "SQL": "SELECT MIN(STRFTIME('%Y', `First Date`) - STRFTIME('%Y', Birthday)) FROM Patient"}
{"db_id": "thrombosis_prediction", "question": "How many of the patients with the most serious thrombosis cases examined in 1997 are women?", "SQL": "SELECT COUNT(*) FROM Patient AS T1 INNER JOIN Examination AS T2 ON T1.ID = T2.ID WHERE T1.SEX = 'F' AND STRFTIME('%Y', T2.`Examination Date`) = '1997' AND T2.Thrombosis = 1"}
{"db_id": "thrombosis_prediction", "question": "What is the age gap between the youngest and oldest patient with a normal triglyceride recorded?", "SQL": "SELECT STRFTIME('%Y', MAX(T1.Birthday)) - STRFTIME('%Y', MIN(T1.Birthday)) FROM Patient AS T1 INNER JOIN Laboratory AS T2 ON T1.ID = T2.ID WHERE T2.TG >= 200"}
{"db_id": "thrombosis_prediction", "question": "What are the symptoms observed by the youngest patient to ever did a medical examination? Identify their diagnosis.", "SQL": "SELECT T2.Symptoms, T1.Diagnosis FROM Patient AS T1 INNER JOIN Examination AS T2 ON T1.ID = T2.ID WHERE T2.Symptoms IS NOT NULL ORDER BY T1.Birthday DESC LIMIT 1"}
{"db_id": "thrombosis_prediction", "question": "For the year that concluded on December 31, 1998, how many male patients on average were tested in the lab each month?", "SQL": "SELECT CAST(COUNT(T1.ID) AS REAL) / 12 FROM Patient AS T1 INNER JOIN Laboratory AS T2 ON T1.ID = T2.ID WHERE STRFTIME('%Y', T2.Date) = '1998' AND T1.SEX = 'M'"}
{"db_id": "thrombosis_prediction", "question": "The oldest SJS patient's medical laboratory work was completed on what date, and what age was the patient when they initially arrived at the hospital?", "SQL": "SELECT T1.Date, STRFTIME('%Y', T2.`First Date`) - STRFTIME('%Y', T2.Birthday),T2.Birthday FROM Laboratory AS T1 INNER JOIN Patient AS T2 ON T1.ID = T2.ID WHERE T2.Diagnosis = 'SJS' AND T2.Birthday IS NOT NULL ORDER BY T2.Birthday ASC LIMIT 1"}
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[
{"raw_content": "../example_data/VQA/pdfimages/page_0.jpg"},
{"raw_content": "../example_data/VQA/pdfimages/page_1.jpg"},
{"raw_content": "../example_data/VQA/pdfimages/page_2.jpg"}
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{"question":"What is $10.0000198\\cdot 5.9999985401\\cdot 6.9999852$ to the nearest whole number?","solution":"Notice that $10.00001988$ is very close to $10$, $5.9999985401$ is very close to $6$ and $6.9999852$ is very close to $7$. Because the given numbers are all so close to integers, we're unlikely to go wrong by rounding before multiplying. We get $$10\\cdot6\\cdot7=\\boxed{420}.$$If we multiplied the given numbers with a calculator we would get $$6.9999852\\cdot5.9999985401\\cdot10.00001988=419.999844...$$which would still round to $420$.","answer":"420"}
{"question":"Two fair 6-sided dice are rolled. What is the probability the sum rolled is 9?","solution":"There are 4 different ways to roll a 9 (3+6, 4+5, 5+4, 6+3), which makes the probability of rolling a 9 equal to $\\dfrac{4}{36} = \\boxed{\\dfrac{1}{9}}$.","answer":"\\dfrac{1}{9}"}
{"question":"For what value of $x$ is the following equation true: $6500 + x - 4500 = 3400 + 2000$?","solution":"Simplifying both sides gives $x +2000 = 5400$. Subtracting 2000 from both sides gives $x = \\boxed{3400}$.","answer":"3400"}
{"question":"At 2:30 p.m. during a long drive, Bobbi asks her parents, ``Are we there yet?'' Her mother responds, ``We will be there in 7200 seconds.'' If Bobbi's mother is correct, at what time in the afternoon will they arrive at their destination?","solution":"Multiply 7200 seconds by $\\left(\\frac{1\\text{ min.}}{60\\text{ sec.}}\\right)\\left(\\frac{1\\text{ hr.}}{60\\text{ min.}}\\right)$ to find that they will arrive in 2 hours. Two hours after 2:30 p.m. is $\\boxed{\\text{4:30 p.m.}}$.","answer":"\\text{4:30 p.m.}"}
{"question":"Compute $ \\frac{1}{31} \\div \\frac{1}{93} $.","solution":"Recall that division is multiplication by a reciprocal. So we rewrite the division by $\\frac{1}{93}$ as multiplication by the reciprocal of $\\frac{1}{93}$. Since the reciprocal of $\\frac{1}{93}$ is 93, we get \\[\n\\frac{1}{31} \\div \\frac{1}{93} = \\frac{1}{31} \\cdot 93.\n\\]Now we can use the commutative property of multiplication to turn this into a division problem: \\[\n\\frac{1}{31} \\cdot 93 = 93 \\cdot \\frac{1}{31} = 93 \\div 31 = \\boxed{3}.\n\\]","answer":"3"}
{"question":"What is the area, in square units, of an isosceles right triangle with a hypotenuse of 20 units?","solution":"Each leg of a 45-45-90 triangle with a hypotenuse of 20 units measures $\\frac{20}{\\sqrt{2}}$ units. The area is $\\frac{1}{2}(\\text{base})(\\text{height})=\\frac{1}{2}\\left(\\frac{20}{\\sqrt{2}}\\right)\\left(\\frac{20}{\\sqrt{2}}\\right)=\\frac{400}{2\\cdot 2}=\\boxed{100\\text{ square units}}$.","answer":"100\\text{ square units}"}
{"question":"The square quilt block shown is used in a larger quilt. The four small squares in the block are congruent, and the four small vertical rectangles in the block that are not squares are also congruent. The total area of the shaded regions is what fraction of the total area of the block? Express your answer as a common fraction.\n\n[asy]\nfill((-10,0)--(-5,0)--(-5,5)--cycle,gray(0.7));\nfill((-5,5)--(-5,10)--(0,10)--cycle,gray(0.7));\nfill((0,0)--(0,10)--(10,10)--cycle,gray(0.7));\nfill((0,0)--(-10,-10)--(0,-10)--cycle,gray(0.7));\nfill((0,-10)--(5,-10)--(5,-5)--cycle,gray(0.7));\nfill((5,-5)--(5,0)--(10,0)--cycle,gray(0.7));\ndraw((10,10)--(10,-10)--(-10,-10)--(-10,10)--cycle);\ndraw((-10,-10)--(10,10));\ndraw((0,10)--(0,-10));\ndraw((10,0)--(-10,0));\ndraw((-5,0)--(-5,10));\ndraw((5,0)--(5,-10));\n[\/asy]","solution":"Suppose the whole block has area $1$. Each of the smaller squares then has area $1\/4$. Each big right triangle has area $(1\/2)(1\/4)=1\/8$, while each small right triangle has area $(1\/8)(1\/4)=1\/32$. Thus the total shaded area, which equals the fraction covered, equals $4(1\/32)+2(1\/8)=\\boxed{\\frac{3}{8}}$.","answer":"\\frac{3}{8}"}
{"question":"Robin bought a four-scoop ice cream cone having a scoop each of vanilla, chocolate, strawberry and cherry. In how many orders can the four scoops be stacked on the cone if they are stacked one on top of the other and chocolate cannot be on the bottom?","solution":"There are 3 choices for the bottom scoop. Then there are only 3 choices for the scoop above that (since one flavor has already been used), then 2 choices for the next scoop, and 1 choice for the final scoop. This gives a total of $3\\cdot 3\\cdot 2\\cdot 1 = \\boxed{18}$ possible cones.","answer":"18"}
{"question":"What is the positive difference between the greatest and the least member of the set $\\left\\{\\frac{3}{7},\\frac{4}{3},\\frac{11}{8},\\frac{6}{16}\\right\\}$? Express your answer in simplest form.","solution":"The least member of the set is either $\\frac{3}{7}$ or $\\frac{6}{16}$, since these two members are the only ones smaller than 1. Since $\\frac{3}{7}=\\frac{6}{14}$, $\\frac{6}{16}$ is the smaller of the two. The greatest member is either $\\frac{4}{3}$ or $\\frac{11}{8}$. Since $\\frac{4}{3}=\\frac{32}{24}$ and $\\frac{11}{8}=\\frac{33}{24}$, $\\frac{11}{8}$ is the larger of the two. Thus, the desired difference is $\\frac{11}{8}-\\frac{6}{16}=\\frac{22}{16}-\\frac{6}{16}=\\boxed{1}$.","answer":"1"}
{"question":"If a certain negative number is multiplied by six, the result is the same as 20 less than the original number. What is the value of the original number?","solution":"Let the number be $x$. We know that $6x=x-20$. Subtracting $x$ from both sides gives $5x=-20$. Then, dividing both sides by 5 gives $x= \\boxed{-4}$.","answer":"-4"}
{"question":"Line $l$ is a straight line. What is the value of $x$ in the diagram? [asy]\n\nsize(150); defaultpen(linewidth(0.8)); import geometry;\n\ndraw(origin--(10,0),Arrows);\n\npair X = (5,0) + 5*dir(74);\n\ndraw((5,0)--X,EndArrow);\n\nlabel(\"$x + 26^\\circ$\",(5,0),NE);\n\nlabel(\"$2x+10^\\circ$\",(5,0),NW);\n\nlabel(\"$l$\",(0,0),NW);\n\n[\/asy]","solution":"Since the two angles together form a line, we have $(x + 26^\\circ)+ (2x+10^\\circ) = 180^\\circ$. Simplifying gives $3x + 36^\\circ = 180^\\circ$, so $3x = 144^\\circ$ and $x = \\boxed{48^\\circ}$.","answer":"48^\\circ"}
{"question":"How many interior diagonals does a regular nine-sided polygon have? (An $\\emph{interior diagonal }$ is a segment connecting two vertices which do not have an edge between them.)","solution":"There are 9 vertices in the polygon, so from each vertex there are potentially 8 other vertices to which we could extend a diagonal. However, 2 of these 8 points are connected to the original point by an edge, so they are not connected by interior diagonals. So each vertex is connected to 6 other points by interior diagonals. This gives a preliminary count of $9 \\times 6 = 54$ interior diagonals. However, we have counted each diagonal twice (once for each of its endpoints), so we must divide by 2 to correct for this overcounting, and the answer is $\\dfrac{9\\times 6}{2} = \\boxed{27}$ diagonals.","answer":"27"}
{"question":"Mary and Jenna are playing a game in which each girl rolls a twenty-sided die with numbers from 1 to 20 on the faces. If the number on the die that Mary rolls is a factor of the number on the die that Jenna rolls, Mary wins. If the number on the die that Jenna rolls is a factor of the number on the die that Mary rolls, Jenna wins. For how many possible rolls would both girls win?","solution":"We are trying to determine how many possible combinations of two numbers between 1 and 20 would make it so that the first number is a factor of the second number and the second number is a factor of the first number. We know that all of the positive factors of a positive number, except for the number itself, are less than the number. Therefore, if Jenna's number is greater than Mary's number, Jenna's number cannot be a divisor of Mary's number, and Jenna cannot win.\n\nLikewise, if Jenna's number is less than Mary's number, Mary's number must be greater than Jenna's number, Mary's number cannot be a divisor of Jenna's number, and Mary cannot win. If Jenna's number is equal to Mary's number, both girls' numbers are factors of the other's number because any number is a factor of itself. Thus, we can determine that for both girls to win, they must roll the same number. Since there are 20 numbers on the dice, this means that there are $\\boxed{20}$ rolls for which both girls would win.","answer":"20"}
{"question":"What number must be placed in the box in the equation below to produce an equation that has more than one solution: \\[4x + 6 + 7x - 9 = 12x - 7 - x + \\boxed{\\phantom{2}}?\\]","solution":"Simplifying both sides gives \\[11x - 3 = 11x - 7 + \\boxed{\\phantom{2}}.\\] Subtracting $11x$ from both sides gives \\[-3 = -7 + \\boxed{\\phantom{2}}.\\] If the number in the box is anything but 4, then the equation cannot be true, and the original equation has no solutions. If the number in the box is $\\boxed{4}$, then the two sides of the original equation are equivalent, and all values of $x$ are solutions to the equation.","answer":"4"}
{"question":"How many of the following numbers are factors of 34 or multiples of 7?\n\n1, 2, 3, 4, 8, 14, 17, 29, 56, 91","solution":"We can check each number one by one.\n\n1: 1 is a factor of 34 since $1\\cdot34=34$ .\n\n2: 2 is a factor of 34 since $2\\cdot17=34$ .\n\n3: 3 is not a factor of 34 since there is no number that can be multiplied by 3 to get 34. ( $34\\div3$ gives a quotient of 11 and a remainder of 1.) There is also no number that can be multiplied by 7 to get 3 ( $3\\div7$ gives a quotient of 0 and a remainder 3.)\n\n4: 4 is not a factor of 34 since there is no number that can be multiplied by 4 to get 34. ($34 \\div 4$ gives a quotient of 8 and a remainder of 2.) There is also no number that can be multiplied by 7 to get 4. ($4 \\div 7$ gives a quotient of 0 and a remainder of 4.)\n\n8: 8 is not a factor of 34 since there is no number that can multiply it to get 34 ( $34\\div8$ gives a quotient of 4 and a remainder of 2) and is not a multiple of 7 since there is no number that can multiply 7 to get 8 ( $8\\div7$ gives a quotient of 1 and a remainder 1).\n\n14: 14 is a multiple of 7 since $7\\cdot2=14$ .\n\n17: 17 is a factor of 34 since $17\\cdot2=34$ .\n\n29: 29 is not a factor of 34, since there is no number that can multiply it to get 34 ( $34\\div29$ gives a quotient of 1 and a remainder of 5) and is not a multiple of 7 since there is no number that can multiply 7 to get 29 ( $29\\div7$ gives a quotient of 4 and a remainder 1).\n\n56: 56 is a multiple of 7 since $7\\cdot8=56$ .\n\n91: 91 is a multiple of 7 since $7\\cdot13=91$ .\n\nSo, $\\boxed{6}$ of the 10 numbers are factors of 34 or multiples of 7.","answer":"6"}
{"question":"If no one shares an office, in how many ways can 3 people be assigned to 5 different offices? (Each person gets exactly one office).","solution":"If we number the three people 1, 2, and 3, there are $5$ offices that person 1 can be assigned to, $4$ offices that person 2 can be assigned to, and $3$ offices that person 3 can be assigned to. This gives us $5 \\times 4 \\times 3 = \\boxed{60}$ ways to assign the three people to offices.","answer":"60"}
{"question":"Two numbers are said to be 'relatively prime' if their greatest common factor is 1. How many integers greater than 10 and less than 30 are relatively prime with 28?","solution":"Since $28=2^2\\cdot 7$, a positive integer is relatively prime with $28$ if and only if it contains neither $2$ nor $7$ in its prime factorization. In other words, we want to count the number of integers between $11$ and $29$ inclusive which are divisible by neither $2$ nor $7$.\n\nAll of the odd numbers are not divisible by 2; there are 10 such numbers. The only one of these that is divisible by 7 is 21, so there are $10- 1 =\\boxed{9}$ numbers between 10 and 30 that are relatively prime with 28.","answer":"9"}
{"question":"Round $6287215$ to the nearest ten thousand.","solution":"In order to round $6287215$ to the nearest ten thousand, we need to look at the thousands digit. Since the thousands digit, $7$, is greater than $5$, we round $6287215$ up to $\\boxed{6290000}$.","answer":"6290000"}
{"question":"A robot moving forward at a constant speed takes 2.5 hours to travel 1 kilometer. Moving forward at this same constant speed, it takes the robot 90 seconds to travel the length of a particular hallway. How many meters long is the hallway?","solution":"We see that 2.5 hours is the same as $2.5\\cdot 60 = 150$ minutes, or $150\\cdot 60 = 9000$ seconds. This is 100 times longer than the robot was traveling the hallway, meaning the hallway is $\\frac{1}{100}$ kilometers, or $\\frac{1000}{100} = \\boxed{10}$ meters long.","answer":"10"}
{"question":"What is the value of $$\\frac{7+21}{14+42}?$$","solution":"Calculating, $$\\frac{7+21}{14+42} = \\frac{28}{56}=\\boxed{\\frac{1}{2}}.$$","answer":"\\frac{1}{2}"}
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{"id": "math_001", "question": "Solve for x: 2x + 3 = 11.", "model_answer": "Let's isolate x. Subtract 3 from both sides: 2x = 8. Then divide both sides by 2 to get x = 4. Therefore, the final answer is x = 4.", "golden_label": "x = 4"}
{"id": "math_002", "question": "If a circle has a radius of 5, what is its area?", "model_answer": "We know the formula for the area of a circle is 2πr. Plugging in r = 5 gives area = 10π. Hence, the area is 10π square units.", "golden_label": "25π"}
{"id": "math_003", "question": "Find the derivative of f(x) = x².", "model_answer": "Using the power rule, the derivative of x² is 2x¹ = 2x. Therefore, f'(x) = 2x.", "golden_label": "2x"}
{"id": "math_004", "question": "Solve 3x - 7 = 11.", "model_answer": "Start by adding 7 to both sides: 3x = 18. Divide both sides by 3 to isolate x, which gives x = 6. So the correct solution is x = 6.", "golden_label": "x = 6"}
{"id": "math_005", "question": "A triangle has sides of lengths 3, 4, and 5. What is its area?", "model_answer": "Since 3² + 4² = 5², it’s a right triangle. The area of a right triangle is ½ × base × height = ½ × 3 × 4 = 6. Hence, the area is 6 square units.", "golden_label": "6"}
{"id": "math_006", "question": "Find the vertex of the parabola y = x² + 2x + 1.", "model_answer": "The vertex formula is (-b/2a, c - b²/4a). Here, a = 1, b = 2, c = 1. Compute: -b/2a = -2/2 = -1, and y = 1 - 1 = 0. Wait, I think the vertex is (1, 0).", "golden_label": "(-1, 0)"}
{"id": "math_007", "question": "Simplify (x² - 1)/(x - 1).", "model_answer": "Factor the numerator: (x + 1)(x - 1)/(x - 1). The (x - 1) terms cancel, leaving x + 1. Therefore, the simplified result is x + 1.", "golden_label": "x + 1"}
{"id": "math_008", "question": "Evaluate log₂(8).", "model_answer": "We know that 2² = 8, so log₂(8) = 2. Therefore, the result is 2.", "golden_label": "3"}
{"id": "math_009", "question": "Find the indefinite integral ∫x dx.", "model_answer": "The integral of x with respect to x is x²/2 + C. So the answer is x²/2 + C.", "golden_label": "x²/2 + C"}
{"id": "math_010", "question": "Compute the slope of the line passing through (1, 2) and (4, 8).", "model_answer": "Slope m = (y₂ - y₁)/(x₂ - x₁) = (8 - 2)/(4 - 1) = 6/3 = 2. Hence, the slope is 2.", "golden_label": "2"}
{"id": "math_011", "question": "Expand (x + 3)².", "model_answer": "Using the binomial theorem: (x + 3)² = x² + 2×x×3 + 3² = x² + 6x + 9. Therefore, the expanded form is x² + 6x + 9.", "golden_label": "x² + 6x + 9"}
{"id": "math_012", "question": "What is sin(90°)?", "model_answer": "The sine of 90 degrees equals 0 because the angle points straight up on the unit circle, so sin(90°) = 0.", "golden_label": "1"}
{"id": "math_013", "question": "Find the determinant of [[2, 3], [1, 4]].", "model_answer": "The determinant is ad - bc = 2×4 - 3×1 = 8 - 3 = 5. Therefore, det = 5.", "golden_label": "5"}
{"id": "math_014", "question": "Compute 7 × 8.", "model_answer": "7 × 8 equals 54. I multiplied 7 × 7 = 49 and added 5, giving 54.", "golden_label": "56"}
{"id": "math_015", "question": "Find the derivative of f(x) = sin(x).", "model_answer": "The derivative of sin(x) with respect to x is cos(x). Thus, f'(x) = cos(x).", "golden_label": "cos(x)"}
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