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[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Find the smallest positive integer \\( n \\) that satisfies the following congruences:\n\\[\nn \\equiv 2 \\pmod{3},\\q...	{ "id": "gen-34c78d5bff277479", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Find the smallest positive integer \\( n \\) that satisfies the following congruences:\n\\[\nn \\equiv 2 \\pmod{3},\\quad n \\equiv 3 \\pmod{5},\\quad n \\equiv 2 \...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Consider a 5 × 5 grid of unit squares. A path starts at the bottom-left vertex and ends at the top-right vertex, movin...	{ "id": "gen-1ff8e3a7d795a12a", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Consider a 5 × 5 grid of unit squares. A path starts at the bottom-left vertex and ends at the top-right vertex, moving only right or up along the grid lines. How m...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "We need to write a single intermediate logical deduction puzzle question. Must be self-contained, single correct answe...	{ "id": "gen-35f4942d2041af19", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "We need to write a single intermediate logical deduction puzzle question. Must be self-contained, single correct answer, solvable by reasoning. No answer or hints. ...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Consider a principal-agent setting where a risk-neutral principal hires an agent with constant absolute risk aversion ...	{ "id": "gen-f9a8d292d2e18497", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Consider a principal-agent setting where a risk-neutral principal hires an agent with constant absolute risk aversion (CARA) coefficient \\(r = 2\\). The agent choo...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A hash table with 11 slots (indices 0 through 10) uses open addressing with linear probing to resolve collisions. The ...	{ "id": "gen-b0d30ef4bc133767", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A hash table with 11 slots (indices 0 through 10) uses open addressing with linear probing to resolve collisions. The hash function is h(k) = k mod 11. The followin...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "The following table shows selected financial data for three companies (A, B, and C) for the fiscal year 2023. All mone...	{ "id": "gen-bedddf0876135573", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "The following table shows selected financial data for three companies (A, B, and C) for the fiscal year 2023. All monetary values are in millions of dollars.\n\n\| M...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "The following table presents quarterly revenue (in $ millions) and employee count for a company in 2021 and 2022.\n\n\|...	{ "id": "gen-ccdfaea75b314579", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "The following table presents quarterly revenue (in $ millions) and employee count for a company in 2021 and 2022.\n\n\| Quarter \| 2021 Revenue ($M) \| 2021 Employees ...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Evaluate the double integral\n\\[\n\\int_0^1 \\int_0^1 \\frac{1}{1 - xy} \\, dx \\, dy.\n\\]" }, { "from": "gp...	{ "id": "gen-a76b748b2dc2eb81", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Evaluate the double integral\n\\[\n\\int_0^1 \\int_0^1 \\frac{1}{1 - xy} \\, dx \\, dy.\n\\]", "reasoning": "We need to evaluate the double integral ∫_0^1 ∫_0^1 1...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Consider the reaction of (R)-2-bromobutane with sodium ethoxide (NaOEt) in ethanol at 25°C. The reaction proceeds via ...	{ "id": "gen-51fe5c197809188b", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Consider the reaction of (R)-2-bromobutane with sodium ethoxide (NaOEt) in ethanol at 25°C. The reaction proceeds via an SN2 mechanism. What is the absolute configu...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Alice, Bob, and Carol each have a different favorite fruit: apple, banana, or cherry. Alice does not like banana. Bob’...	{ "id": "gen-6a0422fde352f8e9", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Alice, Bob, and Carol each have a different favorite fruit: apple, banana, or cherry. Alice does not like banana. Bob’s favorite fruit is cherry. What is Carol’s fa...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A delivery robot starts at the depot (location D) with an empty cargo bay. It must pick up packages from three pickup ...	{ "id": "gen-bf247263b1002a9b", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A delivery robot starts at the depot (location D) with an empty cargo bay. It must pick up packages from three pickup locations (A, B, C) and deliver them to their ...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A particle of mass \\( m \\) moves under the influence of a central force derived from the potential \\( V(r) = -k/r \...	{ "id": "gen-09aa79442a3608ca", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A particle of mass \\( m \\) moves under the influence of a central force derived from the potential \\( V(r) = -k/r \\), where \\( k > 0 \\). At a given moment, th...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Consider a 4×4 grid with coordinates (x, y) where x and y range from 0 to 3. A robot starts at (0, 0) and must finish ...	{ "id": "gen-b78480e8e9cae8f3", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Consider a 4×4 grid with coordinates (x, y) where x and y range from 0 to 3. A robot starts at (0, 0) and must finish at (3, 3). There are two items to collect: one...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A fair coin is flipped repeatedly until the first head appears. Let \\(N\\) be the number of flips required. Compute t...	{ "id": "gen-9491b16e6d366372", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A fair coin is flipped repeatedly until the first head appears. Let \\(N\\) be the number of flips required. Compute the expected value of \\(N^2\\).", "reasoning...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "In how many ways can 8 distinct books be arranged on a shelf if 3 particular books must always be placed next to each ...	{ "id": "gen-cd916938c2be29aa", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "In how many ways can 8 distinct books be arranged on a shelf if 3 particular books must always be placed next to each other (in any order)?", "reasoning": "We are...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Consider a particle of mass \\( m \\) sliding without friction on the inner surface of a cone with half-angle \\( \\al...	{ "id": "gen-11855e960a8f5071", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Consider a particle of mass \\( m \\) sliding without friction on the inner surface of a cone with half-angle \\( \\alpha \\) (the cone's axis is vertical, and its ...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A chemist performs the following reaction sequence starting from (E)-3-methylpent-2-en-1-ol:\n\n1. The allylic alcohol...	{ "id": "gen-8feccd5f6bd9d59c", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A chemist performs the following reaction sequence starting from (E)-3-methylpent-2-en-1-ol:\n\n1. The allylic alcohol is treated with pyridinium chlorochromate (PC...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Consider a seller with one indivisible item and two risk-neutral bidders. Each bidder's private value is drawn indepen...	{ "id": "gen-3bcdbe3ced50bbe0", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Consider a seller with one indivisible item and two risk-neutral bidders. Each bidder's private value is drawn independently from the distribution with cumulative d...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "The table below shows the number of units sold for four products (P, Q, R, S) over three consecutive months.\n\n\| Mont...	{ "id": "gen-8e82aeb6db757415", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "The table below shows the number of units sold for four products (P, Q, R, S) over three consecutive months.\n\n\| Month \| Product P \| Product Q \| Product R \| Produc...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Determine whether the infinite series \\(\\sum_{n=1}^{\\infty} \\frac{1}{n(n+2)}\\) converges, and if it does, find it...	{ "id": "gen-0a26588355dd707d", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Determine whether the infinite series \\(\\sum_{n=1}^{\\infty} \\frac{1}{n(n+2)}\\) converges, and if it does, find its exact sum.", "reasoning": "We are asked: \...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Consider a game where you roll a fair six-sided die. If the result is 1 or 2, you lose $5. If the result is 3 or 4, yo...	{ "id": "gen-b48d5ec5426e11c9", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Consider a game where you roll a fair six-sided die. If the result is 1 or 2, you lose $5. If the result is 3 or 4, you win $3. If the result is 5 or 6, you win $10...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "An employee receives a base salary of $50,000 per year plus a bonus of 10% of any profits above $1,000,000. The employ...	{ "id": "gen-4b7362b0c8809f88", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "An employee receives a base salary of $50,000 per year plus a bonus of 10% of any profits above $1,000,000. The employee can choose between a standard effort level ...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A helium-filled balloon is tied to the floor of a car by a string. When the car accelerates forward from rest, does th...	{ "id": "gen-e645d1580af3b2ba", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A helium-filled balloon is tied to the floor of a car by a string. When the car accelerates forward from rest, does the balloon tilt forward, tilt backward, or rema...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "The table below shows the quarterly revenue (in millions of dollars) and the number of active subscribers (in thousand...	{ "id": "gen-78cef16219e15e65", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "The table below shows the quarterly revenue (in millions of dollars) and the number of active subscribers (in thousands) for a streaming service over two years.\n\n...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A fair coin is flipped repeatedly. The process stops as soon as either the sequence HTH or the sequence THT appears as...	{ "id": "gen-c9ad5122e796e7fb", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A fair coin is flipped repeatedly. The process stops as soon as either the sequence HTH or the sequence THT appears as a consecutive block of flips. What is the exp...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A fair six-sided die is rolled repeatedly. The outcomes are summed. What is the expected number of rolls until the cum...	{ "id": "gen-1c57cf74eec057aa", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A fair six-sided die is rolled repeatedly. The outcomes are summed. What is the expected number of rolls until the cumulative sum is a multiple of 7?", "reasoning...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A hospital has only two ventilators available for three patients during a pandemic. The patients’ probabilities of sur...	{ "id": "gen-0dea034e0df25dee", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A hospital has only two ventilators available for three patients during a pandemic. The patients’ probabilities of survival with and without a ventilator, along wit...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "An international health organization has 1,000 doses of a new antiviral medication. It must decide how to distribute t...	{ "id": "gen-7157eaf9bb9312e8", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "An international health organization has 1,000 doses of a new antiviral medication. It must decide how to distribute them between two distinct populations:\n\n- Pop...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Consider the following program designed to find the median of two sorted arrays `A` and `B` of lengths `m` and `n` res...	{ "id": "gen-282fc34f49981ff5", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Consider the following program designed to find the median of two sorted arrays `A` and `B` of lengths `m` and `n` respectively (where `m <= n`), using a binary sea...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A sphere of radius 1 is inscribed in a cube. A second, smaller sphere is placed in one of the corners of the cube such...	{ "id": "gen-9d3869be8bb83535", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A sphere of radius 1 is inscribed in a cube. A second, smaller sphere is placed in one of the corners of the cube such that it is tangent to the three faces meeting...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Let \\( f(x) = \\int_0^x e^{-t^2} \\, dt \\). Evaluate \\( \\int_0^\\infty f(x) e^{-x^2} \\, dx \\)." }, { "fr...	{ "id": "gen-9c1b3280dd760b85", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Let \\( f(x) = \\int_0^x e^{-t^2} \\, dt \\). Evaluate \\( \\int_0^\\infty f(x) e^{-x^2} \\, dx \\).", "reasoning": "We need to evaluate the integral I = ∫_0^∞ f(...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "We need to write an advanced organic chemistry reaction question, self-contained, single correct answer, requires reas...	{ "id": "gen-527e2a5a02665469", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "We need to write an advanced organic chemistry reaction question, self-contained, single correct answer, requires reasoning. No answer, no hints. Just the question ...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A government imposes a tax that raises the price of cigarettes by 20%. The price elasticity of demand for cigarettes i...	{ "id": "gen-00008415b541a9f8", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A government imposes a tax that raises the price of cigarettes by 20%. The price elasticity of demand for cigarettes is estimated to be -0.4. If current annual cons...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A hospital has one remaining dose of a life-saving antivenom. Two patients arrive simultaneously: Patient A is a 25-ye...	{ "id": "gen-b5f8eb4dd564a7cd", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A hospital has one remaining dose of a life-saving antivenom. Two patients arrive simultaneously: Patient A is a 25-year-old researcher who has developed a promisin...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Consider the following Python function intended to compute the sum of the first n positive integers:\n\n```python\nd...	{ "id": "gen-659b96fcff8cf809", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Consider the following Python function intended to compute the sum of the first n positive integers:\n\n```python\ndef sum_first_n(n):\n total = 0\n for i i...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Consider a complete binary tree with n nodes, where n = 2^h - 1 for some integer h ≥ 1. Each node stores a distinct in...	{ "id": "gen-453c74084e74ca76", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Consider a complete binary tree with n nodes, where n = 2^h - 1 for some integer h ≥ 1. Each node stores a distinct integer key. The tree satisfies the following pr...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "Find the exact value of the infinite series \\(\\displaystyle \\sum_{n=1}^{\\infty} \\frac{1}{n(n+1)(n+2)}\\)." }, ...	{ "id": "gen-14a7343b19d194ed", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "Find the exact value of the infinite series \\(\\displaystyle \\sum_{n=1}^{\\infty} \\frac{1}{n(n+1)(n+2)}\\).", "reasoning": "We need to find the exact value of ...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "How many positive integers less than 1000 are divisible by 3 or 5 but not by 15?" }, { "from": "gpt", "val...	{ "id": "gen-83405b64e676c1ef", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "How many positive integers less than 1000 are divisible by 3 or 5 but not by 15?", "reasoning": "We need to count positive integers less than 1000 (so from 1 to 9...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "A 2.0 kg block is placed on a frictionless inclined plane that makes an angle of 30° with the horizontal. The block is...	{ "id": "gen-de5bc56f1980b3f3", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "A 2.0 kg block is placed on a frictionless inclined plane that makes an angle of 30° with the horizontal. The block is released from rest. What is the speed of the ...
[ { "from": "system", "value": "You are an expert tutor. Think step by step and show your full reasoning, then give a clear, correct final answer." }, { "from": "human", "value": "We need to create a competition-level elementary number theory question. It should be self-contained, have a single co...	{ "id": "gen-17ac7b9648ca0323", "source": "generated", "model": "nvidia/nemotron-3-ultra-550b-a55b-20260604:free", "effort": "high", "question": "We need to create a competition-level elementary number theory question. It should be self-contained, have a single correct answer, solvable through explicit reason...