EvalDataset-100.json

[
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "The salaries of A,B,C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?\nAnswer Choices: (A) 3 : 3 : 10 (B) 10 : 11 : 20 (C) 23 : 33 : 60 (D) Cannot be determined (E) None of these",
    "output": "Let's think about the multi-choice question.\nLet A = 2k, B = 3k and C = 5k.\nA\u2019s new salary = 115\u2044100 of 2k = (115\u2044100 \u00d7 2k) = 23\u204410k\nB\u2019s new salary = 110\u2044100 of 3k = (110\u2044100 \u00d7 3k) = 33\u204410k\nC\u2019s new salary = 120\u2044100 of 5k = (120\u2044100 \u00d7 5k) = 6k\n\u2234 New ratio = 23k\u204410 : 33k\u204410 : 6k = 23 : 33 : 60\nThe answer is C"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "The workforce of Company X is 60% female. The company hired 30 additional male workers, and as a result, the percent of female workers dropped to 55%.How many employees did the company have after hiring the additional male workers?\nAnswer Choices: (A) 160 (B) 220 (C) 240 (D) 360 (E) 420",
    "output": "Let's think about the multi-choice question step by step.\nLet's xx be total quantity of employees\n0.6x=females before adding men\n0.55(x+30)=females after adding men\nas quantity of women doesn't change we can make an equation:\n0.6x=0.55(x+30)\n0.05x=16.5\nx=330 - this is quantity of employees before adding 30 men\nSo after adding it will be 360\nThe answer is D"
  },
  {
    "source": "data/CoT/gsm_train.json",
    "instruction": "Margaux owns a money lending company. Her friend pays her $5 per day, her brother $8 per day, and her cousin $4 per day. How much money will she collect after 7 days?",
    "output": "Her friend will pay $5 x 7 = $35 after 7 days.\nHer brother will pay $8 x 7 = $56 after 7 days.\nHer cousin will pay $4 x 7 = $28 after 7 days.\nTherefore, she will be able to collect $35 + $56 + $28 = $119 after 7 days.\nThe answer is 119"
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "Consider the graph G below:\n\n![Graph G image](https://i.imgur.com/zaufhFE.png)\n\nWhat is the maximum size of an independent set in G, and which vertices belong to such a set?",
    "output": "An independent set in a graph is a set of vertices such that no two vertices in the set are adjacent. To find the maximum size of an independent set in G, we can use a greedy algorithm to select non-adjacent vertices.\n\n1. Start with an empty set S.\n2. Choose a vertex with the smallest degree and add it to S. If there are multiple vertices with the same smallest degree, choose any one of them.\n3. Remove the chosen vertex and its neighbors from the graph.\n4. Repeat steps 2 and 3 until there are no vertices left in the graph.\n\nFollowing this algorithm, we can find the maximum size of an independent set in G:\n\n1. S = {}\n2. Choose vertex 1 (smallest degree, 1). S = {1}\n3. Remove vertex 1 and its neighbor (vertex 2) from the graph.\n4. Repeat steps 2 and 3:\n   - Choose vertex 3 (smallest degree, 1). S = {1, 3}\n   - Remove vertex 3 and its neighbor (vertex 4) from the graph.\n   - Choose vertex 5 (smallest degree, 1). S = {1, 3, 5}\n   - Remove vertex 5 and its neighbor (vertex 6) from the graph.\n   - No vertices left in the graph.\n\nThe maximum size of an independent set in G is 3, and the vertices belonging to such a set are {1, 3, 5}."
  },
  {
    "source": "data/PoT/gsm_gpt4.json",
    "instruction": "Mary, Jess, and Christina want to decorate a party room with balloons. Each person inflates balloons at different speeds, and they only have 30 minutes to inflate as many balloons as possible. Mary inflates 10 balloons per minute, Jess inflates 7 balloons per minute and Christina came 15 minutes late and was the slowest one inflating 4 balloons per minute. How many balloons can they inflate before running out of time? Let's write a Python program.",
    "output": "# define the time limit and the rates at which each person inflates balloons\ntime_limit = 30\nmary_rate = 10\njess_rate = 7\nchristina_rate = 4\nchristina_late = 15\n\n# calculate the number of balloons each person can inflate\nmary_balloons = time_limit * mary_rate\njess_balloons = time_limit * jess_rate\nchristina_balloons = (time_limit - christina_late) * christina_rate\n\n# calculate the total number of balloons\ntotal_balloons = mary_balloons + jess_balloons + christina_balloons\n\n# print the result\nprint(total_balloons)"
  },
  {
    "source": "data/CoT/MATH_train.json",
    "instruction": "The domain of the equation $y = \\frac{3x}{2x^2 - 6x + 4}$ is the set of all real numbers with the exception of the values $x = A$ and $x = B$. What is $A + B$?",
    "output": "The equation is well-defined unless the denominator of the given expression is equal to $0$, that is $2x^2 - 6x + 4 = 0$. Factoring, $2(x-1)(x-2) = 0 \\Longrightarrow x = 1,2$. Hence, $A+B = \\boxed{3}$.\n\n(We can also use Vieta's formulas, which states that the sum of the roots of the equation $ax^2 + bx + c = 0$ is $-b/a$.). The answer is 3"
  },
  {
    "source": "data/PoT/MATH_train.json",
    "instruction": "Sara used $\\frac{3}{10}$ of a roll of wrapping paper to wrap three presents. If she used the same amount of wrapping paper on each present, what fraction of a roll of wrapping paper did she use on each present? Let's write a Python program.",
    "output": "# we simply divide the total paper used by the number of presents\ntotal_paper = 3/10\nnum_presents = 3\npaper_per_present = total_paper / num_presents\nprint(paper_per_present)"
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "Suppose that a company's network is prone to two types of cyber attacks, A and B. The probability of an attack of type A occurring on any given day is 0.2, while the probability of an attack of type B occurring is 0.3. Find the probability that the network will experience at least one cyber attack per day.",
    "output": "To find the probability of at least one cyber attack per day, we can first find the probability of no cyber attacks occurring and then subtract that from 1.\n\nLet's denote the events as follows:\n- A: Attack of type A occurs\n- B: Attack of type B occurs\n- A': No attack of type A occurs\n- B': No attack of type B occurs\n\nWe are given the probabilities of attacks A and B occurring:\nP(A) = 0.2\nP(B) = 0.3\n\nWe can find the probabilities of no attacks A and B occurring:\nP(A') = 1 - P(A) = 1 - 0.2 = 0.8\nP(B') = 1 - P(B) = 1 - 0.3 = 0.7\n\nNow, we need to find the probability of both A' and B' occurring (i.e., no attacks of either type). We will assume that the two types of attacks are independent events. In that case, the probability of both A' and B' occurring is the product of their individual probabilities:\n\nP(A' and B') = P(A') * P(B') = 0.8 * 0.7 = 0.56\n\nFinally, we find the probability of at least one attack occurring by subtracting the probability of no attacks from 1:\n\nP(At least one attack) = 1 - P(A' and B') = 1 - 0.56 = 0.44\n\nSo, the probability that the network will experience at least one cyber attack per day is 0.44."
  },
  {
    "source": "data/CoT/MATH_train.json",
    "instruction": "Let $f : \\mathbb{R} \\to \\mathbb{R}$ be a function such that\n\\[f(x) f(y) - f(xy) = x + y\\]for all real numbers $x$ and $y.$\n\nLet $n$ be the number of possible values of $f(2),$ and let $s$ be the sum of all possible values of $f(2).$  Find $n \\times s.$",
    "output": "Setting $x = y = 1,$ we get\n\\[f(1)^2 - f(1) = 2,\\]so $f(1)^2 - f(1) - 2 = 0.$  This factors as $(f(1) + 1)(f(1) - 2) = 0,$ so $f(1) = -1$ or $f(1) = 2.$\n\nSetting $y = 1,$ we get\n\\[f(x) f(1) - f(x) = x + 1\\]for all $x.$  Then $f(x) (f(1) - 1) = x + 1.$  Since $f(1) \\neq 1,$ we can write\n\\[f(x) = \\frac{x + 1}{f(1) - 1}.\\]If $f(1) = -1,$ then\n\\[f(x) = \\frac{x + 1}{-2},\\]and we can check that this function does not work.\n\nIf $f(1) = 2,$ then\n\\[f(x) = x + 1\\]and we can check that this function works.\n\nTherefore, $n = 1$ and $s = 3,$ so $n \\times s = \\boxed{3}.$. The answer is 3"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "Sandy can do a job in 6 days and Molly can do the same job in 12 days. If they work together, in how many days will they complete the job?\nAnswer Choices: (A) 4 days (B) 6 days (C) 8 days (D) 2 days (E) 9 days",
    "output": "Let's solve the multi-choice question step by step.\nSandy can do 1/6 of the job each day.\nMolly can do 1/12 of the job each day.\nThe combined rate is 1/6 + 1/12 = 1/4 of the job each day.\nThe job will take 4 days.\nThe answer is A."
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "The length of a rectangular landscape is 12 times its breadth. There is a playground in it whose area is 1200 square mtr & which is 1/4rd of the total landscape. What is the length of the landscape?\nAnswer Choices: (A) 90 (B) 120 (C) 240 (D) 180 (E) 110",
    "output": "Let's reason about the multi-choice question.\nSol. x *12x = 4 * 1200\nx = 20\nLength = 12 * 20 = 240\nThe answe is C"
  },
  {
    "source": "data/PoT/numglue.json",
    "instruction": "For his car , Mike spent $ 118.54 on speakers and $ 106.33 on new tires . Mike wanted 3 CD 's for $ 4.58 but decided not to. Mike spent $ _____ more on speakers than he did on new tires. Let's write a Python program to solve it.",
    "output": "mike_spent_on_speakers = 118.54\r\nmike_spent_on_tires = 106.33\r\nans = \"{:.2f}\".format((mike_spent_on_speakers-mike_spent_on_tires))\r\nprint(ans)"
  },
  {
    "source": "data/PoT/aqua_rat_filtered.json",
    "instruction": "What is the remainder when 10^49 + 2 is divided by 11?\nAnswer Choices: (A) 1 (B) 2 (C) 3 (D) 5 (E) 7 Let's write a program.",
    "output": "answers = ['A', 'B', 'C', 'D', 'E']\n# According to the properties of modular arithmetic, we know that 10^n mod 11 = 1 if n is even, and 10^n mod 11 = 10 if n is odd. \n# Therefore, 10^49 mod 11 = 10, and (10^49 + 2) mod 11 = (10 + 2) mod 11 = 1.\n# So the remainder when 10^49 + 2 is divided by 11 is 1.\nremainder = 1\noptions = [1, 2, 3, 5, 7]\nindex = options.index(remainder)\nprint(answers[index])"
  },
  {
    "source": "data/CoT/MATH_train.json",
    "instruction": "Ben rolls four fair 10-sided dice, each numbered with numbers from 1 to 10. What is the probability that exactly two of the dice show a prime number?",
    "output": "The probability that a 10-sided die rolls a prime number is $\\frac{4}{10}=\\frac{2}{5}$ since the primes it can roll are 2, 3, 5, and 7. We can choose which dice show a prime number in $\\binom{4}{2}=6$ ways. Then, there is a $\\frac{2}{5}\\cdot \\frac{2}{5} \\cdot \\frac{3}{5} \\cdot \\frac{3}{5}=\\frac{36}{625}$ chance that the chosen dice will actually roll a prime number and the other dice won't. Therefore, the total probability that exactly two dice show a prime number is $6 \\cdot \\frac{36}{625}=\\boxed{\\frac{216}{625}}$. The answer is \\frac{216}{625}"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 39 degrees. Find the temperature on Friday?\nAnswer Choices: (A) 65 degrees (B) 73 degrees (C) 31 degrees (D) 34 degrees (E) 74 degrees",
    "output": "Let's reason about the multi-choice question.\nM + Tu + W + Th = 4 * 48 = 192\nTu + W + Th + F = 4 * 46 = 184\nM = 39\nTu + W + Th = 192 -39 = 153\nF = 184 \u2013 153 = 31\nThe answer is C"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "In a certain series, each term is m greater than the previous term. If the 14th term is 600 and the 11th term is 540, what is the first term?\nAnswer Choices: (A) 40 (B) 80 (C) 140 (D) 200 (E) 240",
    "output": "Let's think about the multi-choice question.\na + 13m = 660 (14th term)\na + 10m = 540 (11th term)\nYou get a = 140 and m = 40\nThe answer is C"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?\nAnswer Choices: (A) 28 (B) 27 (C) 15 (D) 19 (E) 12",
    "output": "Let's think about the multi-choice question.\nTotal members in the group = 7\nAverage amount = Rs. 20\nTotal amount with them = 7 * 20 = Rs. 140\nOne number has Rs. 50. So, the amount with remaining 6 people = 140 - 50 = Rs. 90\nThe average amount with them = 90/6 = Rs. 15.\nThe answer is C"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "A certain high school has 500 students. Of these students, 30 are taking music, 10 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art?\nAnswer Choices: (A) 430 (B) 440 (C) 450 (D) 460 (E) 470",
    "output": "Let's think about the multi-choice question.\nWe're given a series of facts to work with:\n1) A certain high school has 500 students.\n2) Of these students:\nX are taking music,\nY are taking art, and\nZ are taking BOTH music and art.\nWe're asked how many students are taking NEITHER music nor art?\nLet's TEST\nX = 30\nY = 10\nZ = 10\nSo, we have 30 students taking music, 10 taking art and 10 taking BOTH music and art.\n20 student taking JUST music\n0 student taking JUST art\n10 student taking BOTH music and art\nTotal = 30 students\nWe're asked for the total number of students who are taking NEITHER Course. That is 500 - 30 = 470.\nThe answe is E"
  },
  {
    "source": "data/CoT/gsm_train.json",
    "instruction": "The Dark Lord needs to transport 1200 pounds of swords to the Enchanted Forest for a battle with the elves. He has 10 squads of 8 orcs each. How many pounds of swords does each orc have to carry?",
    "output": "First find how many orcs there are total by multiplying the number of orcs per squad by the number of squads: 8 orcs/squad * 10 squads = 80 orcs\nThen divide the total amount of swords by the number of orcs to find the amount of swords per orc: 1200 pounds / 80 orcs = 15 pounds/orc\nThe answer is 15"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "One man traveled a distance of 61 km in 9hrs. He traveled partly on footat 4 km/hr and partly on bicycle ta 9 km/hr. The distance traveled on foot is?\nAnswer Choices: (A) 11 km (B) 13 km (C) 16 km (D) 18 km (E) 19 km",
    "output": "Let's reason about the multi-choice question.\nLet the distance travelled on foot be x km.\nThen, distance travelled on bicycle = (61 -x) km.\nSo, x + (61 -x) = 9\n4 9\n9x + 4(61 -x) = 9 x 36\n5x = 80\nx = 16 km.\nThe answe is C"
  },
  {
    "source": "data/CoT/MATH_train.json",
    "instruction": "Determine the number of angles between 0 and $2 \\pi,$ other than integer multiples of $\\frac{\\pi}{2},$ such that $\\sin \\theta,$ $\\cos \\theta$, and $\\tan \\theta$ form a geometric sequence in some order.",
    "output": "We divide into cases.\n\nCase 1: $\\sin \\theta \\tan \\theta = \\cos^2 \\theta.$\n\nThe equation becomes $\\sin^2 \\theta = \\cos^3 \\theta,$ which we can write as $1 - \\cos^2 \\theta = \\cos^3 \\theta.$  Letting $x = \\cos \\theta,$ we get\n\\[x^3 + x^2 - 1 = 0.\\]Let $f(x) = x^3 + x^2 - 1.$  Clearly $x = -1$ is not a root.  If $-1 < x \\le 0,$ then $x^2 + x^3 \\le x^2 < 1$, so\n\\[f(x) = x^3 + x^2 - 1 < 0.\\]The function $f(x)$ is increasing for $0 \\le x \\le 1.$  Also, $f(0) = -1$ and $f(1) = 1,$ so $f(x)$ has exactly one root in the interval $[0,1].$  Then the equation $\\cos \\theta = x$ has two solutions for $0 \\le \\theta \\le 2 \\pi.$\n\nCase 2: $\\sin \\theta \\cos \\theta = \\tan^2 \\theta.$\n\nThe equation becomes $\\cos^3 \\theta = \\sin \\theta.$  In the interval $0 \\le \\theta \\le \\frac{\\pi}{2},$ $\\sin \\theta$ increases from 0 to 1 while $\\cos^3 \\theta$ decreases from 1 to 0, so there is one solution in this interval.  Similarly, in the interval $\\pi \\le \\theta \\le \\frac{3 \\pi}{2},$ $\\sin \\theta$ decreases from 0 to $-1$ while $\\cos^3 \\theta$ increases from $-1$ to $0,$ so there is one solution in this interval.\n\nOn the intervals $\\frac{\\pi}{2} < \\theta < \\pi$ and $\\frac{3 \\pi}{2}  < \\theta < 2 \\pi,$ one of $\\sin \\theta$ and $\\cos^3 \\theta$ is positive while the other is negative, so there are no additional solutions.\n\nCase 3: $\\cos \\theta \\tan \\theta = \\sin^2 \\theta.$\n\nThe equation becomes $\\sin \\theta^2 = \\sin \\theta$, so $\\sin \\theta$ is 0 or 1.  The only solutions are integer multiples of $\\frac{\\pi}{2},$ so there are no solutions in this case.\n\nTherefore, there are a total of $\\boxed{4}$ solutions. The answer is 4"
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "What is the treewidth of a complete graph K6?\n\nNote: The treewidth of a graph is defined as the minimum width of a tree decomposition of the graph. The tree decomposition is a representation of the graph by a tree, where each node of the tree corresponds to a subset of vertices, and each edge corresponds to a separator set of vertices that separates the subsets on either side of the edge. The width of a tree decomposition is defined as the size of the largest separator set minus one.",
    "output": "The treewidth of a complete graph K_n is n-1. In the case of a complete graph K6, the treewidth is 6-1 = 5."
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "If one of the roots of the quadratic equation x2 + mx + 24 = 0 is 1.5, then what is the value of m?\nAnswer Choices: (A) -22.5 (B) 16 (C) -10.5 (D) -17.5 (E) None",
    "output": "Let's think about the multi-choice question.\nExplanatory Answer\nWe know that the product of the roots of a quadratic equation ax2 + bx + c = 0 is\nIn the given equation, x2 + mx + 24 = 0, the product of the roots = = 24.\nThe question states that one of the roots of this equation = 1.5.\nIf x1 and x2 are the roots of the given quadratic equation and let x1 = 1.5.\nTherefore, x2 == 16.\nIn the given equation, m is the co-efficient of the x term.\nWe know that the sum of the roots of the quadratic equation ax2 + bx + c = 0 is = -m\nSum of the roots = 16 + 1. 5 = 17 = -17.5.\nTherefore, the value of m = -17.5\nThe answer is D"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "In Solution P, the proportion of water to alcohol is 4:1. In Solution Q, the proportion of water to alcohol is 2:3. If the two solutions are combined, what is the concentration of alcohol in the new solution if the original solutions were mixed in equal amounts?\nAnswer Choices: (A) 40% (B) 48% (C) 50% (D) 56% (E) 60%",
    "output": "Let's solve the multi-choice question step by step.\nLet V be the total volume of the new solution.\nThe amount of alcohol added from Solution P is (1/5)*V/2=(1/10)*V\nThe amount of alcohol added from Solution Q is (3/5)*V/2=(3/10)*V\nThe total amount of alcohol in the new solution is (1/10+3/10)*V=(2/5)*V\nThe alcohol concentration is 2/5=40%\nThe answer is A."
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "How many of the following numbers are divisible by 21 ?\n264, 396, 462, 792, 968, 2178, 5184, 6336\nAnswer Choices: (A) 3 (B) 4 (C) 5 (D) 1 (E) 7",
    "output": "Let's reason about the multi-choice question.\nBy using your calculator you can calculate that the following numbers are divisible by 21 : 462\nRequired number of number = 1.\nThe answe is D"
  },
  {
    "source": "data/PoT/numglue.json",
    "instruction": " \"statement 1\": Raman travelled for less than 20 hours, \"statement 2\" :Raman travelled for 10 hours, \"options: \" Entailment or contradiction or neutral? Let's write a program.",
    "output": "hours_S1 = None\r\nhours_S2 = 10\r\nif hours_S1 is None or hours_S2 is None:\r\n   print('neutral')\r\nelif hours_S1 == hours_S2:\r\n   print('Entailment')\r\nelif hours_S1 != hours_S2:\r\n  print('contradiction')"
  },
  {
    "source": "data/PoT/gsm_gpt4.json",
    "instruction": "Jerry is refilling the duck pond in his backyard during a drought. The pond can hold 200 gallons of water. Jerry's hose can normally pump 6 gallons/minute, but due to drought restrictions, it can only pump 2/3rds as fast right now. How many minutes will it take Jerry to fill his pond? Let's write a Python program.",
    "output": "# define the variables\npond_capacity = 200  # in gallons\nnormal_pump_rate = 6  # in gallons/minute\n\n# due to drought restrictions, the hose can pump 2/3rds as fast\ncurrent_pump_rate = normal_pump_rate * 2/3\n\n# calculate the time needed to fill the pond\ntime_needed = pond_capacity / current_pump_rate\n\n# print the result\nprint(time_needed)"
  },
  {
    "source": "data/PoT/gsm_gpt4.json",
    "instruction": "John received 20 gifts on his 12th birthday.  He received 8 fewer gifts on his 13th birthday.  How many total gifts did he receive between those two birthdays? Let's write a program.",
    "output": "# define the variables\ngifts_12th_birthday = 20\ngifts_13th_birthday = gifts_12th_birthday - 8\n\n# calculate total gifts\ntotal_gifts = gifts_12th_birthday + gifts_13th_birthday\n\n# print the result\nprint(total_gifts)"
  },
  {
    "source": "data/PoT/mathqa.json",
    "instruction": "find the total number of prime factors in the expression ( 4 ) ^ 13 x ( 7 ) ^ 5 x ( 11 ) ^ 2 ? Please write a program to solve it",
    "output": "n0 = 4.0\nn1 = 13.0\nn2 = 7.0\nn3 = 5.0\nn4 = 11.0\nn5 = 2.0\nt0 = n1 * n5\nt1 = n3 + t0\nanswer = n5 + t1\nprint(answer)"
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "Suppose you have been given the following data set: \n\n| x   | y     |\n| --- | ----- |\n| -1  | 1     |\n| 0   | 0.5   |\n| 1   | -0.5  |\n| 2   | -3    |\n| 3   | -8.5  |\n| 4   | -18.5 |\n\nUsing the Lagrange interpolating polynomial, find the value of y when x = 1.5.",
    "output": "To find the value of y when x = 1.5 using the Lagrange interpolating polynomial, we can use the following formula:\n\nL(x) = y0 * l0(x) + y1 * l1(x) + y2 * l2(x) + ... + yn * ln(x)\n\nwhere L(x) is the Lagrange polynomial, y0, y1, ..., yn are the given y values, and l0(x), l1(x), ..., ln(x) are the Lagrange basis polynomials defined as:\n\nli(x) = \u03a0((x - xj) / (xi - xj)) for j = 0, 1, ..., n and j \u2260 i\n\nFor the given data set, we have 6 points, so n = 5. Let's calculate the Lagrange basis polynomials for x = 1.5:\n\nl0(1.5) = ((1.5 - 0) * (1.5 - 1) * (1.5 - 2) * (1.5 - 3) * (1.5 - 4)) / ((-1 - 0) * (-1 - 1) * (-1 - 2) * (-1 - 3) * (-1 - 4)) = 0.075\nl1(1.5) = ((1.5 + 1) * (1.5 - 1) * (1.5 - 2) * (1.5 - 3) * (1.5 - 4)) / ((0 + 1) * (0 - 1) * (0 - 2) * (0 - 3) * (0 - 4)) = -0.25\nl2(1.5) = ((1.5 + 1) * (1.5 - 0) * (1.5 - 2) * (1.5 - 3) * (1.5 - 4)) / ((1 + 1) * (1 - 0) * (1 - 2) * (1 - 3) * (1 - 4)) = 0.5625\nl3(1.5) = ((1.5 + 1) * (1.5 - 0) * (1.5 - 1) * (1.5 - 3) * (1.5 - 4)) / ((2 + 1) * (2 - 0) * (2 - 1) * (2 - 3) * (2 - 4)) = -0.375\nl4(1.5) = ((1.5 + 1) * (1.5 - 0) * (1.5 - 1) * (1.5 - 2) * (1.5 - 4)) / ((3 + 1) * (3 - 0) * (3 - 1) * (3 - 2) * (3 - 4)) = 0.1875\nl5(1.5) = ((1.5 + 1) * (1.5 - 0) * (1.5 - 1) * (1.5 - 2) * (1.5 - 3)) / ((4 + 1) * (4 - 0) * (4 - 1) * (4 - 2) * (4 - 3)) = -0.03125\n\nNow, we can calculate L(1.5):\n\nL(1.5) = 1 * 0.075 + 0.5 * (-0.25) + (-0.5) * 0.5625 + (-3) * (-0.375) + (-8.5) * 0.1875 + (-18.5) * (-0.03125) = 0.075 - 0.125 - 0.28125 + 1.125 + 1.59375 + 0.578125 = 2.965625\n\nSo, the value of y when x = 1.5 using the Lagrange interpolating polynomial is approximately 2.965625."
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "A company produces two products, P1 and P2. Each unit of P1 requires 4 hours of machine time and 2 hours of labor time to produce, while each unit of P2 requires 2 hours of machine time and 3 hours of labor time. The company has 60 hours of machine time and 45 hours of labor time available per week. Each unit of P1 yields a profit of $20, while each unit of P2 yields a profit of $30. Formulate a linear programming problem to determine the optimal number of units of each product the company should produce to maximize profit, and then solve it.",
    "output": "Let x be the number of units of P1 produced and y be the number of units of P2 produced.\n\nObjective function: Maximize profit = 20x + 30y\n\nConstraints:\n1. Machine time: 4x + 2y \u2264 60\n2. Labor time: 2x + 3y \u2264 45\n3. Non-negativity: x \u2265 0, y \u2265 0\n\nNow we will solve the linear programming problem using the graphical method.\n\nFirst, we will find the feasible region by graphing the constraints:\n\n1. 4x + 2y \u2264 60\n   y \u2264 30 - 2x\n\n2. 2x + 3y \u2264 45\n   y \u2264 (45 - 2x) / 3\n\n3. x \u2265 0, y \u2265 0\n\nThe feasible region is the area where all constraints are satisfied. The vertices of the feasible region are the points where the constraints intersect. We will find these vertices and then evaluate the objective function at each vertex to determine the maximum profit.\n\nVertices of the feasible region:\nA. (0, 0)\nB. (0, 15)\nC. (15, 10)\nD. (20, 0)\n\nNow we will evaluate the objective function at each vertex:\n\nA. Profit at (0, 0) = 20(0) + 30(0) = $0\nB. Profit at (0, 15) = 20(0) + 30(15) = $450\nC. Profit at (15, 10) = 20(15) + 30(10) = $600\nD. Profit at (20, 0) = 20(20) + 30(0) = $400\n\nThe maximum profit occurs at vertex C, where 15 units of P1 and 10 units of P2 are produced. The maximum profit is $600."
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "Solve for x: |2x - 3| = 7.",
    "output": "To solve the equation |2x - 3| = 7, we need to consider two cases:\n\nCase 1: 2x - 3 \u2265 0\nIn this case, we can remove the absolute value sign and solve the equation:\n2x - 3 = 7\n2x = 10\nx = 5\n\nCase 2: 2x - 3 < 0\nIn this case, we need to negate the expression inside the absolute value sign and solve the equation:\n-(2x - 3) = 7\n-2x + 3 = 7\n-2x = 4\nx = -2\n\nSo, the solutions for x are 5 and -2."
  },
  {
    "source": "data/PoT/numglue.json",
    "instruction": " \"statement 1\": Aarti had prior experience in that route and mentioned that the speed of stream was 4 kmph, \"statement 2\" :Aarti had prior experience in that route and mentioned that the speed of stream was more than 2 kmph, \"options: \" Entailment or contradiction or neutral? Let's write a Python program to solve it.",
    "output": "speed_of_stream_s1 = 215\nspeed_of_stream_s2 = 0\nspeed_of_stream_s2 > 2\n\nif speed_of_stream_s1 is None or speed_of_stream_s2 is None:\n    print(\"Neutral\")\nelif speed_of_stream_s1 > speed_of_stream_s2 :\n    print(\"Entailment\")\nelif speed_of_stream_s1 != speed_of_stream_s2 :\n    print(\"Contradiction\")"
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "Consider the following first-order chemical reaction between hydrogen peroxide and iodide ions:\n\nH2O2 + 2I^- \u2192 2H2O + I2\n\nThe rate of disappearance of hydrogen peroxide is given by the rate law:\n\nRate = k [H2O2][I^-]\n\nwhere k is the rate constant for the reaction. If the initial concentration of H2O2 is 0.1 M and the initial concentration of I^- is 0.2 M, and the rate constant is 0.5 M^-1 s^-1, find the concentration of H2O2 after 5 seconds.",
    "output": "To find the concentration of H2O2 after 5 seconds, we need to integrate the rate law with respect to time. However, this is not a simple first-order reaction, as the rate law involves both [H2O2] and [I^-]. This is a pseudo-first-order reaction, and we can simplify it by assuming that the concentration of I^- remains relatively constant during the reaction.\n\nUnder this assumption, we can rewrite the rate law as:\n\nRate = k' [H2O2]\n\nwhere k' = k[I^-] is the pseudo-first-order rate constant. In this case, k' = 0.5 M^-1 s^-1 * 0.2 M = 0.1 s^-1.\n\nNow we can integrate the rate law with respect to time:\n\nd[H2O2]/dt = -k' [H2O2]\n\nIntegrating both sides, we get:\n\nln([H2O2]/[H2O2]0) = -k't\n\nwhere [H2O2]0 is the initial concentration of H2O2 (0.1 M) and t is the time (5 seconds). Plugging in the values, we have:\n\nln([H2O2]/0.1) = -0.1 * 5\n\nln([H2O2]/0.1) = -0.5\n\nNow, we can solve for [H2O2]:\n\n[H2O2]/0.1 = e^(-0.5)\n\n[H2O2] = 0.1 * e^(-0.5)\n\n[H2O2] \u2248 0.1 * 0.6065\n\n[H2O2] \u2248 0.06065 M\n\nSo, the concentration of H2O2 after 5 seconds is approximately 0.06065 M."
  },
  {
    "source": "data/PoT/mathqa.json",
    "instruction": "after getting 2 successive discounts , a shirt with a list price of rs 150 is available at rs 105 . if the second discount is 12.55 , find the first discount . Please write a program to solve it",
    "output": "n0 = 2.0\nn1 = 150.0\nn2 = 105.0\nn3 = 12.55\nt0 = n2 * 100.0\nt1 = 100.0 - n3\nt2 = t0 / t1\nt3 = n1 - t2\nt4 = t3 * 100.0\nanswer = t4 / n1\nprint(answer)"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?\nAnswer Choices: (A) 30 min (B) 20 min (C) 25 min (D) 40 min (E) 45 min",
    "output": "Let's think about the multi-choice question step by step.\nSpeed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? 20\nThe answer is B"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "A certain collage has total of 420 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?\nAnswer Choices: (A) 100 (B) 80 (C) 75 (D) 60 (E) 50",
    "output": "Let's reason about the multi-choice question.\nAnswer is A.\nSix majors are as follows: a + b + c + d + e + f\nEach has at least 20 seniors: 20 + 20 + 20 + 20 + 20 + 20\n4 of the majors have 300 seniors: a + b + c +d = 300\nThere are a total of 420 seniors.\nSo e + f = 120. One of the subjects has to be 20 for the other to be maximized. If e = 20, then f = 100.\nThe answe is A"
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "Suppose G is a group of order 9, and let a be an element of G such that a has order 3. Prove that G is isomorphic to either the cyclic group C9 or the non-abelian group of order 9.",
    "output": "Since G has order 9, by the Sylow theorems, G has a subgroup of order 3. Let H be a subgroup of G generated by the element a, so H = {e, a, a^2} where e is the identity element. Since a has order 3, H is a cyclic group of order 3.\n\nNow, consider the quotient group G/H. Since |G| = 9 and |H| = 3, we have |G/H| = 9/3 = 3. Thus, G/H is a cyclic group of order 3. Let G/H = {H, bH, b^2H} where b is an element of G not in H.\n\nNow, we have two cases to consider:\n\nCase 1: G is abelian.\nIn this case, G is the direct product of its subgroups H and the subgroup generated by b. Since H is a cyclic group of order 3 and the subgroup generated by b is a cyclic group of order 3, G is isomorphic to the cyclic group C9.\n\nCase 2: G is non-abelian.\nIn this case, we can show that G is isomorphic to the non-abelian group of order 9. Define a multiplication operation on G by (a^i, b^j) * (a^k, b^l) = (a^(i+k), b^(j+l) * a^(jk)) for i, j, k, l = 0, 1, 2. This operation is well-defined, associative, and has an identity element (e, e). Moreover, every element in G has an inverse under this operation.\n\nNow, we can define a map \u03c6: G \u2192 G' given by \u03c6(a^i * b^j) = (a^i, b^j), where G' is the group with the above-defined multiplication operation. \u03c6 is a homomorphism, and it is easy to see that it is injective and surjective. Therefore, \u03c6 is an isomorphism, and G is isomorphic to the non-abelian group of order 9.\n\nIn conclusion, G is either isomorphic to the cyclic group C9 or the non-abelian group of order 9."
  },
  {
    "source": "data/CoT/gsm_rft.json",
    "instruction": "Joe buys 3 oranges, 7 juices, 3 jars of honey, and 4 plants at the market. The fruit costs $4.50 each, the juice was 50 cents each, the jars of honey were $5, and the plants were 2 for $18. How much does Joe spend at the market?",
    "output": "Joe spends 4.50 * 3 = 13.50 on oranges.\nJoe spends 7 * .50 = 3.50 on juice.\nJoe spends 3 * 5 = 15 on honey.\nEach plant costs 18 / 2 = 9 dollars.\nJoe spends 9 * 4 = 36 dollars on plants.\nJoe spends a total of 13.50 + 3.50 + 15 + 36 = 68 dollars at the market.\nThe answer is 68"
  },
  {
    "source": "data/CoT/gsm_rft.json",
    "instruction": "Cynthia has four times as many water balloons as her husband, Randy. Randy has only half as many water balloons as his daughter, Janice. If Janice throws all 6 of her water balloons at her father, how many water balloons does Cynthia have, which she could also choose to throw at Randy?",
    "output": "Randy has only half as many water balloons as Janice\u2019s 6, for a total of (\u00bd)*6=3 water balloons.\nCynthia has 4 times as many water balloons as Randy, for a total of 4*3=12 water balloons that Cynthia has, which she could throw at Randy.\nThe answer is 12"
  },
  {
    "source": "data/PoT/MATH_train.json",
    "instruction": "For each positive integer $n$, let $f(n) = n^4 - 360n^2 + 400$. What is the sum of all values of $f(n)$ that are prime numbers? Please respond by writing a program in Python.",
    "output": "import sympy as sp\n\n# define the function\ndef f(n):\n    return n**4 - 360*n**2 + 400\n\n# initialize the sum\nsum_primes = 0\n\n# loop over the positive integers\nfor n in range(1, 100): # we are choosing 100 as the upper limit, as it is not mentioned in the problem\n    # calculate the value of the function\n    val = f(n)\n    # check if it is a prime number\n    if sp.isprime(val):\n        # if it is, add it to the sum\n        sum_primes += val\n\n# print the result\nprint(sum_primes)"
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "Consider a graph G with 10 vertices and 16 edges. Determine the treewidth of G.",
    "output": "To determine the treewidth of a graph G with 10 vertices and 16 edges, we can use the following approach:\n\n1. Find an upper bound for the treewidth using the maximum degree of the graph.\n2. Check if the graph can be decomposed into a tree of smaller cliques (subgraphs where every vertex is connected to every other vertex) with the determined treewidth.\n\nStep 1: Find an upper bound for the treewidth\nThe maximum number of edges in a simple graph with 10 vertices is given by the formula n(n-1)/2, where n is the number of vertices. In this case, n = 10, so the maximum number of edges is 10(9)/2 = 45. Since G has 16 edges, it is not a complete graph (a graph where every vertex is connected to every other vertex).\n\nThe maximum degree of a vertex in G is at most 8 (since it cannot be connected to itself). According to the degree-based upper bound for treewidth, the treewidth is at most the maximum degree, so the treewidth of G is at most 8.\n\nStep 2: Check if the graph can be decomposed into a tree of smaller cliques\nTo determine if the graph can be decomposed into a tree of smaller cliques, we can use the following approach:\n\n1. Start with the treewidth upper bound (8 in this case).\n2. Check if it is possible to decompose the graph into a tree of cliques with the current treewidth.\n3. If it is not possible, decrease the treewidth by 1 and repeat step 2.\n\nSince we don't have the exact structure of the graph, we cannot perform this step directly. However, we can provide some general observations:\n\n- If the graph is connected and has a treewidth of 8, it means that there is a tree decomposition where each bag (node in the tree decomposition) contains a clique of size 9 (treewidth + 1).\n- If the graph is not connected, its treewidth is the maximum treewidth of its connected components.\n\nIn conclusion, without knowing the exact structure of the graph, we can only determine that the treewidth of G is at most 8. To find the exact treewidth, more information about the graph's structure is needed."
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "By the how much is two-fifth of 200 greater than three -fifths of 25?\nAnswer Choices: (A) 15 (B) 3 (C) 5 (D) 30 (E) 65",
    "output": "Let's think about the multi-choice question step by step.\nReqd no. = 2\u00e2\u0081\u201e5 \u00c3\u2014 200 - 3\u00e2\u0081\u201e5 \u00c3\u2014 25\n= 80 - 15 = 65\nThe answer is E"
  },
  {
    "source": "data/CoT/gsm_train.json",
    "instruction": "John is trying to save money by buying cheap calorie-dense food.  He can buy 10 burritos for $6 that have 120 calories each.  He could also buy 5 burgers that are 400 calories each for $8.  How many more calories per dollar does he get from the burgers?",
    "output": "The burritos have 10*120=1200 calories\nThat means he gets 1200/6=200 calories per dollar\nThe burgers get 5*400=2000 calories\nSo he gets 2000/8=250 calories per dollar\nSo he gets 250-200=50 more calories per dollar from the burgers\nThe answer is 50"
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "If Sin(\u03b8) = 0.6, find the values of Cos(\u03b8) and Tan(\u03b8).",
    "output": "To find the values of Cos(\u03b8) and Tan(\u03b8) when Sin(\u03b8) = 0.6, we can use the Pythagorean identity and the definition of tangent.\n\n1. Pythagorean identity: Sin\u00b2(\u03b8) + Cos\u00b2(\u03b8) = 1\n2. Definition of tangent: Tan(\u03b8) = Sin(\u03b8) / Cos(\u03b8)\n\nFirst, we'll find the value of Cos(\u03b8) using the Pythagorean identity:\n\nSin\u00b2(\u03b8) + Cos\u00b2(\u03b8) = 1\n(0.6)\u00b2 + Cos\u00b2(\u03b8) = 1\n0.36 + Cos\u00b2(\u03b8) = 1\nCos\u00b2(\u03b8) = 1 - 0.36\nCos\u00b2(\u03b8) = 0.64\n\nNow, we'll find the square root of both sides to get the value of Cos(\u03b8). Note that there are two possible values for Cos(\u03b8) since it can be positive or negative:\n\nCos(\u03b8) = \u00b1\u221a0.64\nCos(\u03b8) = \u00b10.8\n\nNow, we'll find the value of Tan(\u03b8) using the definition of tangent:\n\nTan(\u03b8) = Sin(\u03b8) / Cos(\u03b8)\n\nCase 1: Cos(\u03b8) = 0.8\nTan(\u03b8) = 0.6 / 0.8\nTan(\u03b8) \u2248 0.75\n\nCase 2: Cos(\u03b8) = -0.8\nTan(\u03b8) = 0.6 / -0.8\nTan(\u03b8) \u2248 -0.75\n\nSo, the values of Cos(\u03b8) are \u00b10.8, and the values of Tan(\u03b8) are approximately \u00b10.75."
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "What number should replace the question mark?\n24, 30, ?, 60, 84, 114\nAnswer Choices: (A) 45 (B) 44 (C) 48 (D) 42 (E) 49",
    "output": "D\n42\nThe sequence progresses +6, +12, +18, +24, +30."
  },
  {
    "source": "data/PoT/mathqa.json",
    "instruction": "what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 50 % ? Let's write a Python program.",
    "output": "n0 = 50.0\nt0 = n0 / 100.0\nt1 = t0 + 1.0\nt2 = t1**min(2.0, 5)\nt3 = t2 - 1.0\nanswer = t3 * 100.0\nprint(answer)"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "What is the smallest no. that should be added to 45454 to make it exactly divisible by 9?\nAnswer Choices: (A) 1 (B) 3 (C) 5 (D) 6 (E) 9",
    "output": "Let's think about the multi-choice question.\nIf a number is divisible by 9, the sum of its digits must be a multiple of 9.\nHere, 4+5+4+5+4=22, the next multiple of 9 is 27.\n5 must be added to 45454 to make it divisible by 9\nThe answe is C"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?\nAnswer Choices: (A) 1000 (B) 2996 (C) 2686 (D) 1028 (E) 1013",
    "output": "Let's think about the multi-choice question step by step.\n90%\n104%\n--------\n14% ---- 140\n100% ---- ? => Rs.1000\nThe answer is A"
  },
  {
    "source": "data/CoT/MATH_train.json",
    "instruction": "Given positive integers $x$ and $y$ such that $x\\neq y$ and $\\frac{1}{x} + \\frac{1}{y} = \\frac{1}{18}$, what is the smallest possible value for $x + y$?",
    "output": "Simplifying, we have  $18(x+y)=xy$, so $xy - 18x - 18y = 0$ Applying Simon's Favorite Factoring Trick by adding 324 to both sides, we get $xy-18x-18y +324=324$, so \\[(x-18)(y-18)=324.\\]Now we seek the minimal $x+y,$ which occurs when $x-18$ and $y-18$ are as close to each other in value as possible. The two best candidates are $(x-18,y-18)=(12,27)$ or $(9,36),$ of which $(x,y)=(30,45)$ attains the minimum sum of $\\boxed{75}$. The answer is 75"
  },
  {
    "source": "data/CoT/gsm_rft.json",
    "instruction": "Barry, Thomas and Emmanuel are to share a jar of 200 jelly beans. If Thomas takes 10%, and Barry and Emmanuel are to share the remainder in the ratio 4:5 respectively, how many jelly beans will Emmanuel get?",
    "output": "10% of 200 jelly beans is (10/100)*200 = 20\nThomas takes 20 jelly beans leaving 200-20 = 180 jelly beans\n180 jelly beans are to be shared in the ratio 4:5 so each share is 180/(4+5) = 20 jelly beans\nEmmanuel gets 5 shares which is 5*20 = 100\nThe answer is 100"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "Which one of the following numbers is a solution of the equation\n(x(2sq)-2)(x(2sq) + 6)(x(third3)-8) = 0?\nAnswer Choices: (A) 1 (B) 2 (C) 3 (D) 4 (E) 5",
    "output": "Let's think about the multi-choice question.\nOne checks each of the ve given possible answers. Since 2-3third- - 8 = 0, the answer\nis 2.\nThe answer is B"
  },
  {
    "source": "data/PoT/numglue.json",
    "instruction": " \"statement 1\": How much loss would Indu has suffered had she given it to Bindu for 2 years at 4 % per annum simple interest ?, \"statement 2\" :How much loss would Indu has suffered had she given it to Bindu for less than 7 years at 4 % per annum simple interest ?, \"options: \" Entailment or contradiction or neutral? Please write a program to solve it",
    "output": "indu_loss_s1 = 2\nindu_loss_s2 = 7\n \nif indu_loss_s1 is None or indu_loss_s2 is None:\n print('neutral')\n\nelif indu_loss_s1 < indu_loss_s2:\n print('Entailment')\n\nelif indu_loss_s1 != indu_loss_s2:\n print('contradiction')"
  },
  {
    "source": "data/PoT/numglue.json",
    "instruction": "Jack starts with 62.0 marbles. Rebecca shares 33.0 with him. How many marbles does Jack end with. Let's program in Python in the response.",
    "output": "jack_marbles = 62\r\nrebecca_marbles = 33\r\n\r\ntotal_marbles = jack_marbles + rebecca_marbles\r\n\r\nprint(total_marbles)"
  },
  {
    "source": "data/PoT/mathqa.json",
    "instruction": "each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 26 have long fur , 22 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ? Let's write a Python program.",
    "output": "n0 = 45.0\nn1 = 26.0\nn2 = 22.0\nn3 = 8.0\nt0 = n1 + n2\nt1 = n0 - n3\nanswer = t0 - t1\nprint(answer)"
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "A company has four factories, and it wants to know if there is a difference in the average output between them. The daily production data (in thousands of units) for the 4 factories over a week is given below:\n\nFactory 1: 15, 18, 20, 17, 19, 16, 18\nFactory 2: 21, 23, 19, 20, 22, 23, 21\nFactory 3: 17, 16, 18, 19, 20, 16, 18\nFactory 4: 13, 15, 14, 16, 17, 16, 15\n\nUsing one-way ANOVA, determine whether there are any significant differences in the mean production levels of the four factories. Use an alpha level of 0.05.",
    "output": "To perform a one-way ANOVA, we first need to calculate the means and variances for each factory, as well as the overall mean.\n\nFactory 1:\nMean (M1) = (15+18+20+17+19+16+18)/7 = 17.57\nVariance (V1) = [(15-17.57)^2 + (18-17.57)^2 + ... + (18-17.57)^2]/6 = 3.81\n\nFactory 2:\nMean (M2) = (21+23+19+20+22+23+21)/7 = 21.29\nVariance (V2) = [(21-21.29)^2 + (23-21.29)^2 + ... + (21-21.29)^2]/6 = 2.24\n\nFactory 3:\nMean (M3) = (17+16+18+19+20+16+18)/7 = 17.71\nVariance (V3) = [(17-17.71)^2 + (16-17.71)^2 + ... + (18-17.71)^2]/6 = 2.19\n\nFactory 4:\nMean (M4) = (13+15+14+16+17+16+15)/7 = 15.14\nVariance (V4) = [(13-15.14)^2 + (15-15.14)^2 + ... + (15-15.14)^2]/6 = 2.19\n\nOverall Mean (M) = (17.57 + 21.29 + 17.71 + 15.14)/4 = 17.93\n\nNow, we can calculate the between-group variance (MSG) and within-group variance (MSE).\n\nMSG = [(17.57-17.93)^2 + (21.29-17.93)^2 + (17.71-17.93)^2 + (15.14-17.93)^2]/(4-1) = 30.47\n\nMSE = (3.81 + 2.24 + 2.19 + 2.19)/(4*(7-1)) = 0.36\n\nNow, we can calculate the F-statistic:\n\nF = MSG/MSE = 30.47/0.36 = 84.64\n\nUsing an F-distribution table with degrees of freedom between groups (df1) = 4-1 = 3 and within groups (df2) = 4*(7-1) = 24, we can find the critical F-value for an alpha level of 0.05.\n\nF_critical (0.05, 3, 24) \u2248 3.01\n\nSince F = 84.64 > F_critical = 3.01, we reject the null hypothesis that there is no significant difference in the mean production levels of the four factories. There is evidence to suggest that there are significant differences in the mean production levels of the factories at the 0.05 alpha level."
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "Consider the rational curve in the projective plane with equation: $C: (t^3-3t^2+3t: t^2-2t :1)$.\nFind the intersection of this curve with the line $l: y=z=0$.",
    "output": "To find the intersection of the curve $C$ with the line $l$, we need to find the points on the curve that satisfy the equation of the line. The line $l$ has the equation $y=z=0$. In the projective plane, we can write this line as $[x:0:0]$. \n\nNow, let's find the points on the curve $C$ that satisfy this condition. The curve $C$ is given by the parametric equations:\n\n$x(t) = t^3 - 3t^2 + 3t$\n$y(t) = t^2 - 2t$\n$z(t) = 1$\n\nWe want to find the values of $t$ for which $y(t) = z(t) = 0$. \n\nFirst, let's solve $y(t) = 0$:\n\n$t^2 - 2t = 0$\n$t(t - 2) = 0$\n\nThis gives us two possible values for $t$: $t = 0$ and $t = 2$.\n\nNow, let's check if these values also satisfy $z(t) = 0$. However, we see that $z(t) = 1$ for all values of $t$, so there are no points on the curve $C$ that satisfy both $y(t) = 0$ and $z(t) = 0$. \n\nTherefore, the curve $C$ does not intersect the line $l$."
  },
  {
    "source": "data/PoT/numglue.json",
    "instruction": "Sandy went to the mall to buy clothes. She spent $13.99 on shorts, $12.14 on a shirt, and $7.43 on a jacket. Sandy spent $_____ on clothes. Please respond by writing a program in Python.",
    "output": "Short = 13.99\r\nShirt = 12.14\r\nJacket = 7.43\r\nprint(Short+Shirt+Jacket)"
  },
  {
    "source": "data/PoT/mathqa.json",
    "instruction": "a boy wanted to calculate his speed on his bike . his starting point was 350 meters from the turning point . he made the round trip 5 times in 30 minutes . what was the boy ' s speed in kilometers per hour ? Let's write a program.",
    "output": "n0 = 350.0\nn1 = 5.0\nn2 = 30.0\nt0 = n0 / 1000.0\nanswer = n1 * t0\nprint(answer)"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "A table is bought for Rs.400/- and sold at Rs.300/- find gain or loss percentage\nAnswer Choices: (A) 25%loss (B) 30%gain (C) 25%gain (D) 10%loss (E) 50% loss",
    "output": "Let's think about the multi-choice question.\nFormula = (Selling price ~ Cost price)/Cost price * 100\n= (300 - 400)/400 = 25% loss\nThe answe is A"
  },
  {
    "source": "data/CoT/gsm_rft.json",
    "instruction": "The sum of the ages of Jeremy, Sebastian and Sophia in three years is 150. Currently, Sebastian is 4 years older than Jeremy. If Jeremy's age is 40, calculate Sophia's age three years from now?",
    "output": "The age of Jeremy three years from now will be 40+3 = 43\nIf Sebastian age is four years more than Jeremy's, Sebastian is currently 40+4 = 44 years.\nIn three years, Sebastian will be 44+3 = 47 years.\nThe age of Jeremy and Sebastian in three years will be 43+47 = 90\nThe total age of Jeremy, Sebastian and Sophia in three years will be 150, meaning Sophia's age in three years will be 150-90 = 60\nThe answer is 60"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,74,000 through the lagaan from the village of Mutter. Mutter, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mutter over the total taxable land of the village is:\nAnswer Choices: (A) 0.20833 (B) 0.14544 (C) 0.25632 (D) 0.2139 (E) 0.63435",
    "output": "Let's think about the multi-choice question step by step.\nTotal land of Sukhiya = \\inline \\frac{480x}{0.6} = 800x\n\\therefore Cultivated land of village = 374000x\n\\therefore Required percentage = \\inline \\frac{800x}{374000}\\times 100 = 0.21390\nThe answe is D"
  },
  {
    "source": "data/PoT/numglue.json",
    "instruction": " \"statement 1\": While Kiran playing all but 3 got destroyed, \"statement 2\" :While Kiran playing all but 8 got destroyed, \"options: \" Entailment or contradiction or neutral? Let's program in Python in the response.",
    "output": "kiran_destroyed_s1 = 3\nkiran_destroyed_s2 = 8\n \nif kiran_destroyed_s1 is None or kiran_destroyed_s2 is None:\n print('neutral')\n\nelif kiran_destroyed_s1 == kiran_destroyed_s2:\n print('Entailment')\n\nelif kiran_destroyed_s1 != kiran_destroyed_s2:\n print('contradiction')"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "A water tank, having the shape of a rectangular prism of base 100 square centimeters, is being filled at the rate of 1 liter per minute. Find the rate at which the height of the water in the water tank increases. Express your answer in centimeters per minute.\nAnswer Choices: (A) 40 cm/m (B) 15 cm/m (C) 10 cm/m (D) 35 cm/m (E) 20 cm/m",
    "output": "Let's reason about the multi-choice question.\nThe volume of a rectangular prism is given by\narea of base ? height\nThe rate at which the tank is being filled is 1 liter per minute which we need to convert\n1 liter = 1 dm3\nBut 1 dm = 10 cm. Hence\n1 liter = (10 cm)3 = 1000 cm3\nThe height h of the water is related to the volume by\nvolume = area of base ? h\nIn one minute the volume increases by 1 liter or 1000 cm3 and the height increases by\nh = volume / area of base = 1000 cm3 / 100 cm2 = 10 cm\nThe answer is C"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other\nwithout replacement. What is the probability that both drawn balls are black?\nAnswer Choices: (A) 1/5 (B) 3/7 (C) 2/5 (D) 3/5 (E) 2/7",
    "output": "Let's think about the multi-choice question step by step.\nLet E and F denote respectively the events that first and second ball drawn\nare black. We have to find P(E n F) or P (EF).\nNow PE = P (black ball in first draw) = 10/15\nAlso given that the first ball drawn is black, i.e., event E has occurred, now there are 9 black balls and five white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.\nThat is P(F|E) = 9/14\nBy multiplication rule of probability, we have\nP (E n F) = PE P(F|E)\n= 10/15 \u00d7 9/14 = 3/7\nThe answe is B"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "If t,u, and v are positive integers and 2t=2u+2v, which of the following must be true?\ni. t=u\nii. u is not equal to v\niii. t > v\nAnswer Choices: (A) None (B) I only (C) II only (D) III and I (E) III only",
    "output": "Let's think about the multi-choice question step by step.\nNotice two things: 1. we are asked to find out which of the following MUST be true, not COULD be true and 2. t, u, and v are positive integers.\nGiven: 2st=2u+2v --> t=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. So, we have that only option III must be true.\nThe answer is E"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "If six persons sit in a row, then the probability that three particular persons are always together is\nAnswer Choices: (A) 1/5 (B) 1/8 (C) 1/5 (D) 1/3 (E) 1/1",
    "output": "Let's think about the multi-choice question.\nSix persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5.The answer is C"
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "A certain technology has a 10% chance of failing within the first year of use. If a company purchases 50 of these technologies, what is the probability that less than 5 of them will fail within the first year?",
    "output": "To solve this problem, we can use the binomial probability formula, which is:\n\nP(X = k) = (n choose k) * p^k * (1-p)^(n-k)\n\nwhere n is the number of trials (in this case, the number of technologies purchased), k is the number of successes (in this case, the number of failed technologies), p is the probability of success (in this case, the probability of a technology failing within the first year), and (n choose k) is the number of combinations of n items taken k at a time.\n\nSince we want to find the probability that less than 5 of the technologies will fail within the first year, we need to calculate the sum of the probabilities for 0, 1, 2, 3, and 4 failures:\n\nP(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)\n\nWe can plug in the values for n, p, and k into the binomial probability formula and calculate the probabilities:\n\nn = 50 (number of technologies purchased)\np = 0.1 (probability of a technology failing within the first year)\n\nP(X = 0) = (50 choose 0) * 0.1^0 * (1-0.1)^(50-0)\nP(X = 1) = (50 choose 1) * 0.1^1 * (1-0.1)^(50-1)\nP(X = 2) = (50 choose 2) * 0.1^2 * (1-0.1)^(50-2)\nP(X = 3) = (50 choose 3) * 0.1^3 * (1-0.1)^(50-3)\nP(X = 4) = (50 choose 4) * 0.1^4 * (1-0.1)^(50-4)\n\nNow, we can calculate the probabilities and sum them up:\n\nP(X < 5) \u2248 0.0295 + 0.1454 + 0.2668 + 0.2817 + 0.2002\nP(X < 5) \u2248 0.9236\n\nSo, the probability that less than 5 of the 50 technologies will fail within the first year is approximately 92.36%."
  },
  {
    "source": "data/CoT/gsm_rft.json",
    "instruction": "Cindy tosses 5 dimes into the wishing pond.  Eric flips 3 quarters into the pond.  Garrick throws in 8 nickels.  Ivy then drops 60 pennies in.  If Eric dips his hands into the water and pulls out a quarter, how much money, in cents, did they put into the pond?",
    "output": "Cindy puts in 10 cents x 5 = 50 cents.\nEric puts in 25 cents x 3 = 75 cents.\nGarrick puts in 5 cents x 8 = 40 cents.\nIvy puts in 1 cent x 60 = 60 cents.\nWhen Eric pulls out a quarter, he removes 25 cents from the pond.\nIn total, they put into the pond, and left in the pond, 50 + 75 + 40 + 60 - 25 = 200 cents.\nThe answer is 200"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "How many trailing Zeroes does 53! + 54! have?\nAnswer Choices: (A) 12 (B) 13 (C) 14 (D) 15 (E) 16",
    "output": "Let's think about the multi-choice question.\n53! + 54! = 53! + 54 * 53!\n= 53! (1 + 54)\n= 53! * 55\nNumber of trailing 0s in 53! = number of 5s in the expansion of 53!\n= 10 + 2 = 12\nThere is 1 more 5 in 55.\nHence, total number of trailing 0s = 12 + 1 = 13\nThe answer is B"
  },
  {
    "source": "data/CoT/gsm_train.json",
    "instruction": "Randy had $3,000. Smith gave him another $200. Randy then gave Sally $1,200 and kept the rest. What was the value, in dollars, of the rest?",
    "output": "After Smith gave him $200, Randy had 3000+200=3200 dollars.\nThe value of the rest of the money is 3200-1200=2000 dollars.\nThe answer is 2000"
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "Suppose $E \\to \\mathbb{R}P^2$ is a real vector bundle where $\\mathbb{R}P^2$ is the real projective plane. If we know that $E$ is a rank-2 vector bundle, and that its total Chern class is $1 + 3H$, where $H$ is the hyperplane class, what is the Euler characteristic of $E$?",
    "output": "To compute the Euler characteristic of the vector bundle $E$, we can use the formula:\n\n$$\\chi(E) = \\int_{\\mathbb{R}P^2} e(E),$$\n\nwhere $e(E)$ is the Euler class of $E$. Since $E$ is a rank-2 vector bundle, we can express its total Chern class as:\n\n$$c(E) = 1 + c_1(E) + c_2(E),$$\n\nwhere $c_1(E)$ and $c_2(E)$ are the first and second Chern classes, respectively. We are given that $c(E) = 1 + 3H$, so we can deduce that $c_1(E) = 3H$ and $c_2(E) = 0$.\n\nNow, we can compute the Euler class using the relation between the Euler class and the Chern classes for a rank-2 vector bundle:\n\n$$e(E) = c_1(E)^2 - 2c_2(E).$$\n\nSince $c_1(E) = 3H$ and $c_2(E) = 0$, we have:\n\n$$e(E) = (3H)^2 - 2(0) = 9H^2.$$\n\nNow, we need to integrate this over $\\mathbb{R}P^2$. Recall that the cohomology ring of $\\mathbb{R}P^2$ is given by:\n\n$$H^*(\\mathbb{R}P^2) = \\mathbb{Z}[H]/(H^3),$$\n\nwhere $H$ is the hyperplane class and has degree 1. Thus, $H^2$ has degree 2, and the integral of $9H^2$ over $\\mathbb{R}P^2$ is simply the coefficient of $H^2$ in the expression, which is 9:\n\n$$\\chi(E) = \\int_{\\mathbb{R}P^2} e(E) = \\int_{\\mathbb{R}P^2} 9H^2 = 9.$$\n\nSo, the Euler characteristic of the vector bundle $E$ is 9."
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "Two positive integers differ by 4, and sum of their reciprocals is 5 Then one of the numbers is\nAnswer Choices: (A) a)  3 (B) b)  1 (C) c)  5 (D) d)  21 (E) 4",
    "output": "Let's think about the multi-choice question step by step.\nAlgebraic approach:\nLet n be the smaller integer => 1/n + 1/(n+4) = 5\nor ((n+4)+n)/n(n+4) =6 or (n^2+4n)*5 =2n+4 or n=2 as n cannot be -negative\nSolve for n => n=4. Hence,\nThe answe is E"
  },
  {
    "source": "data/PoT/mathqa.json",
    "instruction": "a flagpole 18 meters high casts a shadow of length 45 meters . if a building under similar conditions casts a shadow of length 65 meters , what is the height of the building ( in meters ) ? Please write a program to solve it",
    "output": "n0 = 18.0\nn1 = 45.0\nn2 = 65.0\nt0 = n0 / n1\nanswer = n2 * t0\nprint(answer)"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "There are 99 people that own pets. 15 people own only dogs, 10 people own only cats, 5 people own only cats and dogs, 3 people own cats, dogs and snakes. How many total snakes are there?\nAnswer Choices: (A) 2 (B) 4 (C) 8 (D) 69 (E) 32",
    "output": "Let's think about the multi-choice question step by step.\nlets assign variables to all the areas in Venn Diagram of Three.\nthree different Units are DOG, Cat, Snake= Total = 99\nOnly Dog= d=15\nOnly Cat = c=10\nOnly Snake = s\nExactly Dog and Cat= 5\nExactly Dog and Snake = x\nExactly Cat and Snake = y\nall three= 3\nso 99=15+10+5+3+x+y+s\nwe need to know total snakes= x+y+s+3 = 69\nThe answer is D"
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "What is the Euler characteristic of the closed orientable surface formed by gluing together two M\u00f6bius strips along their common boundary?\n\nAnswer:\n\nThe Euler characteristic of the surface is -2.",
    "output": "To find the Euler characteristic of the closed orientable surface formed by gluing together two M\u00f6bius strips along their common boundary, we can use the formula:\n\nEuler characteristic (\u03c7) = vertices (V) - edges (E) + faces (F)\n\nFirst, let's analyze the M\u00f6bius strip. A M\u00f6bius strip has one boundary, one face, and no vertices. When we glue two M\u00f6bius strips together along their common boundary, we form a closed surface called the Klein bottle.\n\nNow, let's analyze the Klein bottle. The Klein bottle has no vertices, as it is a smooth surface. It has three edges: the two original edges of the M\u00f6bius strips and the new edge formed by gluing them together. Finally, it has two faces: the two original faces of the M\u00f6bius strips.\n\nUsing the Euler characteristic formula for the Klein bottle:\n\n\u03c7 = V - E + F\n\u03c7 = 0 - 3 + 2\n\u03c7 = -1\n\nHowever, the question asks for the Euler characteristic of the closed orientable surface formed by gluing together two M\u00f6bius strips. The Klein bottle is a non-orientable surface. To obtain an orientable surface, we need to take two copies of the Klein bottle and glue them together along their boundaries. This new surface is called the connected sum of two Klein bottles.\n\nFor the connected sum of two Klein bottles, we have:\n\nVertices (V) = 0 (still no vertices)\nEdges (E) = 6 (each Klein bottle has 3 edges, so 3 + 3 = 6)\nFaces (F) = 4 (each Klein bottle has 2 faces, so 2 + 2 = 4)\n\nNow, we can find the Euler characteristic of the connected sum of two Klein bottles:\n\n\u03c7 = V - E + F\n\u03c7 = 0 - 6 + 4\n\u03c7 = -2\n\nSo, the Euler characteristic of the closed orientable surface formed by gluing together two M\u00f6bius strips along their common boundary is -2."
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "A math student needs to find the general solution of the partial differential equation:\n\n$$\\frac{\\partial u}{\\partial \\bar{z}}=0$$\n\nwhere $u(x,y)$ is a complex-valued function of $z=x+iy$. \n\nWhat is the general solution of this partial differential equation?",
    "output": "To find the general solution of the given partial differential equation, we first need to express the derivative with respect to the complex conjugate $\\bar{z}$ in terms of the partial derivatives with respect to $x$ and $y$. Recall that:\n\n$$\\frac{\\partial}{\\partial z} = \\frac{1}{2} \\left(\\frac{\\partial}{\\partial x} - i \\frac{\\partial}{\\partial y}\\right)$$\n\nand\n\n$$\\frac{\\partial}{\\partial \\bar{z}} = \\frac{1}{2} \\left(\\frac{\\partial}{\\partial x} + i \\frac{\\partial}{\\partial y}\\right)$$\n\nNow, we can rewrite the given partial differential equation as:\n\n$$\\frac{1}{2} \\left(\\frac{\\partial u}{\\partial x} + i \\frac{\\partial u}{\\partial y}\\right) = 0$$\n\nThis equation can be separated into its real and imaginary parts:\n\n$$\\frac{\\partial u}{\\partial x} = 0$$\n$$\\frac{\\partial u}{\\partial y} = 0$$\n\nThese equations tell us that the function $u(x, y)$ is constant with respect to both $x$ and $y$. Therefore, the general solution of the partial differential equation is:\n\n$$u(x, y) = C$$\n\nwhere $C$ is a complex constant."
  },
  {
    "source": "data/CoT/MATH_train.json",
    "instruction": "Two cylindrical cans have the same volume. The height of one can is triple the height of the other. If the radius of the narrower can is 12 units, how many units are in the length of the radius of the wider can? Express your answer in simplest radical form.",
    "output": "Let the height of the wide can be $h$ and the height of the narrow can be $3h$.  Let the wide can have radius $x$ units.  Since the two volumes are equal, we have \\[\\pi (12^2) (3h) = \\pi (x^2) (h).\\] Solving yields $x = 12\\sqrt{3}$ so the wide can has radius $\\boxed{12\\sqrt{3}}$ units. The answer is 12\\sqrt{3}"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "The average weights for Tom,Jack,Rose was 90kg. The average weights for Jack,Rose,John was 100kg. If the weight of John be 50kg, what was the weight of Tom?\nAnswer Choices: (A) 20 (B) 44 (C) 37 (D) 42 (E) None of these",
    "output": "Let's think about the multi-choice question.\nT + J + R = 90 \u00d7 3 = 270\nJ+R+J = 100\u00d7 3 = 300\nAlso, weight of John = 50\nWeight of Tom = 270+50-300 =20kg\nThe answer is Option A"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?\nAnswer Choices: (A) 1000 (B) 3000 (C) 2000 (D) 4000 (E) 5000",
    "output": "Let's think about the multi-choice question.\nLet the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.\nThen, 4x - 3x = 1000\nx = 1000.\nB's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.\nThe answer is C."
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "There are 3 couples. If they will sit 6 chairs in a row such that each couple sits side by side, how many possible cases are there?\nAnswer Choices: (A) 48 (B) 240 (C) 1,200 (D) 2,460 (E) 3,840",
    "output": "Let's think about the multi-choice question.\nTie the couples. Then we have 3 persons that have to be arranged in 3 places. 3! ways.\nNow the couples can change position with each other. 2! ways.\n3! * (2!)^3 = 6*8= 48\nThe answer is A."
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "which number need to add to 859622 to get a number exactly divisible by 456?\nAnswer Choices: (A) 678311 (B) 546576 (C) 465767 (D) 678980 (E) 859622",
    "output": "Let's reason about the multi-choice question.\nDividend = Quotient * Divisor + Reminder\n859622 / 456 gives quotient = 1885 and reminder = 62.\nSo, the next number divisible by 456 is 456 places infront of 456 * 1885\nWhich means 456 \u2013 62 = 394 should be added to 859622.\nThe answe is E"
  },
  {
    "source": "data/CoT/gsm_rft.json",
    "instruction": "If olivine has 5 more precious stones than agate and diamond has 11 more precious stones than olivine, how many precious stones do they have together if agate has 30 precious stones?",
    "output": "Since Agate has 30 precious stones and Olivine has 5 more precious stones than Agate, then Olivine has 30+5 = 35 precious stones.\nThe total number of stones Olivine and Agate has is 35+30 = 65\nDiamond has 11 more precious stones than Olivine, who has 35 stones, meaning Diamond has 35+11 = 46 precious stones.\nTogether, the three have 65+46 = 111 precious stones.\nThe answer is 111"
  },
  {
    "source": "data/PoT/numglue.json",
    "instruction": " \"statement 1\": Peter purchased less than 40 kg of rice at the rate of $ 11.50 per kg and 20 kg of rice at the rate of 14.25 per kg, \"statement 2\" :Peter purchased 30 kg of rice at the rate of $ 11.50 per kg and 20 kg of rice at the rate of 14.25 per kg, \"options: \" Entailment or contradiction or neutral? Please write a program to solve it",
    "output": "\r\nkg_of_rice_s1 = None\r\nkg_of_rice_s2 = 30\r\n\r\nif kg_of_rice_s1 is None or kg_of_rice_s2 is None:\r\n   print('neutral')\r\n\r\nelif kg_of_rice_s1 == kg_of_rice_s2:\r\n   print('Entailment')\r\n\r\nelif kg_of_rice_s1 != kg_of_rice_s2:\r\n  print('contradiction')"
  },
  {
    "source": "data/PoT/mathqa.json",
    "instruction": "how many zeros does 1000 ! end with ? Please respond by writing a program in Python.",
    "output": "n0 = 1000.0\nt0 = 1.0 + 4.0\nt1 = n0 / t0\nt2 = t0**min(2.0, 5)\nt3 = t0**min(3.0, 5)\nt4 = n0 - t0\nt5 = t4 / t2\nt6 = t4 / t3\nt7 = t1 + t5\nanswer = t7 + t6\nprint(answer)"
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "Find the derivative of f(x) = (2x^3 + 3x^2 - 4x + 1)^4 using the chain rule.",
    "output": "To find the derivative of f(x) = (2x^3 + 3x^2 - 4x + 1)^4 using the chain rule, we first identify the outer function and the inner function. In this case, the outer function is g(u) = u^4 and the inner function is h(x) = 2x^3 + 3x^2 - 4x + 1.\n\nThe chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. Mathematically, this is written as:\n\nf'(x) = g'(h(x)) * h'(x)\n\nFirst, we find the derivatives of the outer and inner functions:\n\ng'(u) = d(u^4)/du = 4u^3\nh'(x) = d(2x^3 + 3x^2 - 4x + 1)/dx = 6x^2 + 6x - 4\n\nNow, we apply the chain rule:\n\nf'(x) = g'(h(x)) * h'(x) = 4(2x^3 + 3x^2 - 4x + 1)^3 * (6x^2 + 6x - 4)\n\nSo, the derivative of f(x) = (2x^3 + 3x^2 - 4x + 1)^4 with respect to x is:\n\nf'(x) = 4(2x^3 + 3x^2 - 4x + 1)^3 * (6x^2 + 6x - 4)"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "A train 220 m long passed a pole in 22 sec. How long will it take to pass a platform 550 m long?\nAnswer Choices: (A) 77 (B) 82 (C) 43 (D) 67 (E) 29",
    "output": "Let's think about the multi-choice question step by step.\nSpeed = 220/22 = 10 m/sec.\nRequired time = (220 + 550)/10 = 77 sec.\nThe answer is A"
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "Here's a precise numerical problem for a math student to solve in the context of game theory:\n\nSuppose there are two players competing in a game of rock-paper-scissors, and each player has to choose whether to play rock, paper, or scissors. The payoff matrix for this game is:\n\n|         | Rock | Paper | Scissors |\n|---------|------|-------|----------|\n| Rock    | 0    | -1    | 1        |\n| Paper | 1    | 0      | -1       |\n| Scissors | -1   | 1      | 0        |\n\nAssuming both players play perfectly rational strategies, what is the Nash equilibrium of this game?",
    "output": "In the game of rock-paper-scissors, the Nash equilibrium occurs when both players choose each action (rock, paper, or scissors) with equal probability, i.e., 1/3 chance of playing each action. This is because no player can improve their expected payoff by unilaterally changing their strategy, given the opponent's strategy.\n\nIn this case, the Nash equilibrium strategy for both players is to play rock, paper, and scissors with probabilities (1/3, 1/3, 1/3)."
  },
  {
    "source": "data/CoT/math50k_camel.json",
    "instruction": "Solve for x: cos(2x) + sin(x) = 0. for 0 \u2264 x \u2264 2\u03c0.",
    "output": "To solve the equation cos(2x) + sin(x) = 0 for 0 \u2264 x \u2264 2\u03c0, we can use the double-angle formula for cosine, which is:\n\ncos(2x) = 1 - 2sin^2(x)\n\nNow, substitute this into the original equation:\n\n1 - 2sin^2(x) + sin(x) = 0\n\nRearrange the equation:\n\n2sin^2(x) - sin(x) - 1 = 0\n\nThis is a quadratic equation in terms of sin(x). Let y = sin(x), then the equation becomes:\n\n2y^2 - y - 1 = 0\n\nNow, we can solve this quadratic equation using the quadratic formula:\n\ny = (-b \u00b1 \u221a(b^2 - 4ac)) / 2a\n\nIn this case, a = 2, b = -1, and c = -1. Plugging these values into the formula, we get:\n\ny = (1 \u00b1 \u221a((-1)^2 - 4(2)(-1))) / (2(2))\ny = (1 \u00b1 \u221a(1 + 8)) / 4\ny = (1 \u00b1 \u221a9) / 4\ny = (1 \u00b1 3) / 4\n\nThere are two possible values for y:\n\ny1 = (1 + 3) / 4 = 4 / 4 = 1\ny2 = (1 - 3) / 4 = -2 / 4 = -1/2\n\nNow, we need to find the values of x for each value of y:\n\n1) sin(x) = 1\nx = arcsin(1)\nx = \u03c0/2\n\n2) sin(x) = -1/2\nx = arcsin(-1/2)\nx = -\u03c0/6, 7\u03c0/6 (since 0 \u2264 x \u2264 2\u03c0)\n\nSo, the solutions for x are:\n\nx = \u03c0/2, -\u03c0/6, 7\u03c0/6"
  },
  {
    "source": "data/PoT/MATH_train.json",
    "instruction": "Triangle $ABC$ has sides of length 5, 12 and 13 units, and triangle $DEF$ has sides of length 8, 15 and 17 units. What is the ratio of the area of triangle $ABC$ to the area of triangle $DEF$? Express your answer as a common fraction. Let's write a program.",
    "output": "# As both are right triangles, the area of a triangle is 1/2 * base * height.\n# We can take the two smallest sides as base and height for both triangles.\n\n# Triangle ABC\nbase_abc = 5\nheight_abc = 12\n\n# Triangle DEF\nbase_def = 8\nheight_def = 15\n\n# Calculate the areas\narea_abc = 0.5 * base_abc * height_abc\narea_def = 0.5 * base_def * height_def\n\n# Calculate the ratio\nratio = area_abc / area_def\n\nprint(ratio)"
  },
  {
    "source": "data/CoT/gsm_train.json",
    "instruction": "Terese thinks that running various distances throughout the week can make one healthy.  On Monday, she runs 4.2 miles;  Tuesday, 3.8 miles; Wednesday, 3.6 miles; and on Thursday, 4.4 miles.  Determine the average distance Terese runs on each of the days she runs.",
    "output": "The total distance Terese runs is 4.2 + 3.8+4.4 +3.6 = 16 miles.\nTherefore, she runs with an average distance of 16 /4 = 4 miles.\nThe answer is 4"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "What is the greatest value of n such that 24^n is a factor of 24! ?\nAnswer Choices: (A) 1 (B) 2 (C) 3 (D) 4 (E) 8",
    "output": "Another way to solve this question :\nWe know that 18 = 2 *3^2.\nHence, we need to find total number of 3s in 18! ( As out of 3 and 2 , we will have count of 3 least)\nNo. of 3s = 18/3 =6/3 =2.\nAdd the numbers in Bold, you will get total number of 3s = 8.\nHence, total number of 4^2 = 16/2 = 8.\nHence, answer is 8. E"
  },
  {
    "source": "data/CoT/MATH_train.json",
    "instruction": "In the diagram below, we have $AB = 24$ and $\\angle ADB =90^\\circ$.  If $\\sin A = \\frac23$ and $\\sin C = \\frac13$, then what is $DC$?\n\n\n[asy]\npair A,B,C,D;\nA = (0,0);\nB = (8*sqrt(5),16);\nD = (8*sqrt(5),0);\nC = (8*sqrt(5) + 32*sqrt(2),0);\ndraw(D--B--A--C--B);\nlabel(\"$A$\",A,SW);\nlabel(\"$B$\",B,N);\nlabel(\"$C$\",C,SE);\nlabel(\"$D$\",D,S);\ndraw(rightanglemark(B,D,A,63));\n[/asy]",
    "output": "From right triangle $ABD$, we have $\\sin A = \\frac{BD}{AB} = \\frac{BD}{24}$.  Since $\\sin A = \\frac23$, we have $\\frac23 = \\frac{BD}{24}$, so $BD = \\frac23\\cdot 24 = 16$.\n\nFrom right triangle $BCD$, we have $\\sin C = \\frac{BD}{BC}=\\frac{16}{BC}$.  Since $\\sin C = \\frac13$, we have $\\frac{16}{BC} = \\frac13$.  Therefore, we have $BC = 3\\cdot 16=48$.  Finally, the Pythagorean Theorem gives us \\begin{align*}\nCD &= \\sqrt{BC^2 - BD^2}\\\\\n&= \\sqrt{48^2 - 16^2} \\\\\n&= \\sqrt{(3\\cdot 16)^2 - 16^2} \\\\\n&= \\sqrt{9\\cdot 16^2 - 16^2} = \\sqrt{8\\cdot 16^2} = 2\\cdot 16 \\sqrt{2} = \\boxed{32\\sqrt{2}}.\\end{align*}. The answer is 32\\sqrt{2}"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "If a1 = 1 and an+1= 2an + 5, n = 1, 2 .. , then a10 is equal to ?\nAnswer Choices: (A) a. 6*2^9 -5 (B) b. 5*2^99+6 (C) c. 6*2^99+5 (D) d. 6*2^99-5 (E) e. 6*2^99-6",
    "output": "Let's think about the multi-choice question step by step.\nHere is solution:\nan+1=2an+5............(1)\nlets ADD 5 to both sides....\nso (an+1) + 5= 2 (an+5)....................taking 2 as common factor\nnow a1=1. so for n=1, an+5=6.......\nputting n=1. we get both sides as,\na2 + 5= 2 * 6 ..............as ( an+5=6 .......(for n=1)..)\na2= 2 *6 - 5\na2= 2 * 2 *3 - 5\na2= 2^2 *3 - 5................. so with same progression\na10= 2^10 * 3 - 5\na10=2* 2^9 * 3 - 5\na10= 6 * 2^9 - 5\nThe answe is A"
  },
  {
    "source": "data/CoT/gsm_rft.json",
    "instruction": "Wyatt has 10 blue envelopes. He has 4 fewer yellow envelopes than blue envelopes. How many envelopes does Wyatt have in all?",
    "output": "Wyatt has 10 - 4 = 6 yellow envelopes.\nThe total number of envelopes he has is 10 blue + 6 yellow = 16 envelopes.\nThe answer is 16"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "A pipe is 30 m long and is 45% longer than another pipe. Find the length of the other pipe\nAnswer Choices: (A) 20.68 (B) 20 (C) 20.12 (D) 20.5 (E) None of these",
    "output": "Let's think about the multi-choice question step by step.\nLet length of other pipe be X\nAccording to question,\n30 = 45/100 X + X\n30 = 0.45X + X\n30 = 1.45 X\nX= 30/1.45\nX = 20.68m\nThus the length of the other pipe is 20.68 metres.\nThe answer is A"
  },
  {
    "source": "data/CoT/gsm_rft.json",
    "instruction": "Andy bakes and sells birthday cakes. To make two cakes he spends $12 on ingredients, and $1 on packaging for each cake. Andy sells each cake for $15. How much money does Andy make for each cake?",
    "output": "The cost of ingredients for two cakes is $12.\nThe cost of packaging for two cakes is $1 * 2 = $2.\nThe selling price for two cakes is $15 * 2 = $30.\nFor two cakes, Andy makes $30 - $12 - $2 = $16.\nSo for each cake, Andy makes $16 / 2 = $8.\nThe answer is 8"
  },
  {
    "source": "data/CoT/aqua_rat.json",
    "instruction": "The average monthly income of P and Q is Rs. 5100. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is?\nAnswer Choices: (A) A) Rs.4050 (B) B) Rs.4000 (C) C) Rs.4029 (D) D) Rs.4027 (E) E) Rs.4020",
    "output": "Let's think about the multi-choice question.\nLet P, Q and R represent their respective monthly incomes. Then, we have:\nP + Q = (5050 * 2) = 10200 --- (i)\nQ + R = (6250 * 2) = 12500 --- (ii)\nP + R = (5200 * 2) = 10400 --- (iii)\nAdding (i), (ii) and (iii), we get:\n2(P + Q + R) = 33100 = P + Q + R = 16550 --- (iv)\nSubtracting (ii) from (iv), we get, P = 4050.\nP's monthly income = Rs.4050.\nThe answer is A"
  },
  {
    "source": "data/PoT/mathqa.json",
    "instruction": "if the average ( arithmetic mean ) of ( 2 a + 16 ) and ( 3 a - 8 ) is 74 , what is the value of a ? Let's write a Python program to solve it.",
    "output": "n0 = 2.0\nn1 = 16.0\nn2 = 3.0\nn3 = 8.0\nn4 = 74.0\nt0 = n0 + n2\nt1 = n0 * n4\nt2 = n1 - n3\nt3 = t1 - t2\nanswer = t3 / t0\nprint(answer)"
  },
  {
    "source": "data/CoT/college_math.json",
    "instruction": "Determine the cyclic subgroup generated by the element 5 in the group Z_12.  Answer Choices: (A) {0, 5} (B) {0, 2, 4, 6, 8, 10} (C) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} (D) {0, 5, 10}",
    "output": "The cyclic subgroup generated by an element a in a group G under an operation *, denoted by <a>, is the set of all powers of a. In the group of integers modulo n under addition, this translates to multiples of the element. Here, we have the group Z_12 and the element 5. Z_12 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} is the group of addition modulo 12. We want to find the cyclic subgroup generated by the element 5. This is equivalent to finding all multiples of 5 modulo 12. Doing this, we get: 5*0 = 0 (mod 12) 5*1 = 5 (mod 12) 5*2 = 10 (mod 12) 5*3 = 15 = 3 (mod 12) 5*4 = 20 = 8 (mod 12) 5*5 = 25 = 1 (mod 12) 5*6 = 30 = 6 (mod 12) 5*7 = 35 = 11 (mod 12) 5*8 = 40 = 4 (mod 12) 5*9 = 45 = 9 (mod 12) 5*10 = 50 = 2 (mod 12) 5*11 = 55 = 7 (mod 12) After this, the multiples start repeating, so the cyclic subgroup <5> = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}. The answer is B."
  }
]