messages listlengths 2 2 |
|---|
[
{
"role": "user",
"content": "MASTERING Complex Analysis Master (Residue Theorem): Calculate the residue of f(z) = e^z / (z^2 + 1) at z = i."
},
{
"role": "assistant",
"content": "<|thought|>\nApplying step-by-step elite reasoning:\nThe function f(z) = e^z / ((z-i)(z+i)) has a simple pole at z =... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the smallest positive integer $x$ such that:\n$x \\equiv 1 \\pmod{5... |
[
{
"role": "user",
"content": "A rectangular field is to be fenced on three sides leaving a side of 25 feet uncovered. If the area of the field is 1000 sq. feet, how many feet of fencing will be required? Additionally, a 15-foot square obstacle is located in the middle of the field which also needs to be fen... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nLet $p = 5$. Let $a = 27$ and $b = 2$. Find the largest power of $5$ tha... |
[
{
"role": "user",
"content": "One integer is 2 more than 5 times another . If the difference of the two integers is 26 , what is the smaller integer ?"
},
{
"role": "assistant",
"content": "<|thought|>\nLogical breakdown:\nLet's call the smaller integer x. According to the problem, the larger in... |
[
{
"role": "user",
"content": "In 5 years, Raven will be 4 times as old as Phoebe. If Raven is currently 55 years old, how old is Phoebe now?"
},
{
"role": "assistant",
"content": "<|thought|>\nLogical breakdown:\nLet's denote Phoebe's current age as P.\n\nIn 5 years, Raven will be 55 + 5 = 60 ye... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nHow many ways can we choose non-negative integers $x_1, x_2, \\dots, x_4... |
[
{
"role": "user",
"content": "find the compound interest on $ 1200 for 4 years at 20 % p . a . if ci is component yearly ?"
},
{
"role": "assistant",
"content": "<|thought|>\nLogical breakdown:\nTo calculate the compound interest (CI) on $1200 for 4 years at an annual interest rate of 20%, compo... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nIn $\\triangle ABC$, side $a = 5$, side $b = 5$, and $\\angle C = 60^\\c... |
[
{
"role": "user",
"content": "Biff is getting ready for a long bus trip. He spends $11 on the ticket, $3 on drinks and snacks, and $16 on a new pair of headphones to listen to music. Biff plans to do online tasks using the bus's WiFi during his trip. If Biff makes $12/hour working online, he has to pay to a... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nThree merchants — Nadia, Samir, and Dina — have 45, 26, and 19 points re... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA main office has 838 bags of rice. Day 1: Ships 25% (floor) to Satellit... |
[
{
"role": "user",
"content": "Given the system of equations:\n\n1. 7x + y = 19\n2. x + 3y = 1\n3. 2x + y - 4z = 10\n\nFind the value of 2x + y + 3z."
},
{
"role": "assistant",
"content": "<|thought|>\nLogical breakdown:\nTo find the value of 2x + y + 3z, we first need to solve the system of equa... |
[
{
"role": "user",
"content": "MASTERING Number Theory Mastery (Modular Arithmetic): Solve for x in the congruence 7x ≡ 1 (mod 101). Use the Extended Euclidean Algorithm."
},
{
"role": "assistant",
"content": "<|thought|>\nApplying step-by-step elite reasoning:\nTo find the modular inverse of 7 m... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the number of non-negative integer solutions to $x_1 + x_2 + x_3 = ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nLet $\\omega = e^{2\\pi i / 4}$. Find the value of the product $\\prod_{... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA function $f(x)$ satisfies $f(x+y) = f(x) + f(y)$ for all $x, y$. If $f... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nCalculate the area of a triangle with vertices at $(0,0)$, $(6, 0)$, and... |
[
{
"role": "user",
"content": "a cylindrical cube of radius 12 cm contains water upto a depth of 20 cm . a spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75 cm . the radius of the ball is :"
},
{
"role": "assistant",
"content": "<|thought|>\nLogical breakdo... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA farmer harvested crops worth 3007 silver. A 25% tax is applied (floor)... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nLet $\\omega = e^{2\\pi i / 5}$. Find the value of the product $\\prod_{... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nHow many ways can we choose non-negative integers $x_1, x_2, \\dots, x_3... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA convex quadrilateral has vertices at $(0, 0)$, $(4, 0)$, $(9, 9)$, and... |
[
{
"role": "user",
"content": "Tony has a bucket that holds 2 pounds of sand. He has a sandbox out back that is two feet deep, four feet wide, and 5 feet long. A cubic foot of sand weighs 3 pounds. Because it's hot outside, he wants to make sure he stays hydrated, so every 4 trips he takes he drinks 3 ounces... |
[
{
"role": "user",
"content": "Emily is making bead necklaces for her friends. She has twenty-eight beads and each necklace takes seven beads. How many necklaces can Emily make?"
},
{
"role": "assistant",
"content": "<|thought|>\nLogical breakdown:\nTo find out how many necklaces Emily can make, ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the value of $(1 + i)^{4}$, where $i$ is the imaginary unit ($i^2 =... |
[
{
"role": "user",
"content": "There are regular hexagonal prisms and square pyramids with the same edges. The sum of the lengths of all the edges of the hexagonal prism is 81 centimeters (cm). What is the sum of the lengths of all the edges of the pyramid in centimeters (cm)?"
},
{
"role": "assistan... |
[
{
"role": "user",
"content": "MASTERING Complex Analysis Master (Residue Theorem): Calculate the residue of f(z) = e^z / (z^2 + 1) at z = i."
},
{
"role": "assistant",
"content": "<|thought|>\nApplying step-by-step elite reasoning:\nThe function f(z) = e^z / ((z-i)(z+i)) has a simple pole at z =... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nIn $\\triangle ABC$, $AC = 5$ and $AB = 5$. A cevian $AD$ is drawn to si... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nIn $\\triangle ABC$, side $a = 4$, side $b = 8$, and $\\angle C = 60^\\c... |
[
{
"role": "user",
"content": "Logan makes $65,000 a year. He spends $20,000 on rent every year, $5000 on groceries every year, and $8000 on gas every year. If he needs to make $10,000 more each year, how much money does he want to have left each year?"
},
{
"role": "assistant",
"content": "<|tho... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nThree accounts (Khalid, Fatima, Jaber) hold 164, 467, and 257 barrels of... |
[
{
"role": "user",
"content": "MASTERING Complex Analysis Master (Residue Theorem): Calculate the residue of f(z) = e^z / (z^2 + 1) at z = i."
},
{
"role": "assistant",
"content": "<|thought|>\nApplying step-by-step elite reasoning:\nThe function f(z) = e^z / ((z-i)(z+i)) has a simple pole at z =... |
[
{
"role": "user",
"content": "Tony, Moses and Esther are to share $50. Moses will take 40% of the total amount while Tony and Esther will split the remainder equally among themselves. How much more than Esther will Moses get?"
},
{
"role": "assistant",
"content": "<|thought|>\nLogical breakdown:... |
[
{
"role": "user",
"content": "Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 10 kilograms of solution Y and 2 kilograms of solution Y are added to a certain amount of remaining liquid, the new solution is 36 percent liquid X. What was the weight of the remaini... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the smallest positive integer $x$ such that:\n$x \\equiv 1 \\pmod{5... |
[
{
"role": "user",
"content": "Frank put 11 pieces of candy in each bag. If he had 22 pieces of candy, how many bags would he have?"
},
{
"role": "assistant",
"content": "<|thought|>\nLogical breakdown:\nIf Frank put 11 pieces of candy in each bag and he had 22 pieces of candy, he would have:\n\n... |
[
{
"role": "user",
"content": "A certain clock marks every hour by striking a number of times equal to the hour, and the time required for a stroke is exactly equal to the time interval between strokes. At some hour, the time lapse between the beginning of the first stroke and the end of the last stroke is 5... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nLet $\\omega = e^{2\\pi i / 4}$. Find the value of the product $\\prod_{... |
[
{
"role": "user",
"content": "A man started driving at a constant speed, from the site of a blast, the moment he heard the blast. He heard a second blast after a time of 30 minutes and 20 seconds. If the second blast occurred exactly 30 minutes after the first, how many meters was he from the site when he h... |
[
{
"role": "user",
"content": "I am going to melt one large iron ball to make several small iron balls. If the length of the radius of the small iron ball is 1/4 of the length of the radius of the large iron ball, how many small iron marbles can be made?"
},
{
"role": "assistant",
"content": "<|t... |
[
{
"role": "user",
"content": "MASTERING Number Theory Mastery (Modular Arithmetic): Solve for x in the congruence 7x ≡ 1 (mod 101). Use the Extended Euclidean Algorithm."
},
{
"role": "assistant",
"content": "<|thought|>\nApplying step-by-step elite reasoning:\nTo find the modular inverse of 7 m... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the number of non-negative integer solutions to $x_1 + x_2 + x_3 = ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nKhalid and Fatima start with 120 and 102 bags of rice. Each round, the o... |
[
{
"role": "user",
"content": "The average of 30 numbers is zero. Of them, at the most, how many may be greater than zero?"
},
{
"role": "assistant",
"content": "<|thought|>\nLogical breakdown:\nIf the average of 30 numbers is zero, it means that the sum of all 30 numbers is zero. \n\nFor the sum... |
[
{
"role": "user",
"content": "A thief runs away from a location with a certain speed. A police officer from a station 60 km away started chasing him after 1 hr with a speed of 40 km/hr. The time taken by the police to catch the thief is 4 hours. What is the speed of the thief?"
},
{
"role": "assista... |
[
{
"role": "user",
"content": "MASTERING Number Theory Mastery (Modular Arithmetic): Solve for x in the congruence 7x ≡ 1 (mod 101). Use the Extended Euclidean Algorithm."
},
{
"role": "assistant",
"content": "<|thought|>\nApplying step-by-step elite reasoning:\nTo find the modular inverse of 7 m... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA budget of 1000 dollars is allocated: Research gets 25%, Marketing gets... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the smallest positive integer $x$ such that:\n$x \\equiv 2 \\pmod{3... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA function $f(x)$ satisfies $f(x+y) = f(x) + f(y)$ for all $x, y$. If $f... |
[
{
"role": "user",
"content": "Tim found 679 seashells and 110 starfish on the beach. He gave some of the seashells to Sara and now has 507 seashells. How many seashells did Tim give to Sara?"
},
{
"role": "assistant",
"content": "<|thought|>\nLogical breakdown:\nTim originally had 679 seashells.... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nAn investment of 4221 dollars shrinks by 5% each step (floor). What is t... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA bus picks up 11 students at Stop 1. At Stop 2, 40% exit (floor) and 8 ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA sequence is defined by $a_0 = 0$, $a_1 = 1$, and $a_n = 2a_{n-1} + 1a_... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA company earned 7149 dollars. A 10% tax is applied (floor). How much ta... |
[
{
"role": "user",
"content": "MASTERING Complex Analysis Master (Residue Theorem): Calculate the residue of f(z) = e^z / (z^2 + 1) at z = i."
},
{
"role": "assistant",
"content": "<|thought|>\nApplying step-by-step elite reasoning:\nThe function f(z) = e^z / ((z-i)(z+i)) has a simple pole at z =... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFrom an external point $P$, a tangent $PT$ and a secant $PAB$ are drawn ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nConsider the quadratic equation $1x^2 +0x -4 = 0$. If $r_1$ and $r_2$ ar... |
[
{
"role": "user",
"content": "Some friends went hiking for 3.5 hours. They traveled a certain distance in that time. Birgit was 4 minutes/km faster than the average time. If Birgit kept the same pace, it would take her 48 minutes to go 8 kilometers. How far did the friends travel?"
},
{
"role": "ass... |
[
{
"role": "user",
"content": "Ajay can ride 50 km in 1 hour. How many hours does it take for Ajay to ride a certain distance? He can ride this distance in 18 hours."
},
{
"role": "assistant",
"content": "<|thought|>\nLogical breakdown:\nIf Ajay can ride 50 km in 1 hour, then in 18 hours he would... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nIn $\\triangle ABC$, $AC = 5$ and $AB = 5$. A cevian $AD$ is drawn to si... |
[
{
"role": "user",
"content": "A certain good has successive discounts applied to it, and after a discount of 20%, 10%, and some percentage, it is sold for Rs. 6800. The actual price of the good is Rs. 9941.52. What was the third discount percentage?"
},
{
"role": "assistant",
"content": "<|thoug... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the smallest positive integer $x$ such that:\n$x \\equiv 2 \\pmod{3... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the smallest positive integer $x$ such that:\n$x \\equiv 6 \\pmod{7... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA bus picks up 15 students at Stop 1. At Stop 2, 30% exit (floor) and 6 ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA convex quadrilateral has vertices at $(0, 0)$, $(6, 0)$, $(5, 5)$, and... |
[
{
"role": "user",
"content": "MASTERING Number Theory Mastery (Modular Arithmetic): Solve for x in the congruence 7x ≡ 1 (mod 101). Use the Extended Euclidean Algorithm."
},
{
"role": "assistant",
"content": "<|thought|>\nApplying step-by-step elite reasoning:\nTo find the modular inverse of 7 m... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA sequence is defined by $a_0 = 1$, $a_1 = 2$, and $a_n = 1a_{n-1} + 3a_... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nHow many ways are there to distribute 12 identical gold coins among 5 di... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nConsider the quadratic equation $1x^2 +4x -5 = 0$. If $r_1$ and $r_2$ ar... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nA merchant sold goods worth 107 gold coins. A 12% tax is applied (floor)... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nHow many ways can we choose non-negative integers $x_1, x_2, \\dots, x_3... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the smallest positive integer $x$ such that:\n$x \\equiv 1 \\pmod{5... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFour players have scores: Ada=98, Ben=36, Cal=92, Dee=21. The lowest sco... |
[
{
"role": "user",
"content": "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 . 500 more than d , what is a ' s share ?"
},
{
"role": "assistant",
"content": "<|thought|>\nLogical breakdown:\nLet's denote the shares of A, B, C, and D as 5... |
[
{
"role": "user",
"content": "MASTERING Number Theory Mastery (Modular Arithmetic): Solve for x in the congruence 7x ≡ 1 (mod 101). Use the Extended Euclidean Algorithm."
},
{
"role": "assistant",
"content": "<|thought|>\nApplying step-by-step elite reasoning:\nTo find the modular inverse of 7 m... |
[
{
"role": "user",
"content": "MASTERING Number Theory Mastery (Modular Arithmetic): Solve for x in the congruence 7x ≡ 1 (mod 101). Use the Extended Euclidean Algorithm."
},
{
"role": "assistant",
"content": "<|thought|>\nApplying step-by-step elite reasoning:\nTo find the modular inverse of 7 m... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nThree accounts (Layla, Omar, Rania) hold 280, 303, and 451 gold coins (t... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nHow many ways can we choose non-negative integers $x_1, x_2, \\dots, x_5... |
[
{
"role": "user",
"content": "James earns $20 an hour while working at his main job. He earns 20% less while working his second job. He works a certain number of hours at his main job and half that much at his second job. He earns $840 per week. How many hours does he work at his main job?"
},
{
"ro... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nThree tanks have gallons: Tank A=71, Tank B=64, Tank C=90. Each step, po... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nIn $\\triangle ABC$, side $a = 7$, side $b = 4$, and $\\angle C = 60^\\c... |
[
{
"role": "user",
"content": "A train with a length of 100 meters, is traveling at a speed of 72 km/hr. The train enters a tunnel of certain length. It takes the train 2 minutes to pass through the tunnel from the moment the front enters to the moment the rear emerges. What is the length of the tunnel?"
}... |
[
{
"role": "user",
"content": "In 7 years, Kaylee will be 3 times as old as Matt is now. If Matt is currently 5 years old, and their friends, Alex and Bella, have a combined age that is 4 years greater than twice Matt's age. Also, Alex is 3 years younger than Bella. If the sum of Kaylee's and Bella's age is ... |
[
{
"role": "user",
"content": "MASTERING Number Theory Mastery (Modular Arithmetic): Solve for x in the congruence 7x ≡ 1 (mod 101). Use the Extended Euclidean Algorithm."
},
{
"role": "assistant",
"content": "<|thought|>\nApplying step-by-step elite reasoning:\nTo find the modular inverse of 7 m... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nLet $\\omega = e^{2\\pi i / 4}$. Find the value of the product $\\prod_{... |
[
{
"role": "user",
"content": "A person buys an article at Rs. 500. At what price should he sell the article so as to make a profit of 45%?"
},
{
"role": "assistant",
"content": "<|thought|>\nLogical breakdown:\nTo calculate the selling price that would result in a 45% profit, we first need to de... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the smallest positive integer $x$ such that:\n$x \\equiv 2 \\pmod{3... |
[
{
"role": "user",
"content": "An uneducated retailer marks all his goods at 50% above the cost price and thinking that he will still make 15% profit, offers a discount of 15% on the marked price. What is his actual profit on the sales?"
},
{
"role": "assistant",
"content": "<|thought|>\nLogical ... |
[
{
"role": "user",
"content": "Janet uses her horses' manure as fertilizer. One horse produces 5 gallons of fertilizer per day. Once Janet has collected enough fertilizer, she'll spread it over 20 acres of farmland. Each acre needs 400 gallons of fertilizer and Janet can spread fertilizer over 4 acres per da... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nCalculate the area of a triangle with vertices at $(0,0)$, $(5, 0)$, and... |
[
{
"role": "user",
"content": "The smallest number when increased by 1 is exactly divisible by some numbers. The smallest number is 1441. One of the numbers it is divisible by is 40. What are the other numbers it is divisible by?"
},
{
"role": "assistant",
"content": "<|thought|>\nLogical breakdo... |
[
{
"role": "user",
"content": "The difference between the value of a number increased by 12.5% and the value of the original number decreased by some percentage is 30. The original number is 80. What is the percentage decrease of the number?"
},
{
"role": "assistant",
"content": "<|thought|>\nLog... |
[
{
"role": "user",
"content": "The water pressure of a sink has a steady flow of 2 cups per 10 minutes for the first some minutes. It still flows at 2 cups per 10 minutes for the same amount of time after. For the next hour, the water pressure maximizes to 4 cups per 10 minutes and stops. Shawn now has to du... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the value of $(1 + i)^{6}$, where $i$ is the imaginary unit ($i^2 =... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nLet $\\omega = e^{2\\pi i / 3}$. Find the value of the product $\\prod_{... |
[
{
"role": "user",
"content": "A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 940 grams. What is the shopkeeper's profit percent?"
},
{
"role": "assistant",
"content": "<|thought|>\nLogical breakdown:\nThe shopkeeper is selling goods at the cost price but is using ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nFind the number of non-negative integer solutions to $x_1 + x_2 + x_3 = ... |
[
{
"role": "user",
"content": "You are AF-MATH, an advanced mathematical reasoning assistant. You excel at solving math problems step-by-step with clear explanations. Think carefully through each problem before providing your answer.\n\nHow many ways are there to distribute 8 identical gold coins among 4 dis... |
[
{
"role": "user",
"content": "Jerry had 9 action figures, but needed 27 total for a complete collection. If each one costs $12, how much money would he need to finish his collection?"
},
{
"role": "assistant",
"content": "<|thought|>\nLogical breakdown:\nJerry already has 9 action figures and ne... |
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