__src_index__ int64 0 172k | messages stringlengths 375 66.5k |
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1,038 | [{"role": "user", "content": "For real numbers $a$ and $b$, define $a \\diamond b = \\sqrt{a^2 + b^2}$. What is the value of $(7 \\diamond 24) \\diamond ((-24) \\diamond (-7))$?\n$\\textbf{(A) } 25 \\qquad \\textbf{(B) } 50 \\qquad \\textbf{(C) } 25\\sqrt{2} \\qquad \\textbf{(D) } 50\\sqrt{2} \\qquad \\textbf{(E) } 625... |
1,065 | [{"role": "user", "content": "Mr. Li is planning to change his car recently and has set his eyes on two domestically produced cars with the same price.\n\n| Type of Car | Fuel Car | New Energy Car |\n|-------------|----------|----------------|\n| Tank Capacity | $40$ liters | - |\n| Fuel Price | $9$ yuan per liter | - ... |
1,039 | [{"role": "user", "content": "Let $A = 6 - 2i$, $M = -3 + 4i$, $S = 2i$, and $P = 3$. Also, let $C = 1 + i$. Find $(A - M + S - P) \\cdot C$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\n... |
1,058 | [{"role": "user", "content": "Given the line $x-my-1=0$ intersects the circle $(x-1)^{2}+(y-2)^{2}=4$ at points $A$ and $B$, and the length of chord $AB$ is $2\\sqrt{3}$, find the value of the real number $m$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about a line intersecting a ci... |
1,052 | [{"role": "user", "content": "In a geometric configuration, angle $C$ measures $120^\\circ$ and forms a linear pair with angle $D$. In an adjacent triangle, angle $E$ measures $50^\\circ$ and angle $F$ is congruent to angle $D$. Determine the measure of angle $G$, the third angle in the triangle containing angles $E$ a... |
1,045 | [{"role": "user", "content": "The sum of the squares of two positive integers is 130. The product of the two integers is 27. What is the sum of the two integers?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that the sum of the squares of two positive integers is 130, and their produ... |
955 | [{"role": "user", "content": "A group of 30 friends is discussing a large positive integer. Each sequentially mentions a divisor starting from 1 up to 30. However, exactly two friends were incorrect about their statements, and they are not consecutive, but suggested divisors 17 and 19. What is the smallest possible int... |
1,007 | [{"role": "user", "content": "The Fibonacci sequence is defined as 1, 1, 2, 3, 5, $\\ldots$ where each term is the sum of the two preceding ones. What is the remainder when the $150^{\\mathrm{th}}$ term of the sequence is divided by 9?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging que... |
971 | [{"role": "user", "content": "LeRoy, Bernardo, and Claudia went on a week-long camping trip and agreed to share the costs equally. During the trip, each of them paid for various joint expenses. At the end of the trip, it turned out that LeRoy had paid X dollars, Bernardo had paid Y dollars, and Claudia had paid Z dolla... |
1,000 | [{"role": "user", "content": "In the tetrahedron \\( S A B C \\), the edges \\( S A, S B, \\) and \\( S C \\) are mutually perpendicular and have lengths \\( a, b, \\) and \\( c \\) respectively. \na) Find the side length of the cube with vertex \\( S \\) that has the maximum volume and is entirely contained within the... |
1,094 | [{"role": "user", "content": "Given the sets $M=\\{x \\mid -3 < x < 1\\}$ and $N=\\{x \\mid x \\leq -3\\}$, find $M \\cup N$.\n(A) $\\emptyset$\n(B) $\\{x \\mid x < 1\\}$\n(C) $\\{x \\mid x \\geq 1\\}$\n(D) $\\{x \\mid x \\geq -3\\}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the un... |
1,003 | [{"role": "user", "content": "A palindromic number is a number that reads the same when the order of its digits is reversed. What is the difference between the largest and smallest five-digit palindromic numbers that are both multiples of 45?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challeng... |
1,050 | [{"role": "user", "content": "Given that $0 < \\beta < \\frac{\\pi}{4} < \\alpha < \\frac{3\\pi}{4}$, $\\cos(\\frac{\\pi}{4} + \\alpha) = -\\frac{3}{5}$, and $\\sin(\\frac{3\\pi}{4} + \\beta) = \\frac{5}{13}$, find $\\cos(\\alpha + \\beta) =$ ( ).\n\nA: $\\frac{56}{65}$\nB: $-\\frac{56}{65}$\nC: $\\frac{16}{65}$\nD: $-... |
1,030 | [{"role": "user", "content": "At a costume ball, there were 20 people. Each dance was between a boy and a girl. It turned out that ten people danced with three partners, two people (Sasha and Zhenya) danced with five partners, and the remaining eight danced with six partners. Prove that Sasha and Zhenya are of differen... |
1,089 | [{"role": "user", "content": "As a result of the first successful strike, the number of heads increases by one (event $N$, probability $\\frac{3}{8}$). In this case, event $D$ will occur only if the number of heads decreases by 2 - first by one, and then by another one. Therefore, the conditional probability of event $... |
1,047 | [{"role": "user", "content": "Given that the left focus of the ellipse $\\frac{{x}^{2}}{{a}^{2}}+ \\frac{{y}^{2}}{{b}^{2}}=1$ $(a > b > 0)$ is ${{F}\\_{1}}$, a line passing through ${{F}\\_{1}}$ with a slope angle of $30{}^\\circ$ intersects the circle ${{x}^{2}}+{{y}^{2}}={{b}^{2}}$. The length of the chord formed by ... |
1,015 | [{"role": "user", "content": "On the ellipse $\\frac {x^{2}}{4}+ \\frac {y^{2}}{3}=1$, there is a moving point $P$. For the circle $E: (x-1)^{2}+y^{2}=1$, any line passing through the center of circle $E$ intersects the circle at points $A$ and $B$. For the circle $F: (x+1)^{2}+y^{2}=1$, any line passing through the ce... |
964 | [{"role": "user", "content": "Given the function $f(x)= \\begin{cases} x+ \\frac {1}{x}+a, & x > 0 \\\\ 2^{x}+a, & x\\leqslant 0\\end{cases}$, if the equation $f(x)=-x$ has exactly one solution, then the range of the real number $a$ is \\_\\_\\_\\_\\_\\_."}, {"role": "assistant", "content": "<think>\n\nThis is a comple... |
1,067 | [{"role": "user", "content": "How many units are in the sum of the lengths of the two longest altitudes in a triangle with sides $9,$ $12,$ and $15$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think abo... |
1,101 | [{"role": "user", "content": "Jill and Jack are hiking to a campsite that is 3 miles away from their starting point. Jill hikes at a constant speed of 6 miles per hour, while Jack hikes at a constant speed of 3 miles per hour. How many minutes before Jack does Jill arrive?\nA) 20 minutes\nB) 25 minutes\nC) 30 minutes\n... |
1,020 | [{"role": "user", "content": "Given that $\\tan(2\\alpha) = \\frac{3}{4}$, with $\\alpha \\in \\left(- \\frac{\\pi}{2}, \\frac{\\pi}{2}\\right)$, let $f(x) = \\sin(x + \\alpha) + \\sin(\\alpha - x) - 2\\sin\\alpha$, and for any $x \\in \\mathbb{R}$, it always holds that $f(x) \\geq 0$. Find the value of $\\sin\\left(\\... |
1,104 | [{"role": "user", "content": "Jeongho's farm has chickens and pigs. If the sum of all the legs is 48, and there are 9 pigs, how many chickens are there on the farm?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about Jeongho's farm with chickens and pigs. We need to find out how many c... |
1,092 | [{"role": "user", "content": "Find the principle on a certain sum of money at 11 % per annum for some years if the amount being rs. 1120. The principle is rs. 886.0759493670886. What is the duration in years?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking for the duration in year... |
1,073 | [{"role": "user", "content": "Given the function $f(x)=x^{3}+x-16$. \n$(1)$ Find the equation of the tangent line to the curve $y=f(x)$ at the point $(2,6)$. \n$(2)$ If line $l$ is the tangent to the curve $y=f(x)$ and passes through the origin, find the equation of line $l$ and the coordinates of the tangent point."... |
1,075 | [{"role": "user", "content": "The numbers $a$ and $b$ are inversely proportional. When the sum of $a$ and $b$ is 60, $a$ is three times $b$. Find the value of $b$ when $a=12$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct a... |
1,088 | [{"role": "user", "content": "Among the following lines, one that is parallel to the line $x - 2y + 1 = 0$ is ( ) \nA: $2x - y + 1 = 0$ \nB: $2x - 4y + 2 = 0$ \nC: $2x + 4y + 1 = 0$ \nD: $2x - 4y + 1 = 0$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is asking which of the given line... |
1,086 | [{"role": "user", "content": "A girl purchases oranges in bulk: 4 oranges for 15 cents, and she sells them in a pack of 6 for 30 cents. She wants to make a profit of $150$ cents. How many oranges does she need to sell to achieve this profit target?\nA) 100 oranges\nB) 110 oranges\nC) 120 oranges\nD) 130 oranges"}, {"ro... |
1,102 | [{"role": "user", "content": "The general term formula of the sequence \\\\(\\{a_n\\}\\) is \\\\(a_n= \\dfrac{1}{\\sqrt{n} + \\sqrt{n+1}}\\), if the sum of the first \\\\(n\\\\) terms is \\\\(10\\\\), then the number of terms \\\\(n\\\\) is ( )\nA: \\\\(11\\\\)\nB: \\\\(99\\\\)\nC: \\\\(120\\\\)\nD: \\\\(121\\\\)"}, {... |
1,046 | [{"role": "user", "content": "Find the number of distinct points in the $xy$-plane common to the graphs of $(x+2y-7)(2x-y+4)=0$ and $(x-2y+3)(4x+3y-18)=0$.\n$\\text{(A) } 1\\quad \\text{(B) } 2\\quad \\text{(C) } 3\\quad \\text{(D) } 4\\quad \\text{(E) } 5\\quad \\text{(F) } \\infty$"}, {"role": "assistant", "content":... |
1,031 | [{"role": "user", "content": "A spiral staircase turns $180^\\circ$ as it rises 12 feet. The radius of the staircase is 3 feet. What is the number of feet in the length of the handrail? Express your answer as a decimal to the nearest tenth."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challengin... |
1,107 | [{"role": "user", "content": "In right triangle $ABC$, $\\angle C=90^{\\circ}$, $a=4$, $b=3$, then the value of $\\cos A$ is ( ).\n\nA: $\\dfrac{5}{4}$\n\nB: $\\dfrac{3}{5}$\n\nC: $\\dfrac{4}{3}$\n\nD: $\\dfrac{4}{5}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of cos A in ... |
1,006 | [{"role": "user", "content": "The number \\( x \\) is such that \\( \\log _{2}\\left(\\log _{4} x\\right) + \\log _{4}\\left(\\log _{8} x\\right) + \\log _{8}\\left(\\log _{2} x\\right) = 1 \\). Find the value of the expression \\( \\log _{4}\\left(\\log _{2} x\\right) + \\log _{8}\\left(\\log _{4} x\\right) + \\log _{... |
1,111 | [{"role": "user", "content": "Determine the distance between the points $(2, 3)$ and $(7, -2)$. Is the result expressible in simplest radical form?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the distance between the points (2, 3) and (7, -2). Hmm, I remember there's a distance formu... |
1,110 | [{"role": "user", "content": "Given that the parametric equation of line $l$ is $\\begin{cases} x=-1-\\frac{\\sqrt{2}}{2}t, \\\\ y=2+\\frac{\\sqrt{2}}{2}t \\end{cases}$ ($t$ is the parameter), find the slope of line $l$ ( ).\nA: $1$\nB: $-1$\nC: $\\frac{\\sqrt{2}}{2}$\nD: $-\\frac{\\sqrt{2}}{2}$"}, {"role": "assistant"... |
1,071 | [{"role": "user", "content": "Find the quotient when $9x^4 + 5x^3 - 7x^2 + 4x - 12$ is divided by $x - 3$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I need to find the quotien... |
1,022 | [{"role": "user", "content": "Given $(x^{2}+1)(2x+1)^{9}=a\\_0+a\\_1(x+1)+a\\_2(x+1)^{2}+...+a_{11}(x+1)^{11}$, find $a\\_1+a\\_2+a_{11}=$ ___."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.... |
1,109 | [{"role": "user", "content": "There are many fascinating connections between mathematics and literature. For example, there is the palindrome poem, such as \"云边月影沙边雁，水外天光山外树\", which if read backwards, becomes \"树外山光天外水，雁边沙影月边云\", offering a delightful sense and rhyme both ways! Similarly, mathematics features palindro... |
1,115 | [{"role": "user", "content": "Let set $A = \\{x | y = \\ln(x - 1)\\}$, and set $B = \\{y | y = 2^x\\}$. Then $A \\cup B$ is\n\nA: $(0, +\\infty)$ \nB: $(1, +\\infty)$ \nC: $(0, 1)$ \nD: $(1, 2)$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step. So, we have two s... |
1,081 | [{"role": "user", "content": "If \\( f(n) = a^n + b^n \\), where \\( n \\) is a positive integer and \\( f(3) = [f(1)]^3 + f(1) \\), find the value of \\( a \\cdot b \\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer... |
1,076 | [{"role": "user", "content": "In front of you are a pair of caskets with inscriptions:\n\nOn the golden casket: \"The silver casket was made by Cellini.\"\nOn the silver casket: \"The golden casket was made by someone other than Cellini.\"\n\nProve that at least one of these two caskets was made by Cellini's son."}, {"... |
1,034 | [{"role": "user", "content": "In a right triangle, the longer leg is 3 feet longer than twice the length of the shorter leg. The area of the triangle is 84 square feet. What is the length of the hypotenuse?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the hypotenuse of a right triangl... |
1,105 | [{"role": "user", "content": "The value of $\\sin(-1740^\\circ)$ is ( )\nA: $-\\frac{\\sqrt{3}}{2}$\nB: $-\\frac{1}{2}$\nC: $\\frac{1}{2}$\nD: $\\frac{\\sqrt{3}}{2}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of sin(-1740°). Hmm, first, I remember that sine is an odd func... |
1,118 | [{"role": "user", "content": "If line $l_1: 2x-y-1=0$ is parallel to line $l_2: 2x+(a+1)y+2=0$, then the value of $a$ is ( ).\nA: $-2$\nB: $-1$\nC: $1$\nD: $2$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that line \\( l_1: 2x - y - 1 = 0 \\) is parallel to line \\( l_2: 2x + (a + ... |
1,127 | [{"role": "user", "content": "Let set $M=\\{x|x>1\\}$, and $P=\\{x|x>1 \\text{ or } x<-1\\}$. Among the following relations, the correct one is ( )\n\nA: $M=P$\n\nB: $M\\cup P=M$\n\nC: $M\\cup P=P$\n\nD: $M\\cap P=P$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is about sets M and P. Fir... |
1,120 | [{"role": "user", "content": "The green piece of yarn is 156 cm long. The red yarn is 8 cm more than three times the length of the green yarn. The blue yarn is half the sum of green and red yarns' lengths. There's also a yellow piece of yarn, which is 12 cm less than the average length of the first three pieces of yarn... |
1,126 | [{"role": "user", "content": "Given $f(\\sin x) = \\sin 3x$, then $f(\\cos x) =$ （ ）\nA: $\\sin 3x$\nB: $\\cos 3x$\nC: $-\\sin 3x$\nD: $-\\cos 3x$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to solve this problem. The question says that given \\( f(\\sin x) = \\sin 3x \\), we need to find \\( f(\\c... |
1,131 | [{"role": "user", "content": "The Huawei Kirin 990 chip uses the latest $0.000000007$ meter manufacturing process. Express $0.000000007$ in scientific notation as ( ).\n\nA: $7\\times 10^{-9}$\n\nB: $7\\times 10^{-8}$\n\nC: $0.7\\times 10^{-9}$\n\nD: $0.7\\times 10^{-8}$"}, {"role": "assistant", "content": "<think>\n\n... |
1,129 | [{"role": "user", "content": "John started a blog and decided to track the number of visitors. On the first day, he had 10 visitors. Each subsequent day, he had 5 more visitors than the previous day. If John tracked his visitors for 7 consecutive days, what was the average number of visitors per day?"}, {"role": "assis... |
1,133 | [{"role": "user", "content": "Mom, Dad, and Grandpa bought clothes at the department store. Dad bought more clothes than Mom, and Grandpa bought more clothes than Dad. If you lined up people based on the number of clothes they bought in ascending order, in what position will Mom be? Please answer using an natural numbe... |
1,069 | [{"role": "user", "content": "Let \\( n \\) be a natural number less than 50. Find the sum of all possible values of \\( n \\) such that \\( 4n + 5 \\) and \\( 7n + 6 \\) have a common divisor greater than 1."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult ... |
1,135 | [{"role": "user", "content": "Maxwell leaves his home and walks toward Brad's house at 4 km/h. One hour later, Brad leaves his home and runs toward Maxwell's house at a certain speed. The distance between their homes is 74 kilometers. The total time it takes Maxwell before he meets up with Brad is 8 hours. What is Brad... |
1,011 | [{"role": "user", "content": "$A, B, C, D, E$, and $F$ are cities consecutive along a route. We know the following about the consecutive straight segments of the route: $AB>BC>CD>DE>EF$; the length of each segment is an integer; $AB=2EF$. The total route length from $A$ to $F$ is $53 \\mathrm{~km}$. What could be the l... |
1,130 | [{"role": "user", "content": "If $a=0.3^4$, $b=4^{0.3}$, and $c=\\log_{0.3}4$, determine the relationship among $a$, $b$, and $c$ in terms of their magnitude."}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out the relationship between a, b, and c. First, let's recall what each of them is. \n\... |
1,122 | [{"role": "user", "content": "At Lakeview High School, the $135$ students who participate in the Math Circle meet fortnightly to prepare for the Math Olympiad and consume an average of three cookies each. Paul and Harriet are planning to make Auntie Anne's Famous Square Cookies this time. Their recipe, which yields a t... |
1,140 | [{"role": "user", "content": "Given $\\sin \\alpha > 0$ and $\\cos \\alpha < 0$, the terminal side of angle $\\alpha$ is in the $(\\quad)$ quadrant.\nA: First\nB: Second\nC: Third\nD: Fourth"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that sin α is greater than 0 and cos α is less ... |
1,141 | [{"role": "user", "content": "A wall clock takes 6 seconds to strike 3 times at 3 o'clock. How many seconds will it take for the clock to strike 12 times at 12 o'clock?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this clock problem. So, the question is: A wall clock takes 6 seconds to ... |
1,123 | [{"role": "user", "content": "Determine the polynomial \\( h(x) \\) if:\n\\[7x^4 - 4x^3 + x + h(x) = 5x^3 - 7x + 6.\\]"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I need to find... |
1,087 | [{"role": "user", "content": "Schoolchildren are eating chocolate from their New Year's gifts. Each chocolate bar consists of 12 pieces. It was found that if each girl eats 7 pieces and each boy eats 2 pieces, then three chocolate bars will not be enough. However, if four chocolate bars are taken, each girl will get 8 ... |
1,138 | [{"role": "user", "content": "If $g(x)=2-x^3$ and $f(g(x))=x^3-2x$, then compute $f(0)$.\nA) $3 - 2\\sqrt[3]{2}$\nB) $2 - 2\\sqrt[3]{2}$\nC) $3 - 3\\sqrt[3]{2}$\nD) $2\\sqrt[3]{2} - 2$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out how to solve this problem. The question says that \\( g(x... |
1,090 | [{"role": "user", "content": "Driving along a highway, Noah noticed that his odometer showed $12321$ miles, a palindrome. Three hours later, the odometer displayed the next highest palindrome. What was his average speed, in miles per hour, during this 3-hour period?\n$\\textbf{(A)}\\ 30 \\qquad\\textbf{(B)}\\ 33.33 \\q... |
1,113 | [{"role": "user", "content": "Find all integers \\( a \\) for which the fraction\n\n$$\n\\frac{a^{2} - 21a + 17}{a}\n$$\n\nis an integer."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell... |
1,134 | [{"role": "user", "content": "$(1)$ Calculate: $\\sqrt{8}-(\\frac{1}{2})^{-1}+4\\sin 30^{\\circ}$<br/>$(2)$ Simplify first, then evaluate: $\\frac{{m}^{2}-9}{{m}^{2}+6m+9}\\div (1-\\frac{2}{m+3})$, where $m=2$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's tackle these two problems one by one. Starting wi... |
1,082 | [{"role": "user", "content": "Given the function $f(x)=2^{x}- \\frac{1}{2^{x}}$, the sequence $\\{a\\_n\\}$ satisfies $f(\\log _{2}a_{n})=-2n$.\n\n(1) Find the general term formula for the sequence $\\{a\\_n\\}$;\n\n(2) Prove that the sequence $\\{a\\_n\\}$ is decreasing."}, {"role": "assistant", "content": "<think>\n\... |
1,147 | [{"role": "user", "content": "(5 points) Given lines $a$, $b$, $c$, and plane $\\alpha$, which of the following conditions makes $a \\parallel b$ true?\n\nA: $a \\parallel \\alpha$ and $b \\parallel \\alpha$ \nB: $a \\perp c$ and $b \\perp c$ \nC: $a \\parallel c$ and $b \\parallel c$ \nD: $a \\parallel \\alpha$ and... |
1,144 | [{"role": "user", "content": "a and b can finish a work in 16 days while a alone can do the same work in 20 days . in how many days b alone will complete the work ?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says that A and B together can finish a work in 16 days, and A alone can do it... |
1,079 | [{"role": "user", "content": "Compute the smallest base-10 positive integer greater than 6 that is a palindrome when written in both base 2 and 4."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about ... |
1,100 | [{"role": "user", "content": "A mathematician \\( M' \\) is called a descendant of mathematician \\( M \\) if there is a sequence of mathematicians \\( M = M_1, M_2, \\ldots, M_k = M' \\) such that \\( M_i \\) was \\( M_{i+1} \\)'s doctoral advisor for all \\( i \\). Estimate the number of descendants that the mathemat... |
1,153 | [{"role": "user", "content": "Jared likes to draw monsters. He drew a monster family portrait. The mom had 1 eye, the dad had some eyes, and they had 3 kids, each with 4 eyes. The whole family had 16 eyes. How many eyes did the dad have?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. Jared drew a mons... |
1,112 | [{"role": "user", "content": "Find \\(n\\) such that \\(2^6 \\cdot 3^3 \\cdot n = 10!\\)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I need to find n such that when I multiply ... |
1,145 | [{"role": "user", "content": "A right triangle has a side length of 24 inches and a hypotenuse of 40 inches. A second triangle is similar to the first and has a hypotenuse of 120 inches. What is the length of the shortest side of the second triangle?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I ne... |
1,070 | [{"role": "user", "content": "What is the largest positive integer with only even digits that is less than $10,000$ and is a multiple of $9$?"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\n... |
1,157 | [{"role": "user", "content": "There are some ducks in a pond. 50 percent of the ducks are Muscovy and 30 percent of the Muscovies are female. There are 6 female Muscovy ducks. How many ducks are there in the pond?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem step by step. S... |
1,154 | [{"role": "user", "content": "Given the inequality system $\\left\\{\\begin{array}{l}2x-1≥1\\\\ x≥a\\end{array}\\right.$ and the solution set is $ x\\geqslant 2$, then the value of $a$ is ______."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the value of \\( a \\) such that the solutio... |
1,155 | [{"role": "user", "content": "In an arithmetic sequence $\\{a_n\\}$, $a_1=2$, $a_{17}=66$,\n(1) Find the general formula for the $n^{th}$ term of the sequence $\\{a_n\\}$;\n(2) Determine whether 88 is a term in the sequence $\\{a_n\\}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's tackle this arithmetic ... |
1,099 | [{"role": "user", "content": "Suppose that there exist nonzero complex numbers $a$ , $b$ , $c$ , and $d$ such that $k$ is a root of both the equations $ax^3+bx^2+cx+d=0$ and $bx^3+cx^2+dx+a=0$ . Find all possible values of $k$ (including complex values)."}, {"role": "assistant", "content": "<think>\n\nThis... |
1,163 | [{"role": "user", "content": "Given proposition $p$: $\\forall x \\in (0, +\\infty)$, $x + \\frac{1}{2} > 2$, and proposition $q$: $\\exists x\\_0 \\in \\mathbb{R}$, $2^{x\\_0} < 0$, determine the true proposition among the following options:\nA: $p \\land q$\nB: $\\lnot p \\lor q$\nC: $p \\lor q$\nD: $\\lnot p \\land ... |
1,166 | [{"role": "user", "content": "Three positive integers have a sum of 90 and are in the ratio 1:3:5. What is the least of these three integers?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says three positive integers have a sum of 90 and are in the ratio 1:3:5. We need to find the least o... |
1,128 | [{"role": "user", "content": "Determine the mass of calcium sulfate (CaSO₄) formed when 25 g of calcium oxide (CaO) reacts with 35 g of sulfuric acid (H₂SO₄) in the following balanced chemical reaction:\n\nCaO + H₂SO₄ → CaSO₄ + H₂O"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to find the mass... |
1,093 | [{"role": "user", "content": "Prove that for any positive integers \\(a, b, c,\\) and \\(d\\), the integer \\((a-b)(a-c)(a-d)(b-c)(b-d)(c-d)\\) is divisible by 12."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I nee... |
1,137 | [{"role": "user", "content": "Given the arithmetic sequence $\\\\{a_{n}\\\\}$, where $a_{2}=3$, $a_{4}=7$, and $b_{n}=a_{2n}$,\n(1) Find $b_{n}$;\n(2) Find the sum of the first $n$ terms of the sequence $\\\\{ \\frac {1}{a_{n}a_{n+1}}\\\\}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's tackle this proble... |
1,158 | [{"role": "user", "content": "Points $P_{1}(-1$,$y_{1})$, $P_{2}(3$,$y_{2})$, $P_{3}(5$,$y_{3})$ are all on the graph of the quadratic function $y=-x^{2}+2x+c$. The relationship between $y_{1}$, $y_{2}$, and $y_{3}$ is ( ).\n\nA: $y_{3} \\gt y_{2} \\gt y_{1}$\n\nB: $y_{3} \\gt y_{1}=y_{2}$\n\nC: $y_{1} \\gt y_{2} \\gt ... |
1,116 | [{"role": "user", "content": "The angles of elevation of the top of a pole from points A, B, and C on the ground are α, β, and γ respectively. The points are 10 meters, 20 meters, and 30 meters away from the bottom of the pole, and the sum of the angles is 90°. What is the height of the pole in meters?"}, {"role": "ass... |
1,156 | [{"role": "user", "content": "Last night Kannon had 3 apples, a banana, 4 oranges, 2 strawberries, and 3 kiwis for dinner. Today she is planning to eat her fruits in the following order and specific amounts:\n\n1. 4 more apples than last night.\n2. 10 times as many bananas as she ate last night.\n3. Twice as many orang... |
1,041 | [{"role": "user", "content": "The minimum value of the algebraic expression \\( 9 \\cos ^{2} \\alpha - 10 \\cos \\alpha \\sin \\beta - 8 \\cos \\beta \\sin \\alpha + 17 \\) is $\\quad$"}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and ... |
1,091 | [{"role": "user", "content": "Vasya can make the number 100 using ten threes, parentheses, and arithmetic operations: $100=(33: 3-3: 3) \\cdot(33: 3-3: 3)$. Improve his result: use fewer threes to obtain the number 100. (One example is enough)."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challe... |
1,169 | [{"role": "user", "content": "Tossing a coin three times in succession, the probability of getting heads facing up at least once is __________."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is: Tossing a coin three times in succession, the probability of getting heads facing up at least o... |
1,143 | [{"role": "user", "content": "The statement p: The equation $\\frac {x^{2}}{m-5} - \\frac {y^{2}}{m+3} = 1$ represents a hyperbola if and only if $-3 < m < 5$; \nThe statement q: There exists $x_0 \\in \\mathbb{R}$ such that $\\sin x_0 - \\cos x_0 = 2$. Then:\n\nA: The statement \"p or q\" is false\nB: The statement \... |
1,152 | [{"role": "user", "content": "There were some roses and 84 orchids in the vase. Jessica cut some more roses and orchids from her flower garden. There are now 91 orchids and 14 roses in the vase. How many roses were initially in the vase before Jessica cut more?"}, {"role": "assistant", "content": "<think>\n\nOkay, let'... |
1,181 | [{"role": "user", "content": "The range of the independent variable $x$ in the function $y=\\sqrt{x+2}-\\left(x+1\\right)^{0}$ is ( ).\n\nA: $x\\geqslant -2$\n\nB: $x \\gt -2$\n\nC: $x \\gt -2$ and $x\\neq -1$\n\nD: $x\\geqslant -2$ and $x\\neq -1$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need... |
1,175 | [{"role": "user", "content": "A compound has a certain number of Carbon, 4 Hydrogen, and 2 Oxygen atoms. The molecular weight of the compound is 60. How many Carbon atoms are in the compound?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem says a compound has a certain number of Carbon atom... |
1,165 | [{"role": "user", "content": "The solution set of the inequality $|x-2| \\geq |x|$ is:\n\nA: $\\{x | x \\leq 1\\}$\nB: $\\{x | x \\geq 1\\}$\nC: $\\{x | x \\leq 0 \\text{ or } x \\geq 2\\}$\nD: $\\{x | 0 \\leq x \\leq 2\\}$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to solve the inequality ... |
1,103 | [{"role": "user", "content": "Calculate the value of $(1-i)^{2016} + (1+i)^{2016}$."}, {"role": "assistant", "content": "<think>\n\nThis is a complex or challenging question, and it is difficult to provide a direct and correct answer. I need to think about it.\nWell, so I need to calculate (1 - i)^2016 + (1 + i)^2016. ... |
1,168 | [{"role": "user", "content": "The curve represented by the equation $x^4 - y^4 - 4x^2 + 4y^2 = 0$ is ( )\nA: Two circles\nB: Four straight lines\nC: Two intersecting straight lines and a circle\nD: Two parallel straight lines and a circle"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out wha... |
1,172 | [{"role": "user", "content": "Toby wants to walk an average of 9,000 steps per day over the next week. On Sunday he walked 9,400 steps. On Monday he walked 9,100 steps. On Tuesday he walked 8,300 steps. On Wednesday he walked 9,200 steps. He needs to average 9,050 steps on Friday and Saturday to meet his goal. How many... |
1,032 | [{"role": "user", "content": "Given that $x=x_{1}$ and $x=x_{2}$ are respectively the local minimum and maximum points of the function $f(x)=2a^{x}-ex^{2}$ where $a>0$ and $a\\neq 1$. If $x_{1} < x_{2}$, then the range of values for $a$ is $\\underline{\\hspace{1cm}}$."}, {"role": "assistant", "content": "<think>\n\nTh... |
1,179 | [{"role": "user", "content": "39 persons can repair a road in 12 days, working a certain number of hours a day. In 13 days, 30 persons, working 6 hours a day, can complete the work. How many hours a day does the first group work?"}, {"role": "assistant", "content": "<think>\n\nOkay, let's try to figure out this problem... |
1,037 | [{"role": "user", "content": "Six people are standing in a circle, each of whom is either a knight (who always tells the truth) or a liar (who always lies). Each person said one of two statements: \"There is a liar next to me\" or \"There is a liar opposite me.\" What is the minimum number of liars that can be among th... |
1,178 | [{"role": "user", "content": "Simplify $\\sqrt{360000}$."}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. I need to simplify the square root of 360000. Hmm, square roots can often be simplified by factoring out perfect squares. First, maybe I should recall that the square root of a product is the produc... |
1,190 | [{"role": "user", "content": "Joan decided to sell all of her old books. She gathered up 75 books to sell. She sold 33 books in a yard sale, and decided to sell the rest on an online platform. On the first day, she managed to sell 15 books online and on the following two days, she sold 8 books and 12 books respectively... |
1,177 | [{"role": "user", "content": "Let $S_{n}$ be the sum of the first $n$ terms of an arithmetic sequence $\\{a_{n}\\}$. If $a_{2}+a_{6}=10$ and $a_{4}a_{8}=45$, then $S_{5}=\\left(\\ \\ \\right)$\n\nA: $25$\n\nB: $22$\n\nC: $20$\n\nD: $15$"}, {"role": "assistant", "content": "<think>\n\nOkay, let's see. The problem is abo... |
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