messages listlengths 2 2 |
|---|
[
{
"role": "user",
"content": "The complement of an angle is $5^{\\circ}$ more than four times the angle. What is the number of degrees in the measure of the angle?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem again. The complement of an angle is 5 degrees more ... |
[
{
"role": "user",
"content": "If $f(x) = 3x+2$ and $g(x) = (x-1)^2$, what is $f(g(-2))$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to solve this problem again step by step to make sure I don't make any mistakes. The problem is asking for $ f(g(-2)) $ where $ f(x) = 3x + 2 ... |
[
{
"role": "user",
"content": "If $f (x) = x^2 - X$, what is the value of $f (-1)$?\nIf we know the answer to the above question is 0, what is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says that $ f(x) = x^2 - X $ and we need to ... |
[
{
"role": "user",
"content": "Suppose I have X shirts, 4 ties, and 3 pairs of pants. If an outfit requires a shirt and pants, and can either have a tie or not have a tie, I can make 90 outfits. What is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's ... |
[
{
"role": "user",
"content": "The arithmetic mean of four numbers is 15. Two of the numbers are 10 and 18 and the other two are equal. What is the product of the two equal numbers?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says the arithmetic mean of four numbe... |
[
{
"role": "user",
"content": "We have a rectangle of dimensions $x - 2$ by $2x + 5$ such that its area is $8x - 6$. What is the value of $x$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is about finding the value of x given the dimensions of a rectangle and its a... |
[
{
"role": "user",
"content": "How many even digits are there in the base-7 representation of the number 403 in base-10?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so the problem is asking how many even digits are in the base-7 representation of the number 403 in base-10. Let me start ... |
[
{
"role": "user",
"content": "How many two-digit numbers can be written in the form $2^n$ where $n$ is an integer?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is asking how many two-digit numbers can be written in the form $2^n$, where $n$ is an integer. Alright,... |
[
{
"role": "user",
"content": "How many positive two-digit integers are there in which each of the two digits is prime?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so the problem is asking how many positive two-digit numbers have each of their digits as prime numbers. Let me think about... |
[
{
"role": "user",
"content": "The vertical drop of a roller coaster is the largest difference in height between any high point and the next low point. The vertical drops of five roller coasters at Mandelbrot Amusement Park are shown in the table. \\begin{tabular}{|l|c|} \\hline\nThe Parabola & 165 feet \\\\... |
[
{
"role": "user",
"content": "What value of $x$ will give the minimum value of $2x^2 - 12x + 3$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure this out again. The problem is asking for the value of $ x $ that gives the minimum value of the quadratic function $ 2x^2 -... |
[
{
"role": "user",
"content": "For a positive integer $x$ that is less than 100, how many solutions does the congruence $x + 13 \\equiv 55 \\pmod{34}$ have?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to solve this problem again step by step. The problem is asking how many po... |
[
{
"role": "user",
"content": "What is the integer value of n, where 0 ≤ n ≤ 11, such that n is congruent to 10389 modulo 12?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure this out again. The problem is to find an integer $ n $ between 0 and 11 (inclusive) such that $... |
[
{
"role": "user",
"content": "Find the largest integer value of $x$ that satisfies the inequality $5 - 4x > 17$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to find the largest integer value of $ x $ that satisfies the inequality $ 5 - 4x > 17 $. Alright, so f... |
[
{
"role": "user",
"content": "Determine the nonnegative difference between the roots of the equation $x^2 + 30x + 180 = -36$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question is asking for the nonnegative difference between the roots of t... |
[
{
"role": "user",
"content": "What is the total number of unique diagonals that can be drawn in a convex heptagon (a polygon with 7 sides)?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is asking for the total number of unique diagonals in a convex heptagon. Hmm, f... |
[
{
"role": "user",
"content": "Triangle $ABC$ with vertices $A(-2, 0)$, $B(1, 4)$ and $C(-3, 2)$ is reflected over the $y$-axis to form triangle $A'B'C'$. What is the length of a segment drawn from $C$ to $C'$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says tria... |
[
{
"role": "user",
"content": "What is the value of $x$ in the equation $-2x - 7 = 7x + 2$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. I need to solve the equation -2x -7 = 7x + 2 for x. Alright, first step is to get all the terms with x on one side and the constants on the ... |
[
{
"role": "user",
"content": "Given that $f(x) = x + 3$ and $g(x) = x^2 - 6$, what is the value of $f(g(2))$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to find $ f(g(2)) $ where $ f(x) = x + 3 $ and $ g(x) = x^2 - 6 $. Alright, so first, I need to remember h... |
[
{
"role": "user",
"content": "Suppose $x$ and $y$ are integers such that $xy+5x+4y=-5$. Find the greatest possible value of $y$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem again. The equation given is $xy + 5x + 4y = -5$, and we need to find the great... |
[
{
"role": "user",
"content": "The circumference of a circle $A$ is 60 feet. How many feet long is $\\widehat{BC}$? [asy]\nimport markers;\n\nimport olympiad; import geometry; import graph; size(150); defaultpen(linewidth(0.9));\ndraw(Circle(origin,1));\ndraw(dir(90)--origin--dir(30));\nlabel(\"$B$\",dir(90)... |
[
{
"role": "user",
"content": "What is the period of $y = \\tan x + \\cot x$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the period of the function $ y = \\tan x + \\cot x $. Let me start by recalling what the period of a trigonometric function is. I remember that bot... |
[
{
"role": "user",
"content": "If there are 46 people to be seated and each row of a seating arrangement can seat either 7 or 8 people, how many rows will seat exactly 8 people when all seats are filled?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is about seating... |
[
{
"role": "user",
"content": "What is the total volume in cubic feet of three boxes if each box is a cube with edge length X feet?\nIf we know the answer to the above question is 192, what is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to figu... |
[
{
"role": "user",
"content": "How many prime numbers are between 30 and 40?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to figure out how many prime numbers are between 30 and 40. So, first, I need to remember what a prime number is. A prime number is a number greater than 1 ... |
[
{
"role": "user",
"content": "Determine the remainder when $2^{87} + 3$ is divided by 7."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. I need to find the remainder when $2^{87} + 3$ is divided by 7. Hmm, modular arithmetic. So, first, I remember that when dealing with exponent... |
[
{
"role": "user",
"content": "In a physical education class, students are arranged in four rows to perform exercises. This class has more than 30 students, with three rows having an equal number of students and one row having one more student than the other three rows. What is the minimum possible class siz... |
[
{
"role": "user",
"content": "What is the number of square meters in the area of a circle with diameter 4 meters? Express your answer in terms of $\\pi$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is asking for the area of a circle with a diameter of 4 meters, a... |
[
{
"role": "user",
"content": "What is the length of the segment with endpoints (2,3) and (7,15)?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. The question is asking for the length of the segment between the points (2, 3) and (7, 15). \n\nFirst, I ... |
[
{
"role": "user",
"content": "If $\\|\\mathbf{v}\\| = 4,$ then find $\\mathbf{v} \\cdot \\mathbf{v}.$"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says that the magnitude of vector v is 4, and we need to find the dot product of v with itself, which is v · v. Hmm, ... |
[
{
"role": "user",
"content": "A function $f$ is defined by $f(z) = i\\overline{z}$, where $i^2 = -1$ and $\\overline{z}$ is the complex conjugate of $z$. How many values of $z$ satisfy both $|z| = 5$ and $f(z) = z$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is ... |
[
{
"role": "user",
"content": "Find the value of X \\times 24 + 36 \\times 12$. The answer is 720. What is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to find the value of X in the equation X multiplied by 24 plus 36 multiplied ... |
[
{
"role": "user",
"content": "Mark has $\\frac{3}{4}$ of a dollar and Carolyn has $\\frac{3}{10}$ of a dollar. How many dollars do they have altogether? (Give your answer as a decimal.)"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says Mark has 3/4 of a dollar and... |
[
{
"role": "user",
"content": "Points $A$ and $B$ have the same $y$-coordinate of X, but different $x$-coordinates. The sum of the slope and the $y$-intercept of the line containing both points is 13. What is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, l... |
[
{
"role": "user",
"content": "When a positive integer is expressed in base 7, it is $AB_7$, and when it is expressed in base 5, it is $BA_5$. What is the positive integer in decimal?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure this problem again. So, the question ... |
[
{
"role": "user",
"content": "The vertices of a $3 - 4 - 5$ right triangle are the centers of three mutually externally tangent circles, as shown. What is the sum of the areas of these circles?\n\n[asy]unitsize(1cm);\ndraw(Circle((1.8,2.4),1),linewidth(0.7));\ndraw(Circle((0,0),2),linewidth(0.7));\ndraw(C... |
[
{
"role": "user",
"content": "How many different ways can George select two colors out of a total of seven to paint his room?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. George wants to paint his room using two colors out of seven available. The question is asking how many d... |
[
{
"role": "user",
"content": "Let $x$ and $y$ be positive real numbers. Find the maximum value of\n\\[\\frac{(x + y)^2}{x^2 + y^2}.\\]"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem step by step. The question is to find the maximum value of the expression ... |
[
{
"role": "user",
"content": "Determine the area of the region described by the equation $x^2+y^2 - 7 = 4y-14x+3$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure out how to solve this problem step by step. The problem is asking for the area of the region described by ... |
[
{
"role": "user",
"content": "Gracie and Joe are choosing numbers on the complex plane. Joe chooses the point $1+2i$. Gracie chooses $-1+i$. How far apart are Gracie and Joe's points?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. So the problem is about finding the distance be... |
[
{
"role": "user",
"content": "Billy wants to determine the average number of cookies in a package of cookies. He purchases 7 packages of cookies, opens them, and counts the number of cookies in each one. He finds that the packages have 8, 10, 12, 15, 16, 17, and 20 cookies. Based on these observations, what... |
[
{
"role": "user",
"content": "What is the greatest multiple of 3 that is less than 500 and is also a multiple of 4?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to figure out this problem again. So, the question is asking for the greatest multiple of both 3 and 4 that is less ... |
[
{
"role": "user",
"content": "Given that $x$, $y$, and $z$ are positive and satisfy the equations $xy=20\\sqrt[3]{2}$, $xz=35\\sqrt[3]{2}$, and $yz=14\\sqrt[3]{2}$, what is the value of $xyz$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the value of xyz given the equa... |
[
{
"role": "user",
"content": "Solve for $x$: $4x^{1/3}-2 \\cdot \\frac{x}{x^{2/3}}=7+\\sqrt[3]{x}$."
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to solve the equation $4x^{1/3} - 2 \\cdot \\frac{x}{x^{2/3}} = 7 + \\sqrt[3]{x}$. Let me start by simplifying the terms on the left... |
[
{
"role": "user",
"content": "If $x - y = X and $x + y = 12$, what is the value of $y$?\nIf we know the answer to the above question is 3, what is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says that if $ x - y = X $ and $ x + y ... |
[
{
"role": "user",
"content": "Find the simplified form of $\\sqrt{50} + \\sqrt{18}$, expressing your answer in simplest radical form."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to simplify √50 + √18 and express the answer in simplest radical form. Alright, so... |
[
{
"role": "user",
"content": "With 40 feet of fencing available, what is the maximum area, in square feet, that can be enclosed by a rectangular pen?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is about finding the maximum area that can be enclosed by a rectangul... |
[
{
"role": "user",
"content": "At Beaumont High School, there are 12 players on the baseball team. All 12 players are taking at least one of biology or chemistry. If X players are taking biology and 2 players are taking both sciences, There are 7 players taking chemistry. What is the value of unknown varia... |
[
{
"role": "user",
"content": "Point $A$ has coordinates $(x,6)$. When Point $A$ is reflected over the $y$-axis it lands on Point $B$. What is the sum of the four coordinate values of points $A$ and $B$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is about reflect... |
[
{
"role": "user",
"content": "A math field day competition is held in a room with many tables, and there are 6 stools at each table. Each stool has X legs, and each table has 4 legs. If there is a total of 484 legs on all the tables and stools in the room, how many tables are in the room?\nIf we know the an... |
[
{
"role": "user",
"content": "A large sphere has a volume of $288\\pi$ cubic units. A smaller sphere has a volume which is $12.5\\%$ of the volume of the larger sphere. What is the ratio of the radius of the smaller sphere to the radius of the larger sphere? Express your answer as a common fraction."
},... |
[
{
"role": "user",
"content": "The integer $x$ has X positive factors. The numbers 12 and 15 are factors of $x$. What is $x$?\nIf we know the answer to the above question is 60, what is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure thi... |
[
{
"role": "user",
"content": "What is the result of cubing the square of the second prime number, starting from the smallest prime number?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is asking for the result of cubing the square of the second prime number, starti... |
[
{
"role": "user",
"content": "Calculate the value of $(-5)^5\\div5^3+3^{4}-6^{1}$ as an integer."
},
{
"role": "assistant",
"content": "<think>\nOkay, let me go through this problem again to make sure I didn't skip any steps or make any mistakes. The problem is to calculate the value of (-5)^5 d... |
[
{
"role": "user",
"content": "Find the largest integer less than 80 that leaves a remainder of 3 when divided by 5."
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the largest integer less than 80 that leaves a remainder of 3 when divided by 5. Let me start by understandi... |
[
{
"role": "user",
"content": "Determine the value of t that satisfies the equation $\\frac{1}{t+2} + \\frac{2t}{t+2} - \\frac{3}{t+2} = 3$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to solve the equation $\\frac{1}{t+2} + \\frac{2t}{t+2} - \\frac{3}{t+2} = 3... |
[
{
"role": "user",
"content": "What is the solution for $x$ in the equation $\\frac{1}{x} + \\frac{2}{x} \\div \\frac{4}{x} = 0.75$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. I need to solve the equation $\\frac{1}{x} + \\frac{2}{x} \\div \\frac{4}{x} = 0.75$. Alright, firs... |
[
{
"role": "user",
"content": "The grade received on a certain teacher's 100-point test varies in direct proportion to the amount of time a student spends preparing for the test. If a student receives 72 points on a test for which she spent 3 hours preparing, what score would she receive on the next test if ... |
[
{
"role": "user",
"content": "If $f(z)$ and $g(z)$ are polynomials in $z$, and the degree of $g(z)$ is less than the degree of $f(z)$, what is the degree of the polynomial $f(z) + g(z)$ if the degree of $f(z)$ is two?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to figure out ... |
[
{
"role": "user",
"content": "Find the real roots of\n\\[x^4 - 2x^3 - x + X = 0. The answer is 2. What is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem step by step. The problem is to find the value of the unknown variable ... |
[
{
"role": "user",
"content": "Our club has 20 members, X boys and 10 girls. In how many ways can we choose a president and a vice-president if they must be of the same gender? Assume no one can hold both offices. The answer is 180. What is the value of unknown variable X?"
},
{
"role": "assistant"... |
[
{
"role": "user",
"content": "Given that the sum of the squares of two positive integers is 90 and the product of the two integers is 27, what is the sum of the two integers?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. So the problem says that the sum of the squares of two p... |
[
{
"role": "user",
"content": "Given that the square has a perimeter of 48 and the triangle has a height of 48, and both the square and the triangle have the same area, what is the value of x?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to solve this problem step by step. So,... |
[
{
"role": "user",
"content": "In a buffet line, Tyler can choose one type of meat, two different vegetables, and one dessert. If the order of food items is not important, how many different meal combinations can he choose?\n\nMeat options: beef, chicken, pork\n\nVegetable options: baked beans, corn, potatoe... |
[
{
"role": "user",
"content": "Find the largest integer $n$ for which $12^n$ evenly divides $20!$."
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to find the largest integer $ n $ such that $ 12^n $ divides $ 20! $. Let me start by breaking down 12 into its prime factors. 12 is 2... |
[
{
"role": "user",
"content": "Solve for $x$:\n\n$$x^2 + 4x + 3 = -(x + 3)(x + 5).$$"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to solve the equation:\n\n$$x^2 + 4x + 3 = -(x + 3)(x + 5).$$\n\nFirst, I need to expand the right-hand side. Let me do that step by... |
[
{
"role": "user",
"content": "If $x^2 = y - X and $x = -5$, The value of $y$ is 28. What is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure this out again. The problem says that x squared equals y minus X, and when x is -5, y is 28. We ... |
[
{
"role": "user",
"content": "If each page costs 2.5 cents to copy, how many pages can be copied with a budget of $20?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure this out again. So, the problem is asking how many pages can be copied with a budget of $20 if each pa... |
[
{
"role": "user",
"content": "A sphere is inscribed in a cube. Given that one edge of the cube is 6 inches, how many cubic inches are in the volume of the inscribed sphere? Express your answer in terms of $\\pi$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem aga... |
[
{
"role": "user",
"content": "Which of the cones below can be formed from a $252^{\\circ}$ sector of a circle of radius 10 by aligning the two straight sides?\n\n[asy]\ndraw((5.8,8.1)..(-10,0)--(0,0)--(3.1,-9.5)..cycle);\nlabel(\"10\",(-5,0),S);\nlabel(\"$252^{\\circ}$\",(0,0),NE);\n[/asy]\n\nA. base radius... |
[
{
"role": "user",
"content": "If $\\begin{vmatrix} a & b \\\\ c & d \\end{vmatrix} = 4,$ then find\n\\[\\begin{vmatrix} a & 7a + 3b \\\\ c & 7c +3d \\end{vmatrix}.\\]"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure out this problem again. The original determinant is g... |
[
{
"role": "user",
"content": "Vanessa set a school record for most points in a single basketball game when her team scored $48$ points. The six other players on her team averaged X points each. Vanessa scored 27 points to set her school record. What is the value of unknown variable X?"
},
{
"role": ... |
[
{
"role": "user",
"content": "Convert $115_{10}$ to base X. Represent $10$ as $A$, if necessary.\nIf we know the answer to the above question is \\text{A5}_{11}, what is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to convert th... |
[
{
"role": "user",
"content": "If $x = 2$ and $y = 1,$ what is the value of $2\\times x - X \\times y?$\nIf we know the answer to the above question is 1, what is the value of unknown variable X?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says that if x = 2 and y... |
[
{
"role": "user",
"content": "As $n$ ranges over the positive integers, what is the sum of all possible values of the greatest common divisor of $3n+4$ and $n$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem step by step. The question is asking for the sum ... |
[
{
"role": "user",
"content": "Calculate the volume, in cubic centimeters, of the cylinder created by rotating a square with a side length of 14 centimeters around its vertical line of symmetry. Express your answer in terms of $\\pi$."
},
{
"role": "assistant",
"content": "<think>\nOkay, so I nee... |
[
{
"role": "user",
"content": "What is the integer value of $n$ that satisfies the inequalities $n + 10 > 11$ and $-4n > -12$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is asking for the integer value of $ n $ that satisfies both inequalities: $ n + 10 > 11 $ an... |
[
{
"role": "user",
"content": "What is the value of the expression $5^3 - 3 \\times 5^2 + 3 \\times 5 - 1$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to evaluate the expression $5^3 - 3 \\times 5^2 + 3 \\times 5 - 1$. Alright, first, I need to remember the or... |
[
{
"role": "user",
"content": "Suppose $f(x) = 6x - 9$ and $g(x) = \\frac{x}{3} + 2$. Find $f(g(x)) - g(f(x))$."
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is to find f(g(x)) minus g(f(x)). The functions given are f(x) = 6x - 9 and g(x) = x/3 + 2. Alright, so firs... |
[
{
"role": "user",
"content": "A $\\emph{convex}$ polygon is a polygon in which every interior angle is less than 180 degrees. A $\\emph{diagonal}$ of a convex polygon is a line segment that connects two non-adjacent vertices. How many diagonals does a convex polygon with X sides have?\nIf we know the answ... |
[
{
"role": "user",
"content": "When listing three consecutive positive odd integers in ascending order, the sum of these integers is equal to one-seventh of their product. What is the middle integer?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem step by ste... |
[
{
"role": "user",
"content": "The Ponde family's Powerjet pumps 420 gallons of water per hour. At this rate, how many gallons of water will it pump in 45 minutes?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem says the Ponde family's Powerjet pumps 420 gallons per h... |
[
{
"role": "user",
"content": "To be eligible for an algebra class a student must have an average of at least $83\\%$ over all four quarters in his or her pre-algebra class. If Fisher had an $82\\%$, $77\\%$, and $75\\%$ in the first three quarters, what is the minimum score he must earn in the 4th quarter t... |
[
{
"role": "user",
"content": "It takes 15 men working steadily 4 days to dig the foundation for a new apartment. How many days would it have taken 25 men working at the same rate to dig the foundation? Express your answer as a decimal to the nearest tenth."
},
{
"role": "assistant",
"content":... |
[
{
"role": "user",
"content": "What is the solution for $n$ in the equation $|n + 6| = 2 - n$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so I need to solve the equation |n + 6| = 2 - n. Let me start by recalling that absolute value equations can have two cases because the expression i... |
[
{
"role": "user",
"content": "Engineers use the formula $L=\\frac{25T^4}{H^2}$ to find the crushing load for square pillars. If $T = 4$ and $H = 8$, what is the value of $L$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem again. The formula given is L equals 25 t... |
[
{
"role": "user",
"content": "If a wrench with a handle length of 9 inches requires 375 pounds of force to loosen a certain bolt, how many pounds of force will be required by a wrench with a handle length of 15 inches to loosen the same bolt?"
},
{
"role": "assistant",
"content": "<think>\nOkay,... |
[
{
"role": "user",
"content": "What is $\\dbinom{n}{n-1}$ for any positive integer $n$? (Answer in terms of $n$.)"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to figure out this problem. So the question is asking for the value of the binomial coefficient $\\dbinom{n}{n-1}$ for... |
[
{
"role": "user",
"content": "If the expression $(x+y+z)(xy+xz+yz)$ is equal to 25 and the expression $x^2(y+z)+y^2(x+z)+z^2(x+y)$ is equal to 7, where $x$, $y$, and $z$ are real numbers, what is the value of $xyz$?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure out t... |
[
{
"role": "user",
"content": "In how many ways can a president and a 2-person committee be chosen from a group of 8 people (where the order in which we choose the 2 people doesn't matter)? (The president cannot be on the committee.)"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's se... |
[
{
"role": "user",
"content": "What is the mean value of 0, 2z, 4z, 8z, and 16z?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure this out again. The problem is asking for the mean value of the numbers 0, 2z, 4z, 8z, and 16z. \n\nFirst, I remember that the mean of a set ... |
[
{
"role": "user",
"content": "Marcus has two numbers, $a$ and $b$. When he divides $a$ by 45 he gets a remainder of 37. When he divides $b$ by 30 he gets a remainder of $9$. What remainder does he get when he divides $a+b$ by 15?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me tr... |
[
{
"role": "user",
"content": "What is the total number of positive divisors for the number 24?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's see. The problem is asking for the total number of positive divisors of 24. Hmm, divisors are numbers that divide 24 without leaving a remain... |
[
{
"role": "user",
"content": "My school's math club has 6 boys and 8 girls. I need to select a team to send to the state math competition. We want 6 people on the team. In how many ways can I select the team to have 3 boys and 3 girls?"
},
{
"role": "assistant",
"content": "<think>\nOkay, so ... |
[
{
"role": "user",
"content": "If a box with a volume of 16 cm^3 can hold 50 paperclips, how many paperclips can a box with a volume of 48 cm^3 hold?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's try to solve this problem step by step. The question is asking how many paperclips a bo... |
[
{
"role": "user",
"content": "A teacher has a class with $24$ students in it. If she wants to split the students into equal groups of at most $10$ students each, what is the least number of groups that she needs?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let me try to figure this pro... |
[
{
"role": "user",
"content": "Three different natural numbers $x$, $y$ and $z$ each have exactly three natural-number factors. How many factors does $x^{2}y^{3}z^{4}$ have?"
},
{
"role": "assistant",
"content": "<think>\nOkay, let's tackle this problem step by step. So, we have three different n... |
[
{
"role": "user",
"content": "What is the smallest positive difference between a number chosen from sequence A and a number chosen from sequence B? Both sequences stop once one of their terms exceeds 300.\n\nSequence A: 2, 4, 8, 16, 32, ...\n\nSequence B: 20, 40, 60, 80, 100, ..."
},
{
"role": "assi... |
[
{
"role": "user",
"content": "The Cubs are playing the Red Sox in the World Series. To win the world series, a team must win X games before the other team does. If the Cubs win each game with probability $\\dfrac{3}{5}$ and there are no ties, what is the probability that the Cubs will win the World Series? ... |
[
{
"role": "user",
"content": "Julie works for 48 hours per week for 12 weeks during the summer, making $\\$5000$. If she works for 48 weeks during the school year at the same rate of pay and needs to make another $\\$5000$, how many hours per week must she work?"
},
{
"role": "assistant",
"conte... |
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