data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Sam places a total of 30 yellow Easter eggs in several purple baskets and a total of 45 pink Easter eggs in some orange baskets. Each basket contains the same number of eggs and there are at least 5 eggs in each basket. How many eggs did Sam put in each basket? Let's think step... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 30549,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the coefficient of $a^3b^3$ in $(a+b)^6\\left(c + \\dfrac{1}{c}\\right)^8$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1400"
} | {
"split": "train",
"index": 30550,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A bagel is cut into sectors. Ten cuts were made. How many pieces resulted? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 30551,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The admission fee for an exhibition is $ \\$25$ per adult and $ \\$12$ per child. Last Tuesday, the exhibition collected $ \\$1950$ in admission fees from at least one adult and at least one child. Of all the possible ratios of adults to children at the exhibition last Tuesda... | math | {
"style": "rule",
"ground_truth": "\\frac{27}{25}"
} | {
"split": "train",
"index": 30552,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The polynomial\n\\[px^4 + qx^3 + rx^2 + sx + t = 0\\]\nhas coefficients that are all integers, and roots $-3$, $4$, $6$, and $\\frac{1}{2}$. If $t$ is a positive integer, find its smallest possible value. Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"split": "train",
"index": 30553,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A parabolic arch has a height of $16$ inches and a span of $40$ inches. The height, in inches, of the arch at the point $5$ inches from the center $M$ is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 30554,
"solution": "1. **Identify the shape and equation of the arch**: Given that the arch is parabolic, we can model it using a quadratic equation of the form:\n \\[\n y = ax^2 + k\n \\]\n where \\(y\\) is the height of the arch at a horizontal distance \\(x\\) from the cent... |
deepscaler | [
{
"role": "user",
"content": "A cylindrical log has diameter $12$ inches. A wedge is cut from the log by making two planar cuts that go entirely through the log. The first is perpendicular to the axis of the cylinder, and the plane of the second cut forms a $45^\\circ$ angle with the plane of the first cut.... | math | {
"style": "rule",
"ground_truth": "216"
} | {
"split": "train",
"index": 30555,
"solution": "The volume of the wedge is half the volume of a cylinder with height $12$ and radius $6$. (Imagine taking another identical wedge and sticking it to the existing one). Thus, $V=\\dfrac{6^2\\cdot 12\\pi}{2}=216\\pi$, so $n=\\boxed{216}$.\n Part 1: \n Part 2: \n - AM... |
deepscaler | [
{
"role": "user",
"content": "A 92-digit natural number \\( n \\) has its first 90 digits given: from the 1st to the 10th digit are ones, from the 11th to the 20th are twos, and so on, from the 81st to the 90th are nines. Find the last two digits of \\( n \\), given that \\( n \\) is divisible by 72. Let's ... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"split": "train",
"index": 30556,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the parabola $C: x^{2}=2py\\left(p \\gt 0\\right)$ with focus $F$, and the minimum distance between $F$ and a point on the circle $M: x^{2}+\\left(y+4\\right)^{2}=1$ is $4$.<br/>$(1)$ Find $p$;<br/>$(2)$ If point $P$ lies on $M$, $PA$ and $PB$ are two tangents to $C$ with... | math | {
"style": "rule",
"ground_truth": "20\\sqrt{5}"
} | {
"split": "train",
"index": 30557,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find $x$ such that $\\lceil x \\rceil \\cdot x = 210$. Express $x$ as a decimal. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 30558,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three vertices of a rectangle are at points $(2, 7)$, $(13, 7)$, and $(13, -6)$. What is the area of the intersection between this rectangle and the circular region described by equation $(x - 2)^2 + (y + 6)^2 = 25$? Let's think step by step and put only the final answer within... | math | {
"style": "rule",
"ground_truth": "\\frac{25}{4}\\pi"
} | {
"split": "train",
"index": 30559,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a circle, parallel chords of lengths 8, 15, and 17 determine central angles of $\\gamma$, $\\delta$, and $\\gamma + \\delta$ radians, respectively, where $\\gamma + \\delta < \\pi$. If $\\cos \\gamma$, which is a positive rational number, is expressed as a fraction in lowest... | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 30560,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the sum of all integer values $n$ for which $\\binom{26}{13}+\\binom{26}{n}=\\binom{27}{14}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "26"
} | {
"split": "train",
"index": 30561,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the largest natural number \\( n \\) so that\n\n\\[ 4^{995} + 4^{1500} + 4^{n} \\]\n\nis a square number. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2004"
} | {
"split": "train",
"index": 30562,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many values of $\\theta$ in the interval $0<\\theta\\le 2\\pi$ satisfy \\[1-3\\sin\\theta+5\\cos3\\theta = 0?\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 30563,
"solution": "1. **Rearrange the given equation**: Start by rearranging the given equation to isolate terms involving $\\theta$:\n \\[\n 1 - 3\\sin\\theta + 5\\cos3\\theta = 0 \\implies 5\\cos3\\theta = 3\\sin\\theta - 1.\n \\]\n\n2. **Analyze the functions**: We need to f... |
deepscaler | [
{
"role": "user",
"content": "Every high school in the city of Euclid sent a team of $3$ students to a math contest. Each participant in the contest received a different score. Andrea's score was the median among all students, and hers was the highest score on her team. Andrea's teammates Beth and Carla pla... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 30564,
"solution": "1. **Understanding the problem setup**: Each high school sends 3 students, and each student has a unique score. Andrea's score is the median of all scores, and she has the highest score on her team. Her teammates Beth and Carla placed 37th and 64th, respectively.\n... |
deepscaler | [
{
"role": "user",
"content": "On Monday at work, David produces $w$ widgets per hour, and works for $t$ hours. Exhausted by this work, on Tuesday, he decides to work for $2$ fewer hours, but manages to produce $4$ additional widgets per hour. If $w = 2t$, how many more widgets did David produce on Monday th... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 30565,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $a,b$ are constants, and $a \\neq 0$, $f\\left( x \\right)=ax^{2}+bx$, $f\\left( 2 \\right)=0$.\n\n(1) If the equation $f\\left( x \\right)-x=0$ has a unique real root, find the analytic expression of the function $f\\left( x \\right)$;\n\n(2) When $a=1$, find the ma... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 30566,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the random variables $\\xi + \\eta = 8$, if $\\xi \\sim B(10, 0.6)$, then calculate $E\\eta$ and $D\\eta$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2.4"
} | {
"split": "train",
"index": 30567,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The numbers $1, 2, 3, 4, 5$ are to be arranged in a circle. An arrangement is $\\textit{bad}$ if it is not true that for every $n$ from $1$ to $15$ one can find a subset of the numbers that appear consecutively on the circle that sum to $n$. Arrangements that differ only by a r... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 30568,
"solution": "1. **Identify the Total Arrangements**: \n The numbers $1, 2, 3, 4, 5$ can be arranged in $5! = 120$ ways in a circle. However, due to rotational symmetry, we can fix one number (e.g., $1$) in a specific position, reducing the arrangements to $4! = 24$. Further c... |
deepscaler | [
{
"role": "user",
"content": "Given that $0 < α < \\dfrac {π}{2}$, and $\\cos ( \\dfrac {π}{3}+α)= \\dfrac {1}{3}$, find the value of $\\cos α$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac {2 \\sqrt {6}+1}{6}"
} | {
"split": "train",
"index": 30569,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $O$ be the origin, and $F$ be the right focus of the ellipse $C: \\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}=1$ where $a > b > 0$. The line $l$ passing through $F$ intersects the ellipse $C$ at points $A$ and $B$. Two points $P$ and $Q$ on the ellipse satisfy\n$$\n\\overright... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 30570,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rectangle has an area of 400 $\\text{cm}^2$. If the rectangle is a square, what is its perimeter? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "80"
} | {
"split": "train",
"index": 30571,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\omega$ be a complex number such that $\\omega^7 = 1$ and $\\omega \\ne 1.$ Let $\\alpha = \\omega + \\omega^2 + \\omega^4$ and $\\beta = \\omega^3 + \\omega^5 + \\omega^6.$ Then $\\alpha$ and $\\beta$ satisfy the quadratic\n\\[x^2 + ax + b = 0\\]for some real numbers $... | math | {
"style": "rule",
"ground_truth": "(1,2)"
} | {
"split": "train",
"index": 30572,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many positive whole numbers have cube roots that are less than $8$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "511"
} | {
"split": "train",
"index": 30573,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A proposal will make years that end in double zeroes a leap year only if the year leaves a remainder of 200 or 600 when divided by 900. Under this proposal, how many leap years will there be that end in double zeroes between 1996 and 4096? Let's think step by step and put only ... | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 30574,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For two lines $ax+2y+1=0$ and $3x+(a-1)y+1=0$ to be parallel, determine the value of $a$ that satisfies this condition. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"split": "train",
"index": 30575,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the remainder when the sum \\(1^2 + 2^2 + 3^2 + \\dots + 20^2\\) is divided by 13? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 30576,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the expression \\(1 \\ast 2 \\ast 3 \\ast 4 \\ast 5 \\ast 6\\).\nEach star in the expression is to be replaced with either ' + ' or ' \\times '.\n\\(N\\) is the largest possible value of the expression. What is the largest prime factor of \\(N\\)? Let's think step by s... | math | {
"style": "rule",
"ground_truth": "103"
} | {
"split": "train",
"index": 30577,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $f\\left(x\\right)=\\ln |a+\\frac{1}{{1-x}}|+b$ is an odd function, then $a=$____, $b=$____. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\ln 2"
} | {
"split": "train",
"index": 30578,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider license plates consisting of a sequence of four digits followed by two letters. Assume each arrangement is equally likely for these plates. What is the probability that such a license plate contains at least one palindrome sequence (either the four-digit sequence or th... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{104}"
} | {
"split": "train",
"index": 30579,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, $\\angle C=90^{\\circ}, \\angle B=30^{\\circ}, AC=2$, $M$ is the midpoint of $AB$. Fold triangle $ACM$ along $CM$ such that the distance between points $A$ and $B$ becomes $2\\sqrt{2}$. Find the volume of the resulting triangular pyramid $A-BCM$. Let's think ... | math | {
"style": "rule",
"ground_truth": "\\frac{2 \\sqrt{2}}{3}"
} | {
"split": "train",
"index": 30580,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the state income tax rate is $q\\%$ for the first $\\$30000$ of yearly income plus $(q + 1)\\%$ for any amount above $\\$30000$, and Samantha's state income tax amounts to $(q + 0.5)\\%$ of her total annual income, determine Samantha's annual income. Let's think step by s... | math | {
"style": "rule",
"ground_truth": "60000"
} | {
"split": "train",
"index": 30581,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Point $(x,y)$ is randomly picked from the rectangular region with vertices at $(0,0),(2017,0),(2017,2018),$ and $(0,2018)$. What is the probability that $x > 9y$? Express your answer as a common fraction. Let's think step by step and put only the final answer within \\boxed{}."... | math | {
"style": "rule",
"ground_truth": "\\frac{2017}{36324}"
} | {
"split": "train",
"index": 30582,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For how many integer values of $n$ between 1 and 120 inclusive does the decimal representation of $\\frac{n}{120}$ terminate? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"split": "train",
"index": 30583,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=4-x^{2}+a\\ln x$, if $f(x)\\leqslant 3$ for all $x > 0$, determine the range of the real number $a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "[2]"
} | {
"split": "train",
"index": 30584,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the positive real value of $t$ that satisfies $|t+2i\\sqrt{3}| |6-4i| = 26$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"split": "train",
"index": 30585,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A right triangle has legs measuring 20 inches and 21 inches. What is the length of the hypotenuse, in inches? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "29"
} | {
"split": "train",
"index": 30586,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "On a long straight stretch of one-way single-lane highway, cars all travel at the same speed and all obey the safety rule: the distance from the back of the car ahead to the front of the car behind is exactly one car length for each 15 kilometers per hour of speed or fraction t... | math | {
"style": "rule",
"ground_truth": "375"
} | {
"split": "train",
"index": 30587,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a right triangle \\( ABC \\) with leg lengths equal to 1, a point \\( P \\) is chosen on one of the sides of the triangle. Find the maximum value of \\( PA \\cdot PB \\cdot PC \\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{4}"
} | {
"split": "train",
"index": 30588,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Inside a right angle with vertex \\(O\\), there is a triangle \\(OAB\\) with a right angle at \\(A\\). The height of the triangle \\(OAB\\), dropped to the hypotenuse, is extended past point \\(A\\) to intersect with the side of the angle at point \\(M\\). The distances from po... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"split": "train",
"index": 30589,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For which natural numbers \\( n \\) is the sum \\( 5^n + n^5 \\) divisible by 13? What is the smallest \\( n \\) that satisfies this condition? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 30590,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A collection of circles in the upper half-plane, all tangent to the $x$-axis, is constructed in layers as follows. Layer $L_0$ consists of two circles of radii $70^2$ and $73^2$ that are externally tangent. For $k \\ge 1$, the circles in $\\bigcup_{j=0}^{k-1}L_j$ are ordered ac... | math | {
"style": "rule",
"ground_truth": "\\frac{143}{14}"
} | {
"split": "train",
"index": 30591,
"solution": "1. **Identify the radii of initial circles**: Let the two circles from $L_0$ be of radius $r_1 = 70^2$ and $r_2 = 73^2$, with $r_1 < r_2$. Let the circle of radius $r_1$ be circle $A$ and the circle of radius $r_2$ be circle $B$.\n\n2. **Constructing the circle in ... |
deepscaler | [
{
"role": "user",
"content": "Calculate \\(3^3 \\cdot 4^3\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1728"
} | {
"split": "train",
"index": 30592,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $a$ and $b$ be even integers such that $ab = 144$. Find the minimum value of $a + b$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-74"
} | {
"split": "train",
"index": 30593,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $α-β=\\frac{π}{3}$ and $tanα-tanβ=3\\sqrt{3}$, calculate the value of $\\cos \\left(\\alpha +\\beta \\right)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{6}"
} | {
"split": "train",
"index": 30594,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A cyclist is riding on a track at a constant speed. It is known that at 11:22, he covered a distance that is 1.4 times greater than the distance he covered at 11:08. When did he start? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10:33"
} | {
"split": "train",
"index": 30595,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that all four roots of the equation $2x^4 + mx^2 + 8 = 0$ are integers, then $m = \\ $, and the polynomial $2x^4 + mx^2 + 8$ can be factored into $\\ $. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-10"
} | {
"split": "train",
"index": 30596,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $x_1, x_2, x_3, \\dots, x_{50}$ be positive real numbers such that $x_1^2 + x_2^2 + x_3^2 + \\dots + x_{50}^2 = 1.$ Find the maximum value of \n\\[\n\\frac{x_1}{1 + x_1^2} + \\frac{x_2}{1 + x_2^2} + \\frac{x_3}{1 + x_3^2} + \\dots + \\frac{x_{50}}{1 + x_{50}^2}.\n\\] Let's ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 30597,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "One half of the water is poured out of a full container. Then one third of the remainder is poured out. Continue the process: one fourth of the remainder for the third pouring, one fifth of the remainder for the fourth pouring, etc. After how many pourings does exactly one t... | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 30598,
"solution": "1. **Model the Remaining Water**: Let's denote the initial amount of water in the container as 1 (representing 100%). We will calculate the remaining fraction of water after each pouring.\n\n2. **Calculate the Remaining Fraction After Each Pouring**:\n - After th... |
deepscaler | [
{
"role": "user",
"content": "In the diagram below, $\\overline{AB}\\parallel \\overline{CD}$ and $\\angle AXF= 118^\\circ$. Find $\\angle FYD$.\n\n[asy]\nunitsize(1inch);\npair A,B,C,D,X,Y,EE,F;\nA = (0,0);\nB=(1,0);\nC = (0,0.8);\nD=(1,0.8);\nEE = (0.35,-0.3);\nF = (0.8,1.1);\ndraw(EE--F);\ndraw(A--B);\n... | math | {
"style": "rule",
"ground_truth": "62^\\circ"
} | {
"split": "train",
"index": 30599,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $S$ is the set of the 1000 smallest positive multiples of $5$, and $T$ is the set of the 1000 smallest positive multiples of $9$, determine the number of elements common to both sets $S$ and $T$. Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "111"
} | {
"split": "train",
"index": 30600,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the coordinate plane, points whose x-coordinates and y-coordinates are both integers are called lattice points. For any natural number \\( n \\), connect the origin \\( O \\) with the point \\( A_n(n, n+3) \\). Let \\( f(n) \\) denote the number of lattice points on the line... | math | {
"style": "rule",
"ground_truth": "1326"
} | {
"split": "train",
"index": 30601,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In a sequence, the first term is \\(a_1 = 2010\\) and the second term is \\(a_2 = 2011\\). The values of the other terms satisfy the relation:\n\\[ a_n + a_{n+1} + a_{n+2} = n \\]\nfor all \\(n \\geq 1\\). Determine \\(a_{500}\\). Let's think step by step and put only the final... | math | {
"style": "rule",
"ground_truth": "2177"
} | {
"split": "train",
"index": 30602,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many positive integers $n$ are there such that $n$ is a multiple of $5$, and the least common multiple of $5!$ and $n$ equals $5$ times the greatest common divisor of $10!$ and $n?$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 30603,
"solution": "1. **Start with the given equation:**\n \\[\n \\text{lcm}(5!, n) = 5 \\cdot \\text{gcd}(10!, n)\n \\]\n Here, $5! = 120$ and $10! = 3628800$.\n\n2. **Express $\\text{lcm}(5!, n)$ in terms of $n$:**\n Since $n$ is a multiple of $5$, we can write $n = 5m$ f... |
deepscaler | [
{
"role": "user",
"content": "Given that the monogram of a person's first, middle, and last initials is in alphabetical order with no letter repeated, and the last initial is 'M', calculate the number of possible monograms. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "66"
} | {
"split": "train",
"index": 30604,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A merchant's cumulative sales from January to May reached 38.6 million yuan. It is predicted that the sales in June will be 5 million yuan, and the sales in July will increase by x% compared to June. The sales in August will increase by x% compared to July. The total sales in S... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"split": "train",
"index": 30605,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the line passing through the focus of the parabola $y^2=x$ intersects the parabola at points A and B, and O is the origin of the coordinates, calculate $\\overrightarrow {OA}\\cdot \\overrightarrow {OB}$. Let's think step by step and put only the final answer within ... | math | {
"style": "rule",
"ground_truth": "-\\frac{3}{16}"
} | {
"split": "train",
"index": 30606,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle $ABC_0$ has a right angle at $C_0$. Its side lengths are pairwise relatively prime positive integers, and its perimeter is $p$. Let $C_1$ be the foot of the altitude to $\\overline{AB}$, and for $n \\geq 2$, let $C_n$ be the foot of the altitude to $\\overline{C_{n-2}B... | math | {
"style": "rule",
"ground_truth": "182"
} | {
"split": "train",
"index": 30607,
"solution": "For this problem, first notice that its an infinite geometric series of $6(a+b+c)=\\frac{ab}{c-b}$ if $c$ is the hypotenuse. WLOG $a<b$, we can generalize a pythagorean triple of $x^2-y^2, 2xy, x^2+y^2$. Let $b=2xy$, then this generalization gives $6(a+b+c)(c-b)=ab... |
deepscaler | [
{
"role": "user",
"content": "There are 4 different colors of light bulbs, with each color representing a different signal. Assuming there is an ample supply of each color, we need to install one light bulb at each vertex $P, A, B, C, A_{1}, B_{1}, C_{1}$ of an airport signal tower (as shown in the diagram)... | math | {
"style": "rule",
"ground_truth": "2916"
} | {
"split": "train",
"index": 30608,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number $695$ is to be written with a factorial base of numeration, that is, $695=a_1+a_2\\times2!+a_3\\times3!+ \\ldots a_n \\times n!$ where $a_1, a_2, a_3 ... a_n$ are integers such that $0 \\le a_k \\le k,$ and $n!$ means $n(n-1)(n-2)...2 \\times 1$. Find $a_4$ Let's thi... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 30609,
"solution": "To solve this problem, we need to express the number 695 in a factorial base. This means we need to find coefficients $a_1, a_2, a_3, \\ldots, a_n$ such that:\n\\[ 695 = a_1 + a_2 \\times 2! + a_3 \\times 3! + \\ldots + a_n \\times n! \\]\nwhere $0 \\leq a_k \\leq ... |
deepscaler | [
{
"role": "user",
"content": "Sides $AB$, $BC$, $CD$ and $DA$ of convex quadrilateral $ABCD$ are extended past $B$, $C$, $D$ and $A$ to points $B'$, $C'$, $D'$ and $A'$, respectively. Also, $AB = BB' = 6$, $BC = CC' = 7$, $CD = DD' = 8$ and $DA = AA' = 9$. The area of $ABCD$ is $10$. The area of $A'B'C'D'$ ... | math | {
"style": "rule",
"ground_truth": "114"
} | {
"split": "train",
"index": 30610,
"solution": "1. **Identify the Triangles and Their Areas**:\n - The quadrilateral $ABCD$ is surrounded by four triangles: $\\triangle A'AB$, $\\triangle BB'C$, $\\triangle CC'D$, and $\\triangle DD'A$.\n - Each of these triangles shares a side with $ABCD$ and has a vertex e... |
deepscaler | [
{
"role": "user",
"content": "Pegs are put in a board $1$ unit apart both horizontally and vertically. A rubber band is stretched over $4$ pegs as shown in the figure, forming a quadrilateral. Its area in square units is\n[asy]\nint i,j;\nfor(i=0; i<5; i=i+1) {\nfor(j=0; j<4; j=j+1) {\ndot((i,j));\n}}\ndraw... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 30611,
"solution": "\n#### Solution 1: Using Pick's Theorem\n\n1. **Identify the number of interior and boundary points:**\n - Interior points: $5$\n - Boundary points: $4$\n\n2. **Apply Pick's Theorem:**\n - Pick's Theorem states that the area $A$ of a simple lattice polygon is... |
deepscaler | [
{
"role": "user",
"content": "Suppose $n$ is a positive integer and $d$ is a single digit in base 10. Find $n$ if\n$\\frac{n}{810}=0.d25d25d25\\ldots$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "750"
} | {
"split": "train",
"index": 30612,
"solution": "Write out these equations:\n$\\frac{n}{180} = \\frac{d25}{999}$\n$\\frac{n}{30} = \\frac{d25}{37}$\n$37n = 30(d25)$\n Thus $n$ divides 25 and 30. The only solution for this under 1000 is $\\boxed{750}$.\n -jackshi2006"
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest positive integer \\( n \\) that satisfies the following condition: If the set \\( A = \\{1, 2, 3, \\ldots, n\\} \\) is arbitrarily divided into 63 pairwise disjoint subsets \\( A_1, A_2, A_3, \\ldots, A_{63} \\) (which are non-empty and their union is the set ... | math | {
"style": "rule",
"ground_truth": "2016"
} | {
"split": "train",
"index": 30613,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the square root of $\\dfrac{9!}{126}$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12\\sqrt{10}"
} | {
"split": "train",
"index": 30614,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x)=x\\ln x-x$, find the monotonic intervals and the extreme values of the function $f(x)$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 30615,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the trapezoid \\(ABCD\\), the base \\(AB\\) is three times longer than the base \\(CD\\). On the base \\(CD\\), point \\(M\\) is taken such that \\(MC = 2MD\\). \\(N\\) is the intersection point of lines \\(BM\\) and \\(AC\\). Find the ratio of the area of triangle \\(MNC\\)... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{33}"
} | {
"split": "train",
"index": 30616,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The amount of algae covering the Smith's backyard pond doubled every day until it was completely covered in algae on day $30$ of the month. On what day of that month was $75\\%$ of the pond algae-free? Let's think step by step and put only the final answer within \\boxed{}."
... | math | {
"style": "rule",
"ground_truth": "28"
} | {
"split": "train",
"index": 30617,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $\\mathbf{M} = \\begin{pmatrix} 2 & 7 \\\\ -3 & -1 \\end{pmatrix}.$ There exist scalars $p$ and $q$ such that\n\\[\\mathbf{M}^2 = p \\mathbf{M} + q \\mathbf{I}.\\]Enter the ordered pair $(p,q).$ Let's think step by step and put only the final answer within \\boxed{}."
}
... | math | {
"style": "rule",
"ground_truth": "(1,-19)"
} | {
"split": "train",
"index": 30618,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the last two digits of $1032^{1032}$. Express your answer as a two-digit number. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "76"
} | {
"split": "train",
"index": 30619,
"solution": "The last two digits of $1032^{1032}$ is the same as the last two digits of $32^{1032}$. The last two digits of $32^{n}$ repeat with a period of four as $32,24,68,76,32,24,68,76, \\ldots$. Therefore, the last two digits are 76."
} |
deepscaler | [
{
"role": "user",
"content": "Calculate the sum of the distances from one vertex of a rectangle with sides of lengths $3$ and $5$ to the midpoints of each of the sides of the rectangle.\nA) $11.2$\nB) $12.4$\nC) $13.1$\nD) $14.5$\nE) $15.2$ Let's think step by step and put only the final answer within \\box... | math | {
"style": "rule",
"ground_truth": "13.1"
} | {
"split": "train",
"index": 30620,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given two lines $l_{1}: ax-y+a=0$ and $l_{2}: (2a-3)x+ay-a=0$ are parallel, determine the value of $a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"split": "train",
"index": 30621,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The number of solution-pairs in the positive integers of the equation $3x+5y=501$ is: Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "33"
} | {
"split": "train",
"index": 30622,
"solution": "1. **Rewrite the equation and express $y$ in terms of $x$:**\n Given the equation $3x + 5y = 501$, we can express $y$ in terms of $x$:\n \\[\n y = \\frac{501 - 3x}{5}\n \\]\n For $y$ to be a positive integer, $501 - 3x$ must be a positive multiple of $5$.... |
deepscaler | [
{
"role": "user",
"content": "In $\\triangle ABC$, if $\\angle B=30^{\\circ}$, $AB=2 \\sqrt {3}$, $AC=2$, find the area of $\\triangle ABC$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2 \\sqrt {3}"
} | {
"split": "train",
"index": 30623,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many positive divisors of 30! are prime? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 30624,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Simplify the expression $20(x+y)-19(y+x)$ for all values of $x$ and $y$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "x+y"
} | {
"split": "train",
"index": 30625,
"solution": "Simplifying, we see that $20(x+y)-19(y+x)=20x+20y-19y-19x=x+y$ for all values of $x$ and $y$."
} |
deepscaler | [
{
"role": "user",
"content": "A computer program evaluates expressions without parentheses in the following way:\n\n1) First, it performs multiplications and divisions from left to right one by one.\n2) Then, it performs additions and subtractions from left to right.\n\nFor example, the value of the express... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 30626,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Team A and team B play a series. The first team to win three games wins the series. Each team is equally likely to win each game, there are no ties, and the outcomes of the individual games are independent. If team B wins the second game and team A wins the series, what is the ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"split": "train",
"index": 30627,
"solution": "To solve this problem, we need to consider all possible sequences of game outcomes where Team A wins the series and Team B wins the second game. We then determine the probability that Team B wins the first game under these conditions.\n\n1. **Identify possible sequ... |
deepscaler | [
{
"role": "user",
"content": "Find the sum of the roots of the equation \\[(2x^3 + x^2 - 8x + 20)(5x^3 - 25x^2 + 19) = 0.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\tfrac{9}{2}"
} | {
"split": "train",
"index": 30628,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three congruent isosceles triangles $DAO$, $AOB$, and $OBC$ have $AD=AO=OB=BC=12$ and $AB=DO=OC=16$. These triangles are arranged to form trapezoid $ABCD$. Point $P$ is on side $AB$ so that $OP$ is perpendicular to $AB$. Points $X$ and $Y$ are the midpoints of $AD$ and $BC$, re... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 30629,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The diagram shows a rhombus and two sizes of regular hexagon. What is the ratio of the area of the smaller hexagon to the area of the larger hexagon? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1:4"
} | {
"split": "train",
"index": 30630,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the function $f(x) = |2x+a| + |2x-2b| + 3$ \n(Ⅰ) If $a=1$, $b=1$, find the solution set of the inequality $f(x) > 8$; \n(Ⅱ) When $a>0$, $b>0$, if the minimum value of $f(x)$ is $5$, find the minimum value of $\\frac{1}{a} + \\frac{1}{b}$. Let's think step by step and pu... | math | {
"style": "rule",
"ground_truth": "\\frac{3+2\\sqrt{2}}{2}"
} | {
"split": "train",
"index": 30631,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many different 7-digit positive integers exist? (Note that we don't allow \"7-digit\" integers that start with 0, such as 0123456; this is actually a 6-digit integer.) Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9,\\!000,\\!000"
} | {
"split": "train",
"index": 30632,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In the trapezoid \\(MPQF\\), the bases are \\(MF = 24\\) and \\(PQ = 4\\). The height of the trapezoid is 5. Point \\(N\\) divides the side into segments \\(MN\\) and \\(NP\\) such that \\(MN = 3NP\\).\n\nFind the area of triangle \\(NQF\\). Let's think step by step and put onl... | math | {
"style": "rule",
"ground_truth": "22.5"
} | {
"split": "train",
"index": 30633,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The equation\n$x^{10}+(13x-1)^{10}=0\\,$\n has 10 complex roots $r_1, \\overline{r_1}, r_2, \\overline{r_2}, r_3, \\overline{r_3}, r_4, \\overline{r_4}, r_5, \\overline{r_5},\\,$ where the bar denotes complex conjugation. Find the value of\n$\\frac 1{r_1\\overline{r_1}}+\\frac ... | math | {
"style": "rule",
"ground_truth": "850"
} | {
"split": "train",
"index": 30634,
"solution": "Divide both sides by $x^{10}$ to get \\[1 + \\left(13-\\dfrac{1}{x}\\right)^{10}=0\\]\n Rearranging: \\[\\left(13-\\dfrac{1}{x}\\right)^{10} = -1\\]\n Thus, $13-\\dfrac{1}{x} = \\omega$ where $\\omega = e^{i(\\pi n/5+\\pi/10)}$ where $n$ is an integer.\n We see tha... |
deepscaler | [
{
"role": "user",
"content": "The real numbers $x, y$ and $z$ satisfy the three equations $x+y=7$, $xz=-180$, and $(x+y+z)^{2}=4$. If $S$ is the sum of the two possible values of $y$, what is $-S$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "42"
} | {
"split": "train",
"index": 30635,
"solution": "Since $x+y=7$, then $x+y+z=7+z$. Thus, the equation $(x+y+z)^{2}=4$ becomes $(7+z)^{2}=4$. Since the square of $7+z$ equals 4, then $7+z=2$ or $7+z=-2$. If $7+z=2$, then $z=-5$. In this case, since $xz=-180$, we get $x=\\frac{-180}{-5}=36$ which gives $y=7-x=-29$. ... |
deepscaler | [
{
"role": "user",
"content": "Suppose $a$ is an integer such that $0 \\le a \\le 14$, and $235935623_{74}-a$ is a multiple of $15$. What is $a$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 30636,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\alpha \\in \\left( 0, \\pi \\right)$ and $3\\cos 2\\alpha = \\sin \\left( \\frac{\\pi}{4} - \\alpha \\right)$, find the value of $\\sin 2\\alpha$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{17}{18}"
} | {
"split": "train",
"index": 30637,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A store sells jellybeans at a fixed price per gram. The price for 250 g of jellybeans is $\\$ 7.50$. What mass of jellybeans sells for $\\$ 1.80$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "60 \\mathrm{~g}"
} | {
"split": "train",
"index": 30638,
"solution": "The store sells 250 g of jellybeans for $\\$ 7.50$, which is 750 cents. Therefore, 1 g of jellybeans costs $750 \\div 250=3$ cents. This means that $\\$ 1.80$, which is 180 cents, will buy $180 \\div 3=60 \\mathrm{~g}$ of jellybeans."
} |
deepscaler | [
{
"role": "user",
"content": "Consider a $4 \\times 4$ grid of squares, each of which are originally colored red. Every minute, Piet can jump on one of the squares, changing the color of it and any adjacent squares (two squares are adjacent if they share a side) to blue. What is the minimum number of minute... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"split": "train",
"index": 30639,
"solution": "Piet can change the colors of at most 5 squares per minute, so as there are 16 squares, it will take him at least four minutes to change the colors of every square. Some experimentation yields that it is indeed possible to make the entire grid blue after 4 minutes;... |
deepscaler | [
{
"role": "user",
"content": "Give an example of a function that, when \\( x \\) is equal to a known number, takes the form \\( \\frac{0}{0} \\), but as \\( x \\) approaches this number, tends to a certain limit. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{8}{7}"
} | {
"split": "train",
"index": 30640,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute \n\\[\n\\sin^2 3^\\circ + \\sin^2 6^\\circ + \\sin^2 9^\\circ + \\dots + \\sin^2 177^\\circ.\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"split": "train",
"index": 30641,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $f$ be a non-constant polynomial such that\n\\[f(x - 1) + f(x) + f(x + 1) = \\frac{[f(x)]^2}{2013x}\\]for all nonzero real numbers $x.$ Find the sum of all possible values of $f(1).$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6039"
} | {
"split": "train",
"index": 30642,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Define $g$ by $g(x) = 3x + 2$. If $g(x) = f^{-1}(x) - 5$ and $f^{-1}(x)$ is the inverse of the function $f(x) = cx + d$, find $7c + 3d$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{14}{3}"
} | {
"split": "train",
"index": 30643,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A classroom has 9 desks arranged in a row. Two students, Alex and Jessie, choose their desks at random. What is the probability that they do not sit next to each other? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7}{9}"
} | {
"split": "train",
"index": 30644,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A sequence of distinct circles $\\omega_1, \\omega_2, \\cdots$ is inscribed in the parabola $y=x^2$ so that $\\omega_n$ and $\\omega_{n+1}$ are tangent for all $n$ . If $\\omega_1$ has diameter $1$ and touches the parabola at $(0,0)$ , find the diameter of $\\om... | math | {
"style": "rule",
"ground_truth": "3995"
} | {
"split": "train",
"index": 30645,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given quadrilateral $ABCD,$ side $\\overline{AB}$ is extended past $B$ to $A'$ so that $A'B = AB.$ Points $B',$ $C',$ and $D'$ are similarly constructed.\n\n[asy]\nunitsize(1 cm);\n\npair[] A, B, C, D;\n\nA[0] = (0,0);\nB[0] = (2,0);\nC[0] = (1.5,2);\nD[0] = (0.2,1.5);\nA[1] =... | math | {
"style": "rule",
"ground_truth": "\\left( \\frac{1}{15}, \\frac{2}{15}, \\frac{4}{15}, \\frac{8}{15} \\right)"
} | {
"split": "train",
"index": 30646,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Currently, 7 students are to be assigned to participate in 5 sports events, with the conditions that students A and B cannot participate in the same event, each event must have at least one participant, and each student can only participate in one event. How many different ways... | math | {
"style": "rule",
"ground_truth": "15000"
} | {
"split": "train",
"index": 30647,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Joe had walked half way from home to school when he realized he was late. He ran the rest of the way to school. He ran 3 times as fast as he walked. Joe took 6 minutes to walk half way to school. How many minutes did it take Joe to get from home to school? Let's think step by s... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 30648,
"solution": "1. **Understanding the problem**: Joe walks half the distance to school and runs the other half. He walks at a certain speed and runs at three times that speed. It takes him 6 minutes to walk the first half.\n\n2. **Setting up the equations**: Let's denote:\n - $... |
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