data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict | ground_truth stringlengths 1 159 |
|---|---|---|---|---|---|
deepscaler | [
{
"content": "Given the hyperbola $mx^{2}+y^{2}=1$ and one of its asymptotes has a slope of $2$, find the value of $m$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"difficulty": 14.84375,
"index": 14453,
"split": "train"
} | -4 |
deepscaler | [
{
"content": "Jack wants to bike from his house to Jill's house, which is located three blocks east and two blocks north of Jack's house. After biking each block, Jack can continue either east or north, but he needs to avoid a dangerous intersection one block east and one block north of his house. In how many w... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"difficulty": 22.65625,
"index": 13903,
"split": "train"
} | 4 |
deepscaler | [
{
"content": "Given that the sum of the first $n$ terms of the sequence ${a_n}$ is $S_n$, and the sum of the first $n$ terms of the sequence ${b_n}$ is $T_n$. It is known that $a_1=2$, $3S_n=(n+m)a_n$, ($m\\in R$), and $a_nb_n=\\frac{1}{2}$. If for any $n\\in N^*$, $\\lambda>T_n$ always holds true, then the min... | math | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"difficulty": 75.78125,
"index": 4217,
"split": "train"
} | \frac{1}{2} |
deepscaler | [
{
"content": "Compute the number of quadruples $(a, b, c, d)$ of positive integers satisfying $12a+21b+28c+84d=2024$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "2024",
"style": "rule"
} | {
"difficulty": 32.03125,
"index": 12480,
"split": "train"
} | 2024 |
deepscaler | [
{
"content": "In triangle \\(ABC\\), the angle bisector of \\(\\angle ABC\\) intersects side \\(AC\\) at point \\(K\\). It is given that \\(BC = 2\\), \\(KC = 1\\), and \\(BK = \\frac{3\\sqrt{2}}{2}\\). Find the area of triangle \\(ABC\\). Let's think step by step and output the final answer within \\boxed{}.",... | math | {
"ground_truth": "\\frac{15 \\sqrt{7}}{16}",
"style": "rule"
} | {
"difficulty": 46.875,
"index": 9102,
"split": "train"
} | \frac{15 \sqrt{7}}{16} |
deepscaler | [
{
"content": "An up-right path between two lattice points $P$ and $Q$ is a path from $P$ to $Q$ that takes steps of 1 unit either up or to the right. A lattice point $(x, y)$ with $0 \\leq x, y \\leq 5$ is chosen uniformly at random. Compute the expected number of up-right paths from $(0,0)$ to $(5,5)$ not pass... | math | {
"ground_truth": "175",
"style": "rule"
} | {
"difficulty": 97.65625,
"index": 436,
"split": "train"
} | 175 |
deepscaler | [
{
"content": "In the trapezoid \\(ABCD\\), the bases \\(AD\\) and \\(BC\\) are 8 and 18 respectively. It is known that the circumcircle of triangle \\(ABD\\) is tangent to the lines \\(BC\\) and \\(CD\\). Find the perimeter of the trapezoid. Let's think step by step and output the final answer within \\boxed{}.... | math | {
"ground_truth": "56",
"style": "rule"
} | {
"difficulty": 96.875,
"index": 769,
"split": "train"
} | 56 |
deepscaler | [
{
"content": "Arrange the numbers 1 to 9 in a row from left to right such that every three consecutive numbers form a three-digit number that is a multiple of 3. How many arrangements are there? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "1296",
"style": "rule"
} | {
"difficulty": 61.71875,
"index": 6549,
"split": "train"
} | 1296 |
deepscaler | [
{
"content": "There exists a unique strictly increasing sequence of nonnegative integers $a_1 < a_2 < \\dots < a_k$ such that\\[\\frac{2^{289}+1}{2^{17}+1} = 2^{a_1} + 2^{a_2} + \\dots + 2^{a_k}.\\]What is $k?$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "137",
"style": "rule"
} | {
"difficulty": 68.75,
"index": 6158,
"split": "train"
} | 137 |
deepscaler | [
{
"content": "The base $ABCD$ of a tetrahedron $P-ABCD$ is a convex quadrilateral with diagonals $AC$ and $BD$ intersecting at $O$. If the area of $\\triangle AOB$ is 36, the area of $\\triangle COD$ is 64, and the height of the tetrahedron is 9, what is the minimum volume of such a tetrahedron? Let's think ste... | math | {
"ground_truth": "588",
"style": "rule"
} | {
"difficulty": 93.75,
"index": 909,
"split": "train"
} | 588 |
deepscaler | [
{
"content": "The circle C is tangent to the y-axis and the line l: y = (√3/3)x, and the circle C passes through the point P(2, √3). Determine the diameter of circle C. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{14}{3}",
"style": "rule"
} | {
"difficulty": 76.5625,
"index": 4419,
"split": "train"
} | \frac{14}{3} |
deepscaler | [
{
"content": "What is the average of all the integer values of $M$ such that $\\frac{M}{42}$ is strictly between $\\frac{5}{14}$ and $\\frac{1}{6}$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "11",
"style": "rule"
} | {
"difficulty": 25.78125,
"index": 13891,
"split": "train"
} | 11 |
deepscaler | [
{
"content": "Let $p, q, r$ be primes such that $2 p+3 q=6 r$. Find $p+q+r$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "7",
"style": "rule"
} | {
"difficulty": 36.71875,
"index": 10953,
"split": "train"
} | 7 |
deepscaler | [
{
"content": "A two-digit positive integer $x$ has the property that when 109 is divided by $x$, the remainder is 4. What is the sum of all such two-digit positive integers $x$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "71",
"style": "rule"
} | {
"difficulty": 28.125,
"index": 13946,
"split": "train"
} | 71 |
deepscaler | [
{
"content": "Mr. Sanchez's students were asked to add two positive integers. Juan subtracted by mistake and got 2. Maria mistakenly multiplied and got 120. What was the correct answer? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "22",
"style": "rule"
} | {
"difficulty": 37.5,
"index": 10830,
"split": "train"
} | 22 |
deepscaler | [
{
"content": "Read the following material and then answer the following questions: When simplifying algebraic expressions, sometimes we encounter expressions like $\\frac{5}{\\sqrt{3}}$, $\\frac{2}{\\sqrt{3}+1}$, in fact, we can further simplify them:<br/>$($1) $\\frac{5}{\\sqrt{3}}=\\frac{5×\\sqrt{3}}{\\sqrt{3... | math | {
"ground_truth": "\\frac{3\\sqrt{11}-1}{2}",
"style": "rule"
} | {
"difficulty": 40.625,
"index": 10003,
"split": "train"
} | \frac{3\sqrt{11}-1}{2} |
deepscaler | [
{
"content": "Given the data from a 2×2 contingency table calculates $k=4.073$, there is a \\_\\_\\_\\_\\_\\_ confidence that the two variables are related, knowing that $P(k^2 \\geq 3.841) \\approx 0.05$, $P(k^2 \\geq 5.024) \\approx 0.025$. Let's think step by step and output the final answer within \\boxed{}... | math | {
"ground_truth": "95\\%",
"style": "rule"
} | {
"difficulty": 20.3125,
"index": 13489,
"split": "train"
} | 95\% |
deepscaler | [
{
"content": "A random simulation method is used to estimate the probability of a shooter hitting the target at least 3 times out of 4 shots. A calculator generates random integers between 0 and 9, where 0 and 1 represent missing the target, and 2 through 9 represent hitting the target. Groups of 4 random numbe... | math | {
"ground_truth": "0.75",
"style": "rule"
} | {
"difficulty": 86.71875,
"index": 1939,
"split": "train"
} | 0.75 |
deepscaler | [
{
"content": "The sum of 81 consecutive integers is $9^5$. What is their median? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "729",
"style": "rule"
} | {
"difficulty": 33.59375,
"index": 11140,
"split": "train"
} | 729 |
deepscaler | [
{
"content": "If the ratio of the legs of a right triangle is $3: 4$, then the ratio of the corresponding segments of the hypotenuse made by a perpendicular upon it from the vertex is:\nA) $\\frac{16}{9}$\nB) $\\frac{9}{16}$\nC) $\\frac{3}{4}$\nD) $\\frac{4}{3}$ Let's think step by step and output the final ans... | math | {
"ground_truth": "\\frac{16}{9}",
"style": "rule"
} | {
"difficulty": 93.75,
"index": 707,
"split": "train"
} | \frac{16}{9} |
deepscaler | [
{
"content": "Given the function f(x) = 3x^2 + 5x - 2, find the minimum value of the function f(x) in the interval [-2, -1]. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-4",
"style": "rule"
} | {
"difficulty": 54.6875,
"index": 7461,
"split": "train"
} | -4 |
deepscaler | [
{
"content": "Parallelepiped $ABCDEFGH$ is generated by vectors $\\overrightarrow{AB},$ $\\overrightarrow{AD},$ and $\\overrightarrow{AE},$ as shown below.\n\n[asy]\nimport three;\n\nsize(220);\ncurrentprojection = orthographic(0.5,0.3,0.2);\n\ntriple I = (1,0,0), J = (0,1,0), K = (0,0,1), O = (0,0,0);\ntriple ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"difficulty": 20.3125,
"index": 13672,
"split": "train"
} | 4 |
deepscaler | [
{
"content": "The asymptotes of a hyperbola are $y = x + 1$ and $y = 3 - x.$ Also, the hyperbola passes through $(3,3).$ Find the distance between the foci of the hyperbola. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "2 \\sqrt{6}",
"style": "rule"
} | {
"difficulty": 32.03125,
"index": 11397,
"split": "train"
} | 2 \sqrt{6} |
deepscaler | [
{
"content": "In triangle $∆ABC$, the angles $A$, $B$, $C$ correspond to the sides $a$, $b$, $c$ respectively. The vector $\\overrightarrow{m}\\left(a, \\sqrt{3b}\\right)$ is parallel to $\\overrightarrow{n}=\\left(\\cos A,\\sin B\\right)$.\n\n(1) Find $A$;\n\n(2) If $a= \\sqrt{7},b=2$, find the area of $∆ABC$.... | math | {
"ground_truth": "\\dfrac{3 \\sqrt{3}}{2}",
"style": "rule"
} | {
"difficulty": 13.28125,
"index": 14447,
"split": "train"
} | \dfrac{3 \sqrt{3}}{2} |
deepscaler | [
{
"content": "Given triangle ABC, where a, b, and c are the sides opposite to angles A, B, and C respectively, sin(2C - $\\frac {π}{2}$) = $\\frac {1}{2}$, and a<sup>2</sup> + b<sup>2</sup> < c<sup>2</sup>.\n(1) Find the measure of angle C.\n(2) Find the value of $\\frac {a + b}{c}$. Let's think step by step an... | math | {
"ground_truth": "\\frac {2 \\sqrt{3}}{3}",
"style": "rule"
} | {
"difficulty": 61.71875,
"index": 5394,
"split": "train"
} | \frac {2 \sqrt{3}}{3} |
deepscaler | [
{
"content": "On a 6 by 6 grid of points, what fraction of the larger square's area is inside the new shaded square? Place the bottom-left vertex of the square at grid point (3,3) and the square rotates 45 degrees (square's sides are diagonals of the smaller grid cells).\n```\n[asy]\nsize(6cm);\nfill((3,3)--(4,... | math | {
"ground_truth": "\\frac{1}{18}",
"style": "rule"
} | {
"difficulty": 35.9375,
"index": 12572,
"split": "train"
} | \frac{1}{18} |
deepscaler | [
{
"content": "Ranu starts with one standard die on a table. At each step, she rolls all the dice on the table: if all of them show a 6 on top, then she places one more die on the table; otherwise, she does nothing more on this step. After 2013 such steps, let $D$ be the number of dice on the table. What is... | math | {
"ground_truth": "10071",
"style": "rule"
} | {
"difficulty": 89.84375,
"index": 2593,
"split": "train"
} | 10071 |
deepscaler | [
{
"content": "Given the real numbers $a, x, y$ that satisfy the equation:\n$$\nx \\sqrt{a(x-a)}+y \\sqrt{a(y-a)}=\\sqrt{|\\lg (x-a)-\\lg (a-y)|},\n$$\n\nfind the value of the algebraic expression $\\frac{3 x^{2}+x y-y^{2}}{x^{2}-x y+y^{2}}$. Let's think step by step and output the final answer within \\boxed{}.... | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"difficulty": 92.1875,
"index": 335,
"split": "train"
} | \frac{1}{3} |
deepscaler | [
{
"content": "Solve the equation \\(3 \\cdot 4^{\\log_{x} 2} - 46 \\cdot 2^{\\log_{x} 2 - 1} = 8\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt[3]{2}",
"style": "rule"
} | {
"difficulty": 35.15625,
"index": 10797,
"split": "train"
} | \sqrt[3]{2} |
deepscaler | [
{
"content": "Professors Alpha, Beta, Gamma, and Delta choose their chairs so that each professor will be between two students. Given that there are 13 chairs in total, determine the number of ways these four professors can occupy their chairs. Let's think step by step and output the final answer within \\boxed... | math | {
"ground_truth": "1680",
"style": "rule"
} | {
"difficulty": 97.65625,
"index": 322,
"split": "train"
} | 1680 |
deepscaler | [
{
"content": "Given positive real numbers \\(a, b, c\\) satisfy \\(2(a+b)=ab\\) and \\(a+b+c=abc\\), find the maximum value of \\(c\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{8}{15}",
"style": "rule"
} | {
"difficulty": 58.59375,
"index": 8703,
"split": "train"
} | \frac{8}{15} |
deepscaler | [
{
"content": "Given a right circular cone with a base radius of \\(1 \\, \\text{cm}\\) and a slant height of \\(3 \\, \\text{cm}\\), point \\(P\\) is on the circumference of the base. Determine the shortest distance from the vertex \\(V\\) of the cone to the shortest path from \\(P\\) back to \\(P\\). Let's thi... | math | {
"ground_truth": "1.5",
"style": "rule"
} | {
"difficulty": 98.4375,
"index": 1482,
"split": "train"
} | 1.5 |
deepscaler | [
{
"content": "The real function $f$ has the property that, whenever $a,$ $b,$ $n$ are positive integers such that $a + b = 2^n,$ the equation\n\\[f(a) + f(b) = n^2\\]holds. What is $f(2002)$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "96",
"style": "rule"
} | {
"difficulty": 43.75,
"index": 10707,
"split": "train"
} | 96 |
deepscaler | [
{
"content": "8 students are practicing for a math contest, and they divide into pairs to take a practice test. In how many ways can they be split up? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "105",
"style": "rule"
} | {
"difficulty": 32.03125,
"index": 10952,
"split": "train"
} | 105 |
deepscaler | [
{
"content": "Suppose that $x$ and $y$ are real numbers that satisfy the two equations: $x^{2} + 3xy + y^{2} = 909$ and $3x^{2} + xy + 3y^{2} = 1287$. What is a possible value for $x+y$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "27",
"style": "rule"
} | {
"difficulty": 74.21875,
"index": 4999,
"split": "train"
} | 27 |
deepscaler | [
{
"content": "What is the product of the numerator and the denominator when $0.\\overline{012}$ is expressed as a fraction in lowest terms? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "1332",
"style": "rule"
} | {
"difficulty": 10.15625,
"index": 15145,
"split": "train"
} | 1332 |
deepscaler | [
{
"content": "Two skiers started from the same point one after another with an interval of 9 minutes. The second skier caught up with the first one 9 km from the starting point. After reaching the “27 km” mark, the second skier turned back and met the first skier at a distance of 2 km from the turning point. Fi... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"difficulty": 83.59375,
"index": 2368,
"split": "train"
} | 15 |
deepscaler | [
{
"content": "From the 4040 integers ranging from -2020 to 2019, three numbers are randomly chosen and multiplied together. Let the smallest possible product be $m$ and the largest possible product be $n$. What is the value of $\\frac{m}{n}$? Provide the answer in simplest fraction form. Let's think step by ste... | math | {
"ground_truth": "-\\frac{2020}{2017}",
"style": "rule"
} | {
"difficulty": 55.46875,
"index": 8809,
"split": "train"
} | -\frac{2020}{2017} |
deepscaler | [
{
"content": "Consider polynomials $P(x)$ of degree at most $3$, each of whose coefficients is an element of $\\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\\}$. How many such polynomials satisfy $P(-1) = -9$?\n$\\textbf{(A) } 110 \\qquad \\textbf{(B) } 143 \\qquad \\textbf{(C) } 165 \\qquad \\textbf{(D) } 220 \\qquad \\textb... | math | {
"ground_truth": "220",
"style": "rule"
} | {
"difficulty": 56.25,
"index": 7646,
"split": "train"
} | 220 |
deepscaler | [
{
"content": "Five persons wearing badges with numbers $1, 2, 3, 4, 5$ are seated on $5$ chairs around a circular table. In how many ways can they be seated so that no two persons whose badges have consecutive numbers are seated next to each other? (Two arrangements obtained by rotation around the table are... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"difficulty": 27.34375,
"index": 13771,
"split": "train"
} | 10 |
deepscaler | [
{
"content": "Suppose $a$ is $150\\%$ of $b$. What percent of $a$ is $3b$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "200",
"style": "rule"
} | {
"difficulty": 11.71875,
"index": 16134,
"split": "train"
} | 200 |
deepscaler | [
{
"content": "8 students are practicing for a math contest, and they divide into pairs to take a practice test. In how many ways can they be split up? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "105",
"style": "rule"
} | {
"difficulty": 32.03125,
"index": 10952,
"split": "train"
} | 105 |
deepscaler | [
{
"content": "Given that \\(\\theta\\) is an angle in the third quadrant, and \\(\\sin^{4}\\theta + \\cos^{4}\\theta = \\frac{5}{9}\\), determine the value of \\(\\sin 2\\theta\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{2\\sqrt{2}}{3}",
"style": "rule"
} | {
"difficulty": 89.0625,
"index": 3498,
"split": "train"
} | -\frac{2\sqrt{2}}{3} |
deepscaler | [
{
"content": "The number $101$ is the smallest three-digit palindromic prime. What is the second-smallest one? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "131",
"style": "rule"
} | {
"difficulty": 32.8125,
"index": 12395,
"split": "train"
} | 131 |
deepscaler | [
{
"content": "What integer should 999,999,999 be multiplied by to get a number consisting of only ones? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "111111111",
"style": "rule"
} | {
"difficulty": 75.78125,
"index": 3769,
"split": "train"
} | 111111111 |
deepscaler | [
{
"content": "The distances from a certain point inside a regular hexagon to three of its consecutive vertices are 1, 1, and 2, respectively. What is the side length of this hexagon? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
"difficulty": 63.28125,
"index": 6854,
"split": "train"
} | \sqrt{3} |
deepscaler | [
{
"content": "Each of the 33 warriors either always lies or always tells the truth. It is known that each warrior has exactly one favorite weapon: a sword, a spear, an axe, or a bow.\n\nOne day, Uncle Chernomor asked each warrior four questions:\n- Is your favorite weapon a sword?\n- Is your favorite weapon a s... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"difficulty": 46.875,
"index": 10685,
"split": "train"
} | 12 |
deepscaler | [
{
"content": "Determine the residue of $-811\\pmod{24}$. Your answer should be an integer in the range $0,1,2,\\ldots,22,23$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"difficulty": 10.15625,
"index": 15886,
"split": "train"
} | 5 |
deepscaler | [
{
"content": "The expression $10y^2 - 51y + 21$ can be written as $(Cy - D)(Ey - F)$, where $C, D, E, F$ are integers. What is $CE + C$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "15",
"style": "rule"
} | {
"difficulty": 60.9375,
"index": 6550,
"split": "train"
} | 15 |
deepscaler | [
{
"content": "When $\\left( 1 - \\frac{1}{a} \\right)^6$ is expanded the sum of the last three coefficients is: Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "10",
"style": "rule"
} | {
"difficulty": 14.84375,
"index": 15649,
"split": "train"
} | 10 |
deepscaler | [
{
"content": "A toy store manager received a large order of Mr. Slinkums just in time for the holidays. The manager places $20\\%$ of them on the shelves, leaving the other 120 Mr. Slinkums in storage. How many Mr. Slinkums were in this order? Let's think step by step and output the final answer within \\boxed{... | math | {
"ground_truth": "150",
"style": "rule"
} | {
"difficulty": 1.5625,
"index": 16588,
"split": "train"
} | 150 |
deepscaler | [
{
"content": "Construct spheres that are tangent to 4 given spheres. If we accept the point (a sphere with zero radius) and the plane (a sphere with infinite radius) as special cases, how many such generalized spatial Apollonian problems exist? Let's think step by step and output the final answer within \\boxed... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"difficulty": 71.09375,
"index": 4918,
"split": "train"
} | 15 |
deepscaler | [
{
"content": "The first term of a given sequence is 1, and each successive term is the sum of all the previous terms of the sequence plus the square of the first term. What is the value of the first term which exceeds 10000? Let's think step by step and output the final answer within \\boxed{}.",
"role": "u... | math | {
"ground_truth": "16384",
"style": "rule"
} | {
"difficulty": 35.15625,
"index": 12002,
"split": "train"
} | 16384 |
deepscaler | [
{
"content": "Given a line $l$ intersects the hyperbola $x^2 - \\frac{y^2}{2} = 1$ at two distinct points $A$ and $B$. If point $M(1, 2)$ is the midpoint of segment $AB$, find the equation of line $l$ and the length of segment $AB$. Let's think step by step and output the final answer within \\boxed{}.",
"r... | math | {
"ground_truth": "4\\sqrt{2}",
"style": "rule"
} | {
"difficulty": 54.6875,
"index": 8249,
"split": "train"
} | 4\sqrt{2} |
deepscaler | [
{
"content": "The parabola with equation $y=ax^2+bx+c$ is graphed below:\n\n[asy]\nxaxis(-3,7);\n\nyaxis(-5,32);\n\nreal g(real x)\n\n{\n\nreturn 4(x-2)^2-4;\n}\n\ndraw(graph(g,-1,5));\ndot((2,-4));\nlabel(\"Vertex: $(2,-4)$\", (2,-4), SE);\ndot((4,12));\nlabel(\"$(4,12)$\", (4,12), E);\n[/asy]\n\nThe zeros of ... | math | {
"ground_truth": "2",
"style": "rule"
} | {
"difficulty": 10.15625,
"index": 16023,
"split": "train"
} | 2 |
deepscaler | [
{
"content": "How many groups of integer solutions are there for the equation $xyz = 2009$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "72",
"style": "rule"
} | {
"difficulty": 81.25,
"index": 3213,
"split": "train"
} | 72 |
deepscaler | [
{
"content": "In parallelogram \\(ABCD\\), points \\(A_{1}, A_{2}, A_{3}, A_{4}\\) and \\(C_{1}, C_{2}, C_{3}, C_{4}\\) are respectively the quintisection points of \\(AB\\) and \\(CD\\). Points \\(B_{1}, B_{2}\\) and \\(D_{1}, D_{2}\\) are respectively the trisection points of \\(BC\\) and \\(DA\\). Given that... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"difficulty": 89.0625,
"index": 2440,
"split": "train"
} | 15 |
deepscaler | [
{
"content": "Convert the point $(\\rho,\\theta,\\phi) = \\left( 12, \\frac{7 \\pi}{6}, \\frac{\\pi}{3} \\right)$ in spherical coordinates to rectangular coordinates. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "(-9, -3 \\sqrt{3}, 6)",
"style": "rule"
} | {
"difficulty": 64.0625,
"index": 6545,
"split": "train"
} | (-9, -3 \sqrt{3}, 6) |
deepscaler | [
{
"content": "Find all pairs $(a,\\, b)$ of positive integers such that $2a-1$ and $2b+1$ are coprime and $a+b$ divides $4ab+1.$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "(a, a+1)",
"style": "rule"
} | {
"difficulty": 99.21875,
"index": 528,
"split": "train"
} | (a, a+1) |
deepscaler | [
{
"content": "A modified sign pyramid with five levels, where a cell gets a \"+\" if the two cells below it have the same sign, and it gets a \"-\" if the two cells below it have different signs. If a \"-\" is to be at the top of the pyramid, calculate the number of possible ways to fill the five cells in the b... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"difficulty": 47.65625,
"index": 9715,
"split": "train"
} | 16 |
deepscaler | [
{
"content": "The numbers \\(a, b, c, d\\) belong to the interval \\([-6.5 ; 6.5]\\). Find the maximum value of the expression \\(a + 2b + c + 2d - ab - bc - cd - da\\). Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "182",
"style": "rule"
} | {
"difficulty": 93.75,
"index": 1705,
"split": "train"
} | 182 |
deepscaler | [
{
"content": "Find one-fourth of 6 times 8. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "12",
"style": "rule"
} | {
"difficulty": 1.5625,
"index": 17202,
"split": "train"
} | 12 |
deepscaler | [
{
"content": "The following is the process of simplifying fractions by Xiaobai. Please read carefully and complete the corresponding tasks.\n\nSolution: $(\\frac{3x+4}{x^2-1}-\\frac{2}{x-1})÷\\frac{x+2}{x^2-2x+1}$\n\n$=[\\frac{3x+4}{(x+1)(x-1)}-\\frac{2}{x-1}]÷\\frac{x+2}{(x-1)^2}\\ldots \\ldots \\ldots \\ldots... | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"difficulty": 10.9375,
"index": 14737,
"split": "train"
} | \frac{1}{3} |
deepscaler | [
{
"content": "Given that $\\binom{23}{5}=33649$, $\\binom{23}{6}=42504$, and $\\binom{23}{7}=33649$, find $\\binom{25}{7}$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "152306",
"style": "rule"
} | {
"difficulty": 49.21875,
"index": 10488,
"split": "train"
} | 152306 |
deepscaler | [
{
"content": "What is the product of the numerator and the denominator when $0.\\overline{018}$ is expressed as a fraction in lowest terms? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "222",
"style": "rule"
} | {
"difficulty": 7.8125,
"index": 16284,
"split": "train"
} | 222 |
deepscaler | [
{
"content": "For real numbers $a$ and $b$ , define $$ f(a,b) = \\sqrt{a^2+b^2+26a+86b+2018}. $$ Find the smallest possible value of the expression $$ f(a, b) + f (a,-b) + f(-a, b) + f (-a, -b). $$ Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "4 \\sqrt{2018}",
"style": "rule"
} | {
"difficulty": 49.21875,
"index": 10088,
"split": "train"
} | 4 \sqrt{2018} |
deepscaler | [
{
"content": "At around 8 o'clock in the morning, two cars left the fertilizer plant one after another, heading toward Happy Village. Both cars travel at a speed of 60 kilometers per hour. At 8:32, the distance the first car had traveled from the fertilizer plant was three times the distance traveled by the sec... | math | {
"ground_truth": "8:11",
"style": "rule"
} | {
"difficulty": 89.0625,
"index": 2972,
"split": "train"
} | 8:11 |
deepscaler | [
{
"content": "How many square units are in the area of the triangle whose vertices are the $x$ and $y$ intercepts of the curve $y = (x-3)^2 (x+2)$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "45",
"style": "rule"
} | {
"difficulty": 4.6875,
"index": 17258,
"split": "train"
} | 45 |
deepscaler | [
{
"content": "There are exactly 120 ways to color five cells in a $5 \\times 5$ grid such that exactly one cell in each row and each column is colored.\n\nThere are exactly 96 ways to color five cells in a $5 \\times 5$ grid without the corner cell, such that exactly one cell in each row and each column is colo... | math | {
"ground_truth": "78",
"style": "rule"
} | {
"difficulty": 39.84375,
"index": 12397,
"split": "train"
} | 78 |
deepscaler | [
{
"content": "Calculate the expression $200(200-5)-(200\\cdot200-5)$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-995",
"style": "rule"
} | {
"difficulty": 60.15625,
"index": 5844,
"split": "train"
} | -995 |
deepscaler | [
{
"content": "For a given integer $n\\ge 2$, let $a_0,a_1,\\ldots ,a_n$ be integers satisfying $0=a_0<a_1<\\ldots <a_n=2n-1$. Find the smallest possible number of elements in the set $\\{ a_i+a_j \\mid 0\\le i \\le j \\le n \\}$. Let's think step by step and output the final answer within \\boxed{}.",
"role... | math | {
"ground_truth": "3n",
"style": "rule"
} | {
"difficulty": 89.0625,
"index": 3281,
"split": "train"
} | 3n |
deepscaler | [
{
"content": "Given a convex quadrilateral \\(ABCD\\) with \\(X\\) as the midpoint of the diagonal \\(AC\\), it turns out that \\(CD \\parallel BX\\). Find \\(AD\\) if it is known that \\(BX = 3\\), \\(BC = 7\\), and \\(CD = 6\\). Let's think step by step and output the final answer within \\boxed{}.",
"rol... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"difficulty": 83.59375,
"index": 2046,
"split": "train"
} | 14 |
deepscaler | [
{
"content": "In $\\triangle ABC$, $P$ is a point on the side $BC$ such that $\\overrightarrow{BP} = \\frac{1}{2}\\overrightarrow{PC}$. Points $M$ and $N$ lie on the line passing through $P$ such that $\\overrightarrow{AM} = \\lambda \\overrightarrow{AB}$ and $\\overrightarrow{AN} = \\mu \\overrightarrow{AC}$ w... | math | {
"ground_truth": "\\frac{8}{3}",
"style": "rule"
} | {
"difficulty": 78.90625,
"index": 3714,
"split": "train"
} | \frac{8}{3} |
deepscaler | [
{
"content": "Given the function $f(x) = -\\frac{1}{3}x^3 + x^2 + ax + b$ reaches an extreme value of $4$ at $x=3$, determine the maximum value of $f(x)$ on the interval $[-2,1]$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{4}{3}",
"style": "rule"
} | {
"difficulty": 28.90625,
"index": 13671,
"split": "train"
} | -\frac{4}{3} |
deepscaler | [
{
"content": "Find the smallest prime which is not the difference (in some order) of a power of $2$ and a power of $3$ . Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "41",
"style": "rule"
} | {
"difficulty": 0.78125,
"index": 17425,
"split": "train"
} | 41 |
deepscaler | [
{
"content": "Let \\( M = \\{1, 2, \\cdots, 1995\\} \\). Suppose \\( A \\) is a subset of \\( M \\) that satisfies the condition: if \\( x \\in A \\), then \\( 15x \\notin A \\). What is the maximum number of elements in \\( A \\)? Let's think step by step and output the final answer within \\boxed{}.",
"ro... | math | {
"ground_truth": "1870",
"style": "rule"
} | {
"difficulty": 42.96875,
"index": 10377,
"split": "train"
} | 1870 |
deepscaler | [
{
"content": "Let $\\mathcal{T}$ be the set of real numbers that can be represented as repeating decimals of the form $0.\\overline{abcd}$ where $a, b, c, d$ are distinct digits. Find the sum of the elements of $\\mathcal{T}.$ Let's think step by step and output the final answer within \\boxed{}.",
"role": ... | math | {
"ground_truth": "2520",
"style": "rule"
} | {
"difficulty": 89.0625,
"index": 1966,
"split": "train"
} | 2520 |
deepscaler | [
{
"content": "How many distinct arrangements of the letters in the word \"balloon\" are there? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "1260",
"style": "rule"
} | {
"difficulty": 53.125,
"index": 7599,
"split": "train"
} | 1260 |
deepscaler | [
{
"content": "Regular hexagon $ABCDEF$ has its center at $G$. Each of the vertices and the center are to be associated with one of the digits $1$ through $7$, with each digit used once, in such a way that the sums of the numbers on the lines $AGC$, $BGD$, and $CGE$ are all equal. In how many ways can this be do... | math | {
"ground_truth": "144",
"style": "rule"
} | {
"difficulty": 50,
"index": 8463,
"split": "train"
} | 144 |
deepscaler | [
{
"content": "If the average of a set of sample data 4, 5, 7, 9, $a$ is 6, then the variance $s^2$ of this set of data is \\_\\_\\_\\_\\_\\_. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{16}{5}",
"style": "rule"
} | {
"difficulty": 78.90625,
"index": 5197,
"split": "train"
} | \frac{16}{5} |
deepscaler | [
{
"content": "An Englishman owns a plot of land in Russia. He knows that, in the units familiar to him, the size of his plot is three acres. The cost of the land is 250,000 rubles per hectare. It is known that 1 acre = 4840 square yards, 1 yard = 0.9144 meters, and 1 hectare = 10,000 square meters. Calculate ho... | math | {
"ground_truth": "303514",
"style": "rule"
} | {
"difficulty": 96.09375,
"index": 785,
"split": "train"
} | 303514 |
deepscaler | [
{
"content": "Each of $2010$ boxes in a line contains a single red marble, and for $1 \\le k \\le 2010$, the box in the $k\\text{th}$ position also contains $k$ white marbles. Isabella begins at the first box and successively draws a single marble at random from each box, in order. She stops when she first draw... | math | {
"ground_truth": "45",
"style": "rule"
} | {
"difficulty": 21.09375,
"index": 13651,
"split": "train"
} | 45 |
deepscaler | [
{
"content": "If $∀x∈(0,+\\infty)$, $ln2x-\\frac{ae^{x}}{2}≤lna$, then find the minimum value of $a$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac{2}{e}",
"style": "rule"
} | {
"difficulty": 71.875,
"index": 4639,
"split": "train"
} | \frac{2}{e} |
deepscaler | [
{
"content": "Alex bakes a total of $24$ pies, and each pie is apple, blueberry, or cherry. The ratio of apple to blueberry to cherry pies is $1:4:3$. How many cherry pies did Alex bake? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"difficulty": 8.59375,
"index": 17634,
"split": "train"
} | 9 |
deepscaler | [
{
"content": "The graph of $y=\\frac{5x^2-9}{3x^2+5x+2}$ has a horizontal asymptote at $y=a$. What is $a$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "\\frac53",
"style": "rule"
} | {
"difficulty": 17.96875,
"index": 15430,
"split": "train"
} | \frac53 |
deepscaler | [
{
"content": "In a press conference before the All-Star Game, eight All-Stars will be taking questions. Three are Cubs, three are Red Sox, and two are Yankees. If teammates insist on sitting together, how many ways can the eight All-Stars be seated in a row? Let's think step by step and output the final answer ... | math | {
"ground_truth": "432",
"style": "rule"
} | {
"difficulty": 16.40625,
"index": 15991,
"split": "train"
} | 432 |
deepscaler | [
{
"content": "A 24-hour digital clock shows times $h: m: s$, where $h, m$, and $s$ are integers with $0 \\leq h \\leq 23$, $0 \\leq m \\leq 59$, and $0 \\leq s \\leq 59$. How many times $h: m: s$ satisfy $h+m=s$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "1164",
"style": "rule"
} | {
"difficulty": 6.25,
"index": 16663,
"split": "train"
} | 1164 |
deepscaler | [
{
"content": "For how many positive integers $n$ does $\\frac{1}{n}$ yield a terminating decimal with a non-zero hundredths digit? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "11",
"style": "rule"
} | {
"difficulty": 59.375,
"index": 7974,
"split": "train"
} | 11 |
deepscaler | [
{
"content": "Given that Tian Ji's top horse is faster than the King of Qi's middle horse, and Tian Ji's middle horse is faster than the King of Qi's bottom horse, but Tian Ji's top horse is slower than the King of Qi's top horse, and Tian Ji's bottom horse is slower than the King of Qi's bottom horse, calculat... | math | {
"ground_truth": "\\frac{2}{3}",
"style": "rule"
} | {
"difficulty": 61.71875,
"index": 6761,
"split": "train"
} | \frac{2}{3} |
deepscaler | [
{
"content": "In the figure, circle $O$ has radius 6 units. Chord $CD$ has length 8 units and is parallel to segment $KB$. If $KA$ = 12 units and points $K$, $A$, $O$ and $B$ are collinear, what is the area of triangle $KDC$? Express your answer in simplest radical form. [asy]\ndraw(Circle((0,0),6));\ndot((0,0)... | math | {
"ground_truth": "8\\sqrt{5}",
"style": "rule"
} | {
"difficulty": 60.15625,
"index": 6058,
"split": "train"
} | 8\sqrt{5} |
deepscaler | [
{
"content": "A lieutenant is training recruits in marching drills. Upon arriving at the parade ground, he sees that all the recruits are arranged in several rows, with each row having the same number of soldiers, and that the number of soldiers in each row is 5 more than the number of rows. After finishing the... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"difficulty": 89.0625,
"index": 2888,
"split": "train"
} | 24 |
deepscaler | [
{
"content": "In right triangle $DEF$, $DE=15$, $DF=9$, and $EF=12$ units. What is the distance from $F$ to the midpoint of segment $DE$? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "7.5",
"style": "rule"
} | {
"difficulty": 81.25,
"index": 2591,
"split": "train"
} | 7.5 |
deepscaler | [
{
"content": "Simplify first, then evaluate: $\\left(\\frac{2}{m-3}+1\\right) \\div \\frac{2m-2}{m^2-6m+9}$, and then choose a suitable number from $1$, $2$, $3$, $4$ to substitute and evaluate. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "-\\frac{1}{2}",
"style": "rule"
} | {
"difficulty": 76.5625,
"index": 3763,
"split": "train"
} | -\frac{1}{2} |
deepscaler | [
{
"content": "Given points $F_{1}$, $F_{2}$ are the foci of the hyperbola $\\frac{x^2}{a^2} - \\frac{y^2}{b^2} = 1$ ($a > 0$, $b > 0$), and point $M(x_{0},y_{0})$ ($x_{0} > 0$, $y_{0} > 0$) lies on the asymptote of the hyperbola such that $MF_{1} \\perp MF_{2}$. If there is a parabola with focus $F_{2}$ describ... | math | {
"ground_truth": "2 + \\sqrt{5}",
"style": "rule"
} | {
"difficulty": 68.75,
"index": 5967,
"split": "train"
} | 2 + \sqrt{5} |
deepscaler | [
{
"content": "In the number $2 * 0 * 1 * 6 * 0 *$, each of the 5 asterisks must be replaced with any of the digits $0,1,2,3,4,5,6,7,8$ (digits can be repeated) so that the resulting 10-digit number is divisible by 18. How many ways can this be done? Let's think step by step and output the final answer within \\... | math | {
"ground_truth": "3645",
"style": "rule"
} | {
"difficulty": 68.75,
"index": 6108,
"split": "train"
} | 3645 |
deepscaler | [
{
"content": "Define $\\#N$ by the formula $\\#N = .5(N) + 1$. Calculate $\\#(\\#(\\#58))$. Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "9",
"style": "rule"
} | {
"difficulty": 10.9375,
"index": 14822,
"split": "train"
} | 9 |
deepscaler | [
{
"content": "The number of values of $x$ satisfying the equation\n\\[\\frac {2x^2 - 10x}{x^2 - 5x} = x - 3\\]is: Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "0",
"style": "rule"
} | {
"difficulty": 3.90625,
"index": 17337,
"split": "train"
} | 0 |
deepscaler | [
{
"content": "Each day 289 students are divided into 17 groups of 17. No two students are ever in the same group more than once. What is the largest number of days that this can be done? Let's think step by step and output the final answer within \\boxed{}.",
"role": "user"
}
] | math | {
"ground_truth": "18",
"style": "rule"
} | {
"difficulty": 53.125,
"index": 7674,
"split": "train"
} | 18 |
deepscaler | [
{
"content": "A factory produces two types of products, A and B, with profits P and Q (in ten thousand yuan), respectively. The relationship between the profits and the invested capital m (in ten thousand yuan) follows the empirical formulas P = (1/3)m + 65 and Q = 76 + 4√m. Now, 150 ten thousand yuan of capita... | math | {
"ground_truth": "203",
"style": "rule"
} | {
"difficulty": 67.96875,
"index": 6665,
"split": "train"
} | 203 |
deepscaler | [
{
"content": "Given that there are 5 balls of each of the three colors: black, white, and red, each marked with the numbers 1, 2, 3, 4, 5, calculate the number of different ways to draw 5 balls such that their numbers are all different and all three colors are present. Let's think step by step and output the fi... | math | {
"ground_truth": "150",
"style": "rule"
} | {
"difficulty": 71.09375,
"index": 3918,
"split": "train"
} | 150 |
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