data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
t01_math | [
{
"role": "user",
"content": "Julia, Olivia, and Rachel are dining at benchmark. Each subsequent course in a meal costs $20 more than the previous course, and they are ordering two courses forela day. Julia orders the less expensive course first. Olivia orders the extensive course twice. Rachel orders the m... | math | {
"ground_truth": "35",
"style": "rule"
} | {
"uid": "kd::b0257efbc7776c186adb7358",
"index": "kd::b0257efbc7776c186adb7358",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 140 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Given a bottle with internal water levels of 20 cm and 28 cm in two different orientations, determine the height of the bottle using the expressions $\\pi h$ and $3^2\\pi h$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Subtrac... | math | {
"ground_truth": "29",
"style": "rule"
} | {
"uid": "kd::554283fdbc72be6b006a8d81",
"index": "kd::554283fdbc72be6b006a8d81",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 9\\pi 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "The length of a rectangle is five times the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 16 sq. units. What is the area (in sq. units) of the rectangle if you know the breadth and the area is 220 sq. units?\n\nSolve the problem.... | math | {
"ground_truth": "11",
"style": "rule"
} | {
"uid": "kd::ddd24d2f0514a747db5d5481",
"index": "kd::ddd24d2f0514a747db5d5481",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 20 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Example 10 Find the smallest positive number $\\lambda$, such that for any triangle with side lengths $a, b, c$, as long as $a \\geqslant \\frac{b+c}{3}$, we have\n$$\na c+b c-c^{2} \\leqslant \\lambda\\left(a^{2}+b^{2}+3 c^{2}+2 a b-4 b c\\right) .\n$$\n(1993 Chinese National ... | math | {
"ground_truth": "\\frac{2\\sqrt{2}+1}{7}",
"style": "rule"
} | {
"uid": "kd::faa25102cd515df1bc53c3fa",
"index": "kd::faa25102cd515df1bc53c3fa",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 -14 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "How many ways are there to color the faces of a regular icosahedron using 2 colors, considering all possible isometries (rotations and reflections)?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Calculate the contribution of the... | math | {
"ground_truth": "9 052",
"style": "rule"
} | {
"uid": "kd::ed01593b5026d41232fd4fbb",
"index": "kd::ed01593b5026d41232fd4fbb",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 256 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Steve has made a US$50000 per year investment and had to pay a US$5000 in capital gains tax. What is the return on Steve's investment, in percentage?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Divide the net profit by the ori... | math | {
"ground_truth": "90",
"style": "rule"
} | {
"uid": "kd::f0d46bf4c8483e98ad6d3448",
"index": "kd::f0d46bf4c8483e98ad6d3448",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 40 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Mary has 4 cats. 3 of the cats have ascites and fluid should be given to them. Two will need food and two will need treats. How many items will Mary need to give to each of her cats?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHi... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"uid": "kd::a1dfc8215060d81bfdd4a21f",
"index": "kd::a1dfc8215060d81bfdd4a21f",
"lang": "en",
"rubrics": [
{
"criterion": "Identify the specific groups of cats and the distinct items required for each group to avoid double counting.",
"points": 2,
"tags": {
"judge": false,
... |
t01_math | [
{
"role": "user",
"content": "56 orange trees rooted in a grove each bear 15 bushels of sugar-crunchy oranges every season. How many bushels of oranges would 28 trees yield?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Use the relationship between 28 trees ... | math | {
"ground_truth": "420",
"style": "rule"
} | {
"uid": "kd::4183db51d59dae002cc47e60",
"index": "kd::4183db51d59dae002cc47e60",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 840 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "3.30: The last non-zero digit at the end is\n$\\qquad$\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Substitute n equals 30 into the recurrence relation and evaluate the resulting powers of 2 modulo 10."
}
] | math | {
"ground_truth": "8",
"style": "rule"
} | {
"uid": "kd::a12697324955c9a4b2d14889",
"index": "kd::a12697324955c9a4b2d14889",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 5040 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Emily plans to buy the sewing machine she saw being sold at $\\$1200$. The tax in her area is so high they have to pay 50% of the total price in tax. If Emily adds 15% of her total price to tip, how much was the entire purchase?\n\nSolve the problem. Show your reasoning, then... | math | {
"ground_truth": "2070",
"style": "rule"
} | {
"uid": "kd::6b8f8caa77e971ce073e9cce",
"index": "kd::6b8f8caa77e971ce073e9cce",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 0.5 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Elijah is building a basketball hoop. He already knows that the hoop requires 24 inches of construction space above the ground. He needs to account for the hoop having an extra 2 inches for moisture gauge purposes before he can calculate the exact height he needs the cage for t... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"uid": "kd::1417291f89b7319efd15a6c6",
"index": "kd::1417291f89b7319efd15a6c6",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 26 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Calculate:<br/>$(1)\\sqrt{27}-6\\sqrt{\\frac{1}{3}}+\\sqrt{(-2)^2}$;<br/>$(2)$ Given $x=2+\\sqrt{3}$ and $y=2-\\sqrt{3}$, find the value of $x^{2}y+xy^{2}$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Factor out the common ter... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"uid": "kd::b0f23a592559ada978020775",
"index": "kd::b0f23a592559ada978020775",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{\\sqrt{3}}{3} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "gener... |
t01_math | [
{
"role": "user",
"content": "Amara is twice as old as An NBA player's wife if she is currently 20. How old was she when she gave birth to the NBA player's wife?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Subtract the wife's current age from Amara's curr... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"uid": "kd::90dbe4dc0969e2ee87f8ebbe",
"index": "kd::90dbe4dc0969e2ee87f8ebbe",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 40 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Evaluate the integral $\\int_0^{\\pi/4}\\!\\frac{\\mathrm dx}{2+\\sin x}$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Complete the square in the denominator and factor out the constant to match the standard arctangent integra... | math | {
"ground_truth": "I=\\frac{2}{\\sqrt3} \\arctan \\bigl(3\\sqrt3-2\\sqrt6\\bigr)",
"style": "rule"
} | {
"uid": "kd::a1c0b8cb7d3bac6233bd51ae",
"index": "kd::a1c0b8cb7d3bac6233bd51ae",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\pi 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Calculate #cos(arcsin(2))+tan(arcsec(3))#.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Recognize that arcsin(2) yields a complex angle and apply the Pythagorean identity to find its cosine value."
}
] | math | {
"ground_truth": "2\\sqrt{2}+i\\sqrt{3}",
"style": "rule"
} | {
"uid": "kd::0dc614b21df2e5b016c9a6aa",
"index": "kd::0dc614b21df2e5b016c9a6aa",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 2.828 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "If $a+b = 12$, then what is the value of $a^3+b^3 + 6ab$?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Substitute the known value of a plus b into the expanded identity to simplify the expression."
}
] | math | {
"ground_truth": "1728",
"style": "rule"
} | {
"uid": "kd::5b5f159f231eafcdfab43651",
"index": "kd::5b5f159f231eafcdfab43651",
"lang": "en",
"rubrics": [
{
"criterion": "Expand the cube of the sum a plus b to relate it to the target expression.",
"points": 2,
"tags": {
"judge": false,
"inject": true,
"scaffold... |
t01_math | [
{
"role": "user",
"content": "Prove that \\( 1 + 3 + 5 + 7 + \\cdots + (2n - 1) = n^2 \\) for all \\( n \\geq 1 \\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Add the next odd term 2k plus 1 to the induction hypothesis and factor the resulting quadratic ... | math | {
"ground_truth": "1 + 3 + 5 + \\cdots + (2n - 1) = n^2 \\text{ for all } n \\geq 1",
"style": "rule"
} | {
"uid": "kd::3efde4141f7d866dc4a19cc8",
"index": "kd::3efde4141f7d866dc4a19cc8",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 23 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Kim can read 40 pages an hour. It takes her 8 hours to finish reading a novel. How many fewer words it took Jack, who can read twice as fast as Kim?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Divide the total page count by ... | math | {
"ground_truth": "4",
"style": "rule"
} | {
"uid": "kd::fd76f8b22dcb5f64888c2b3e",
"index": "kd::fd76f8b22dcb5f64888c2b3e",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 320 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Evaluate the double sum $\\sum_{k,n\\ge 1}{\\frac{(-1)^{n-1}}{n^2+k^2}}$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Apply the partial fraction decomposition to the hyperbolic cotangent term to separate the summation over k f... | math | {
"ground_truth": "\\frac{\\pi^{2}}{24}+\\frac{\\pi}{8}\\ln 2",
"style": "rule"
} | {
"uid": "kd::11f7f07c663c2fa96249d510",
"index": "kd::11f7f07c663c2fa96249d510",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{\\pi}{a} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Jill has $230. She goes to a capsule store and buys a uncaps safe for $85. She also walks past other items that cost $20 each but does not buy them. Once she has bought everything she needs, she has $145 left. How many items did she get from the wallet store?\n\nSolve the probl... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"uid": "kd::fe6693dd36d4d880ce051f9f",
"index": "kd::fe6693dd36d4d880ce051f9f",
"lang": "en",
"rubrics": [
{
"criterion": "Define a variable for the number of $20 items and write an equation representing the total money spent plus the remaining balance.",
"points": 2,
"tags": {
"... |
t01_math | [
{
"role": "user",
"content": "The graph of y = g(x) is shown below. Find g(g(g(g(1)))).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Locate the specific points on the curve corresponding to the sequence of x values generated."
}
] | math | {
"ground_truth": "2",
"style": "rule"
} | {
"uid": "kd::af3d8242a3893681861b2859",
"index": "kd::af3d8242a3893681861b2859",
"lang": "en",
"rubrics": [
{
"criterion": "Read the function value at x equals 1 from the provided graph to find the first output.",
"points": 2,
"tags": {
"judge": false,
"inject": true,
... |
t01_math | [
{
"role": "user",
"content": "Jessica is making a cake that takes 3 cups of sugar. She has 1 cups of sugar left in the store. If she plans to make 2 cakes in total and already used 4 cups of sugar, how many cans of sugar did she use to make the cakes? There are 2 cups of sugar in each can.\n\nSolve the prob... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"uid": "kd::a840025164ee50f79bcac432",
"index": "kd::a840025164ee50f79bcac432",
"lang": "en",
"rubrics": [
{
"criterion": "Calculate the total sugar required for all cakes and determine the total amount of sugar actually used.",
"points": 2,
"tags": {
"judge": false,
"inj... |
t01_math | [
{
"role": "user",
"content": "John bought a ticket for an expandedEns pills. if the normal ticket costs $45 and theExact cost $12 less than two times the normal ticket, how much did John paid than the exact cost if he bought two tickets for the/student in invested \"$150\" in Es?\n\nSolve the problem. Sho... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"uid": "kd::d7ee30300623074356b2791c",
"index": "kd::d7ee30300623074356b2791c",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 306 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "A recent study of mothers of junior high school children in Santa Clara County reported that 76% of the mothers are employed in paid positions. Of those employed mothers, 64% work full-time (over 35 hours per week), and 36% work part-time. Out of all the mothers in the populati... | math | {
"ground_truth": "27.36%",
"style": "rule"
} | {
"uid": "kd::eec763204894d4a4d3074a17",
"index": "kd::eec763204894d4a4d3074a17",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 0.2736 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"... |
t01_math | [
{
"role": "user",
"content": "Solve for $x$ to the nearest integer: $x^2-x-46=0.$\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Calculate the two decimal values of the roots and round each to the closest integer based on the fractional part."
}
] | math | {
"ground_truth": "7 \\text{ and } -6",
"style": "rule"
} | {
"uid": "kd::afa5181e618b07095298ceb7",
"index": "kd::afa5181e618b07095298ceb7",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{1+13.601}{2} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generi... |
t01_math | [
{
"role": "user",
"content": "Consider the dynamical system in 1-d given by $$\\dot x = (x+\\mu)(\\mu+2x-x^2).$$ Find the dependence of the stationary points of the system and their stability with respect to the parameter $\\mu$. Then, draw the bifurcation diagram and determine at which value of $\\mu$ the ... | math | {
"ground_truth": "\\mu = -1",
"style": "rule"
} | {
"uid": "kd::2766c6262fd8e585121e8747",
"index": "kd::2766c6262fd8e585121e8747",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 -0.5 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "How many distinct planes passing through at least $3$ distinct vertices of a regular icosahedron cut the solid into $2$ not necessarily equal parts?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Calculate the signed distance of ... | math | {
"ground_truth": "47",
"style": "rule"
} | {
"uid": "kd::e74d3e8a0218c85175cf0874",
"index": "kd::e74d3e8a0218c85175cf0874",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{1+\\sqrt{5}}{2} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "gen... |
t01_math | [
{
"role": "user",
"content": "Cody planted 5 rows of new\\dnd trees in his random back yard. Each row has 11 trees. He received 8 more seedlings to plant, and placed them all successfully into the ground. Hairu had 6 fewer trees than Cody. How many more trees did Hairu have than Cody?\n\nSolve the proble... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"uid": "kd::96f90c8d3a20f8c4c6efc59e",
"index": "kd::96f90c8d3a20f8c4c6efc59e",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 55 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Marvin buys a vehicle with a listed cost of $50,000. An agent charges a fee of 10% of the value of the vehicle for his furADCs. Once Marvin then alt intention to resell the vehicle for the listed cost plus the agent's furADCs, he had to pay a 30% tax on the profits he made. How... | math | {
"ground_truth": "3500",
"style": "rule"
} | {
"uid": "kd::2e0df55625a8b510d367926f",
"index": "kd::2e0df55625a8b510d367926f",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 0.10 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "In any triangle, there is a point \\( X \\) which is the point of intersection of 3 circles of equal radii, each of which is internally tangent to 2 sides of the given triangle. Describe a method by which \\( X \\) may be constructed.\n\nSolve the problem. Show your reasoning, ... | math | {
"ground_truth": "X\\text{ is the internal homothety centre of the incircle and circumcircle of }\\triangle ABC,\\text{ obtained by dividing }OI\\text{ in the ratio }R{:}r_i",
"style": "rule"
} | {
"uid": "kd::3959d1d2f5a5e1474e34f943",
"index": "kd::3959d1d2f5a5e1474e34f943",
"lang": "en",
"rubrics": [
{
"criterion": "Identify the geometric relationship between the three equal circles and the triangle's incircle to determine the nature of point X.",
"points": 2,
"tags": {
... |
t01_math | [
{
"role": "user",
"content": "Let \\( f:[a,b] \\rightarrow \\mathbb{R} \\) be a continuous function such that for every \\( x \\in [a,b] \\), there exists a \\( y \\in [a,b] \\) such that \\( |f(y)| \\leq |f(x)|/2 \\). Prove that there exists a \\( \\xi \\in [a,b] \\) such that \\( f(\\xi) = 0 \\).\n\nSolve... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"uid": "kd::315e9004beb4ac3d96abd0e6",
"index": "kd::315e9004beb4ac3d96abd0e6",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{m}{2} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Mark bought five liters of water. But, he lost 1/4 marks after the rainfall. The whole drop was used to put some tiles at 2 liters per tile. How many tiles did Mark put in the bathroom?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHi... | math | {
"ground_truth": "1",
"style": "rule"
} | {
"uid": "kd::01b07a724fdbc89b4d37b238",
"index": "kd::01b07a724fdbc89b4d37b238",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 1.875 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "Find, in simple closed form, the generating functions \\( F_k(x, y) = \\sum_{n, m \\geq 0} f(n, m, k) x^n y^m \\) for \\( k = 1, 2, \\ldots \\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Apply the operator x times the partia... | math | {
"ground_truth": "F_k(x,y)=\\frac{(xy)^k}{\\bigl(1-x-y\\bigr)^{ k+1}}",
"style": "rule"
} | {
"uid": "kd::bfe0b7556dd0d6b000705cb6",
"index": "kd::bfe0b7556dd0d6b000705cb6",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{(n+m-k)!}{(n-k)!m-k)!\\k!} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_... |
t01_math | [
{
"role": "user",
"content": "1. Let $a, d$ be non-negative real numbers, $b, c$ be positive real numbers, and $b+c \\geq a+d$. Then the minimum value of $\\frac{b}{c+d}+\\frac{c}{a+b}$ is\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Analyze the boundary ca... | math | {
"ground_truth": "\\sqrt{2}-\\frac{1}{2}",
"style": "rule"
} | {
"uid": "kd::a29de4a457482214a1cd09f1",
"index": "kd::a29de4a457482214a1cd09f1",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{b}{2(b+c)-x} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generi... |
t01_math | [
{
"role": "user",
"content": "모든 양의 정수 $a$에 대해 $n$이 $a^{25} - a$를 나누는 모든 양의 정수 $n$을 구하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: 소수 p의 제곱 p^2이 모든 a에 대해 a^25 - a를 나누지 않음을 확인하여 n이 제곱인수를 갖지 않는 정수여야 함을 보이라."
}
] | math | {
"ground_truth": "2730",
"style": "rule"
} | {
"uid": "kd::a6548974ec9e0d8ef70f6abb",
"index": "kd::a6548974ec9e0d8ef70f6abb",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 794 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "sophia finished 2323 of a book . she calculated that she finished 90 more pages than she has yet to read . how long is her book ?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Set up an equation stating that the pages read equal... | math | {
"ground_truth": "4556",
"style": "rule"
} | {
"uid": "kd::322cfdb41001c83d43bee0e6",
"index": "kd::322cfdb41001c83d43bee0e6",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 4646 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "실수 계수를 가진 3차 다항함수의 실수 서로 다른 근의 개수가 그 미분함수의 실수 서로 다른 근의 개수보다 적을 수 있는지 판별하시오. 가능하다면, 그러한 다항식의 예를 제시하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: 극대값과 극소값이 모두 양수이거나 모두 음수인 구체적인 다항식을 구성하여 예시를 제시하라."
}
] | math | {
"ground_truth": "x^3 - 3x + 3",
"style": "rule"
} | {
"uid": "kd::a86eb1a516061a4c861b7fab",
"index": "kd::a86eb1a516061a4c861b7fab",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 -27 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "A car rental company offers two plans for renting a car: \n- Plan A: \\$25 per day and \\$0.10 per mile. \n- Plan B: \\$40 per day with free unlimited mileage. \nHow many miles would you need to drive for Plan B to save you money compared to Plan A?\n\nSolve the problem. Sho... | math | {
"ground_truth": "150",
"style": "rule"
} | {
"uid": "kd::2a5b5edb5c2b681d97ddfeb4",
"index": "kd::2a5b5edb5c2b681d97ddfeb4",
"lang": "en",
"rubrics": [
{
"criterion": "Define the total cost for each plan as a linear function of the number of miles driven.",
"points": 2,
"tags": {
"judge": false,
"inject": true,
... |
t01_math | [
{
"role": "user",
"content": "Determine whether the following series converges: $$\\sum_{n=1}^\\infty \\frac{1}{\\cot(\\frac{\\pi}{2} - \\frac{1}{n})^2}$$\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Apply the small-angle approximation for tangent to find t... | math | {
"ground_truth": "Diverges",
"style": "rule"
} | {
"uid": "kd::92861ddd6530fc563f3a9030",
"index": "kd::92861ddd6530fc563f3a9030",
"lang": "en",
"rubrics": [
{
"criterion": "Simplify the trigonometric expression using co-function identities to rewrite the general term.",
"points": 2,
"tags": {
"judge": false,
"inject": tr... |
t01_math | [
{
"role": "user",
"content": "$\\frac{(a+b+c)^2}{abc}$ 형태로 나타낼 수 있는 모든 자연수를 구하시오. 여기서 $a, b, c \\in \\mathbb{N}$이다.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: 상한 함수가 감소함을 이용해 s 의 범위를 제한한 후, 각 경우마다 N 이 s 제곱의 약수인지 확인하여 가능한 자연수를 거르라."
}
] | math | {
"ground_truth": "\\{1, 2, 3, 4, 5, 6, 8, 9\\}",
"style": "rule"
} | {
"uid": "kd::748829d4598f87568aa83798",
"index": "kd::748829d4598f87568aa83798",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 8100 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Tom has four cylinders in the shape of an hyperbola that each provide 6 liters of water. The volume of water in each cylinder is exactly double the volume of water below it. If the bottom cylinder has 500 liters of water, calculate how many liters of water are all together in... | math | {
"ground_truth": "7500",
"style": "rule"
} | {
"uid": "kd::f410858623fecfe34efe5aec",
"index": "kd::f410858623fecfe34efe5aec",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 1000 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "$10 \\cdot 771^{2}, 2^{2}, 3^{2}, \\cdots, 123456789^{2}$ What is the digit in the units place of the sum? \n(China Junior High School Mathematics League, 1990)\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Divide the total cou... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"uid": "kd::138a88fb4f7388d04e26139c",
"index": "kd::138a88fb4f7388d04e26139c",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 12345678 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Roger spends 50% of his allowance money each week. He has three job-days, where he earns $4 an hour buter is only half as long as it should be. After four weeks, he has earned $176 less than his monthlyPersonal Allowance. What is hisyang{k}/Q tend'' for the whole month, express... | math | {
"ground_truth": "368",
"style": "rule"
} | {
"uid": "kd::ef981c222a1d5ba80b02086f",
"index": "kd::ef981c222a1d5ba80b02086f",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 320 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Mary has 1/4 more jelly beans than Tom. Tom has 1/5 more jelly beans than Phillip. If Phillip has 20 jelly beans, calculate the percentage of jelly beans Tom has than Phillip.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Divide... | math | {
"ground_truth": "120",
"style": "rule"
} | {
"uid": "kd::abe0a2788487c0937fa9b055",
"index": "kd::abe0a2788487c0937fa9b055",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{6\\times20}{5} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "gene... |
t01_math | [
{
"role": "user",
"content": "What is the value of the most significant third digit to the left of the decimal point of the product of $1.5 \\times 1.5 \\times 1.5$?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Perform the multiplication step by step to ens... | math | {
"ground_truth": "3",
"style": "rule"
} | {
"uid": "kd::5529805d1d547c57083d1247",
"index": "kd::5529805d1d547c57083d1247",
"lang": "en",
"rubrics": [
{
"criterion": "Calculate the exact numerical value of the product by multiplying the three factors together.",
"points": 2,
"tags": {
"judge": false,
"inject": true... |
t01_math | [
{
"role": "user",
"content": "Given a hash table with 64,000 buckets and a chain length of 4, calculate the probability that at least one bucket will exceed its chain length when 4,000 random values are inserted into the table.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\bo... | math | {
"ground_truth": "0.00048",
"style": "rule"
} | {
"uid": "kd::6b9633ba98562868031c1fee",
"index": "kd::6b9633ba98562868031c1fee",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 7.5 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "부등식 \\( \\frac{\\sqrt{n}(\\sqrt{n}-\\log(n))}{\\log(n)}>1 \\)을 부등식 \\( \\log t \\le t-1 \\)을 이용하여 풀어라.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: 변형된 부등식의 우변에 유도한 로그 상한식을 대입하여 n 에 대한 간단한 부등식으로 축소하라."
}
] | math | {
"ground_truth": "(1, 2)",
"style": "rule"
} | {
"uid": "kd::9fdf89a81799f156ea921304",
"index": "kd::9fdf89a81799f156ea921304",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 1.414 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "Given three circles with centers X, Y, and Z, each having a radius of \\( \\sqrt{\\frac{1}{\\pi}} \\), and the area of intersection between circles A and B is 0.23, calculate the distance between the centers of these circles. Use the formula for the area of a lens:\n\\[\nA_{\\t... | math | {
"ground_truth": "0.74",
"style": "rule"
} | {
"uid": "kd::52bd5a501f09cf7179f5abb0",
"index": "kd::52bd5a501f09cf7179f5abb0",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 0.5476 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"... |
t01_math | [
{
"role": "user",
"content": "Suppose that $S$ is a series of real numbers between $2$ and $8$ inclusive, and that for any two elements $y > x$ in $S,$ $$ 98y - 102x - xy \\ge 4. $$ What is the maximum possible size for the set $S?$ $$ \\mathrm a. ~ 12\\qquad \\mathrm b.~14\\qquad \\mathrm c... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"uid": "kd::092e5846a146d316480bc4cc",
"index": "kd::092e5846a146d316480bc4cc",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{74}{13} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Arnaldo will be going to a concert. He is going to buy three tickets for himself and four family members. Tickets are $12 and the service charge is $8 per ticket. How much does Arnaldo need to contribute as a whole to the purchase?\n\nSolve the problem. Show your reasoning, the... | math | {
"ground_truth": "140",
"style": "rule"
} | {
"uid": "kd::405b4af100ad450fd2ce683b",
"index": "kd::405b4af100ad450fd2ce683b",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 84 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "What number added to itself 4 times will equal 20?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Divide both sides of the simplified equation by the coefficient to isolate the variable."
}
] | math | {
"ground_truth": "5",
"style": "rule"
} | {
"uid": "kd::8bcc184e4af4ea23008efbda",
"index": "kd::8bcc184e4af4ea23008efbda",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{20}{4} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Find all directional derivatives of the function $f(x,y) = 2x + y - \\pi^2$ at the point $(0,0)$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Recognize that the directional derivative equals the dot product of the gradient and... | math | {
"ground_truth": "D_{\\mathbf u}f(0,0)=2\\cos\\theta+\\sin\\theta",
"style": "rule"
} | {
"uid": "kd::2d4f34384171eb2d0f6d5a36",
"index": "kd::2d4f34384171eb2d0f6d5a36",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\sqrt{5} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Nellie and her husband were shopping for their receivers at the store. Nellie found three $800groupon tickets while her husband saved $1000. How much did they pay together for the reservation fees?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\b... | math | {
"ground_truth": "3400",
"style": "rule"
} | {
"uid": "kd::a6de669a8fcf783e47fc2339",
"index": "kd::a6de669a8fcf783e47fc2339",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 2400 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "How can the yearly interest be calculated, with at least three decimals, when the monthly interest is 3.4%?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Raise one plus the monthly interest rate to the twelfth power and subtract... | math | {
"ground_truth": "49.364%",
"style": "rule"
} | {
"uid": "kd::cd9880b38d75605f355d0a93",
"index": "kd::cd9880b38d75605f355d0a93",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 1.49364 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Given that $0$ represents $10\\%$, $15$ represents $100\\%$, and $30$ represents $200\\%$, what percent value does $25$ represent?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Apply the calculated rate of change to the differen... | math | {
"ground_truth": "166\\(\\frac{2}{3}\\)%",
"style": "rule"
} | {
"uid": "kd::047d666d4c4af01be62b7273",
"index": "kd::047d666d4c4af01be62b7273",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{200-100}{30-15} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "gen... |
t01_math | [
{
"role": "user",
"content": "What is the minimum number of tourists such that at least 2 have the same birthday (the same date and day but not necessarily the same year)?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Add one to the number of possible birthd... | math | {
"ground_truth": "366",
"style": "rule"
} | {
"uid": "kd::aceaa399efb4f3aa078256f4",
"index": "kd::aceaa399efb4f3aa078256f4",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 365 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Ronny is collecting stickers. He has collected 128 different stickers which he creamed and thenCas flecked. If continuously Cas flecking his stickers, and he could fit 5 per sticker, what would be the total number of stickers on his head after he dyes all his stickers yellow?\n... | math | {
"ground_truth": "640",
"style": "rule"
} | {
"uid": "kd::7384b426c0b830653b8a7a15",
"index": "kd::7384b426c0b830653b8a7a15",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 500 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Given two circles \\( s_1 \\) and \\( s_2 \\), construct a line \\( \\ell \\) that is parallel to a given line and creates equal segments in both circles.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Project the segment connect... | math | {
"ground_truth": "\\ell\\text{ is the unique line parallel to }g\\text{ that meets the normal line through }O_{1} \\text{ at the point }P\\text{ with } O_{1}P=\\frac{d}{2}-\\frac{R_{2}^{2}-R_{1}^{2}}{2d}, d= \\text{perpe",
"style": "rule"
} | {
"uid": "kd::9732d509420162aff8d2ba99",
"index": "kd::9732d509420162aff8d2ba99",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{r_{1}^{2}-r_{2}^{2}+h^{2}}{2h} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaff... |
t01_math | [
{
"role": "user",
"content": "Paul is trying to find a good deal for a long-sleeved T-shirt. He decides to buy two sets of a t-shirt at best buy. Lemon &limes cost $15.00 each. Honey & banana cost $12.00 each. Valu-Go cost $8.50 each. How much will he pay for the entire deal?\n\nSolve the problem. Show your... | math | {
"ground_truth": "71.00",
"style": "rule"
} | {
"uid": "kd::bc5c1a75917c22fd0455a497",
"index": "kd::bc5c1a75917c22fd0455a497",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 35.5 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Find integers \\( a \\) and \\( b \\), and a prime number \\( p \\) such that \\( pa^5 = b^4 + 3 \\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Test small integer values for a to see if b^4 plus 3 becomes a multiple of a pri... | math | {
"ground_truth": "(a, b, p) = (1, 2, 19)",
"style": "rule"
} | {
"uid": "kd::c0e99b514993efd2aa6f408b",
"index": "kd::c0e99b514993efd2aa6f408b",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 19 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Find a function $\\theta(n)$ such that\n$$ \\lim_{n \\rightarrow \\infty} \\frac{|\\pi(n) - \\text{Li}(n)|}{\\theta(n) } \\rightarrow 1. $$\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Recognize that the problem asks for a func... | math | {
"ground_truth": "\\theta(n)=|\\pi(n)-\\operatorname{Li}(n)|",
"style": "rule"
} | {
"uid": "kd::30128c8d8328e3ea385a4f0c",
"index": "kd::30128c8d8328e3ea385a4f0c",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\pi 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "[left] Brody looks down at the ground and eats an apple then climbs up his evidence box to eat an apple on the top. He continues to eat apples on the top of each piece of evidence he climbs, all the way up his 1 asset. 5 by 10 story house. How many appl... | math | {
"ground_truth": "51",
"style": "rule"
} | {
"uid": "kd::94c92dfb6d97f9d242e708cf",
"index": "kd::94c92dfb6d97f9d242e708cf",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 50 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Kenances-q wraps their own party in a circle. If each of the people around the circle shakes Kenances q's hand 2 times, and there are 200 handshakes total, how many people are included on the shake-up party?\n\nSolve the problem. Show your reasoning, then put the final answer i... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"uid": "kd::31cbb163c37bb96346d76a34",
"index": "kd::31cbb163c37bb96346d76a34",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{200}{2} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "51. For each of the two months - January and February - the factory produced more than $\\frac{1}{3}$ of the highest quality products. What part of the highest quality products was released by the factory in January and February separately, if it is known that each of these fra... | math | {
"ground_truth": "\\frac{2}{3}",
"style": "rule"
} | {
"uid": "kd::09037e57f8ebf9622787b140",
"index": "kd::09037e57f8ebf9622787b140",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{2+2}{2\\cdot3} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "gene... |
t01_math | [
{
"role": "user",
"content": "Solve the following system of congruences:\n\\[\n\\begin{cases}\n2000x + 200y + 20z \\equiv 2 \\mod 7 \\\\\n100000x + 1000y + 10z \\equiv 4 \\mod 11 \\\\\n2000x + 200y + 20z \\equiv 7 \\mod 13\n\\end{cases}\n\\]\n\nSolve the problem. Show your reasoning, then put the final answ... | math | {
"ground_truth": "(x,y,z)=(3,1,3) \\text{or} (4,9,5)",
"style": "rule"
} | {
"uid": "kd::2943c9c1717e7078d5f3ed8e",
"index": "kd::2943c9c1717e7078d5f3ed8e",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 100 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "A factory produces 41 three-person triangles every day. Three-quarters of them are equilateral, and two-fifths of the equilateral triangles are yellow. How many yellow three-person triangles does the factory produce every day?\n\nSolve the problem. Show your reasoning, then put... | math | {
"ground_truth": "12",
"style": "rule"
} | {
"uid": "kd::385f3d079148dd8c1fafea9d",
"index": "kd::385f3d079148dd8c1fafea9d",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 123 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "The length of a rectangular race track is fifteen 15.0-kilometer laps. If the width of the track is 1.4 times the length, what is the perimeter of the track in kilometers, in an acceptable form?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxe... | math | {
"ground_truth": "72.0",
"style": "rule"
} | {
"uid": "kd::342fbbd0b8e130f10d4dd1c4",
"index": "kd::342fbbd0b8e130f10d4dd1c4",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 4.375 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "Adam gets 2foot cakes for each birthday, with 4 slices. Each slice is 6inches long. How many slices are left after 3 cakes are given away?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Subtract the number of slices given away fr... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"uid": "kd::e72eb45dd9afca365296eb2f",
"index": "kd::e72eb45dd9afca365296eb2f",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 12 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Given the function \\( f(x^3 + x^2 + x) = x + 2 \\), find \\( f(x) \\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Apply Cardano's formula to solve the cubic equation for x, then substitute this expression into the right-hand... | math | {
"ground_truth": "f(x)=\\frac{1}{3\\sqrt[3]{2}} \\Bigl(\\sqrt[3]{ 27x+7+\\sqrt{(27x+7)^{2}+32} } +\\sqrt[3]{ 27x+7-\\sqrt{(27x+7)^{2}+32} }\\Bigr) +\\frac{5}{3}",
"style": "rule"
} | {
"uid": "kd::82094346493f97cd301ab55a",
"index": "kd::82094346493f97cd301ab55a",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{2}{3} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Find all functions \\( f: \\mathbb{R} \\to \\mathbb{R} \\) such that for a real number \\( k \\),\n\\[ f(x) + f(y)^2 = k f(x + y^2). \\]\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Substitute y equals zero to derive a relation... | math | {
"ground_truth": "f(x) = 0 \\) or \\( f(x) = k - 1",
"style": "rule"
} | {
"uid": "kd::80e615d4b586f5142a4e19b0",
"index": "kd::80e615d4b586f5142a4e19b0",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{1}{k} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Tony divides 160 by 5. Yvette multiplies 160 by 2/5. How many more does Tony get than Yvette?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Subtract Yvette's product from Tony's quotient to find how much more Tony gets."
}
] | math | {
"ground_truth": "32",
"style": "rule"
} | {
"uid": "kd::c8f39c90b89934f0929085ab",
"index": "kd::c8f39c90b89934f0929085ab",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{160\\cdot2}{5} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "gene... |
t01_math | [
{
"role": "user",
"content": "Given a $m \\times n$ rectangular board ($m, n \\geq 2$), each unit square is colored either red, green, blue, or black. A coloring of the board is called \"good\" if for any $2 \\times 2$ square, its four squares have distinct colors. Count the number of ways to achieve a \"go... | math | {
"ground_truth": "6(2^m + 2^n - 4)",
"style": "rule"
} | {
"uid": "kd::98722a5a94f11cb04f464894",
"index": "kd::98722a5a94f11cb04f464894",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 12 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "In the Anchuria checkers championship, there are eight cities and the event spans eight days. Each round must be held in a different city and on a different day. Determine the number of rounds that should be held so that the organizing committee has the highest probability of w... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"uid": "kd::417967212b07fffb4ee16fc9",
"index": "kd::417967212b07fffb4ee16fc9",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 564480 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"... |
t01_math | [
{
"role": "user",
"content": "Solve the system of equations for positive integers \\(a\\), \\(b\\), \\(c\\), and \\(d\\):\n\\[ ab + cd = 34 \\]\n\\[ ac - bd = 19 \\]\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Solve the resulting system of linear equations... | math | {
"ground_truth": "(a,b,c,d)=(4,1,6,5) \\text{or} (6,5,4,1)",
"style": "rule"
} | {
"uid": "kd::e1da2eedf075bdcf295a264c",
"index": "kd::e1da2eedf075bdcf295a264c",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{34-cd}{b} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",... |
t01_math | [
{
"role": "user",
"content": "A 32-year-old man has two complexions. When he goes to the airport frequently, a video survey shows that each day he would be at the airport a total of x hours. On the rare occasions he goes to the airport weekly, each week he spends four times more time than in a daily trip. H... | math | {
"ground_truth": "11x",
"style": "rule"
} | {
"uid": "kd::7f1515cf3e75624324ce7c08",
"index": "kd::7f1515cf3e75624324ce7c08",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 11 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Calculate the efficiency of the usual unbiased estimator \\( \\frac{1}{n-1} \\sum_{i=1}^{n}(X_i - \\bar{X})^2 \\) relative to the estimator found in Problem 1, where the relative efficiency is defined as the ratio of the mean squared errors.\n\nSolve the problem. Show your reas... | math | {
"ground_truth": "\\frac{n-1}{n+1}",
"style": "rule"
} | {
"uid": "kd::274a023e7d0f33dd91edd8a0",
"index": "kd::274a023e7d0f33dd91edd8a0",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{1}{n-1} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "What is the number of ways to tile an \\( m \\times n \\) rectangle with \\( 1 \\times 2 \\) dominoes such that the tiling is exact (no holes or overlaps)? Consider the cases where \\( m \\) and \\( n \\) are both odd, or at least one is even.\n\nSolve the problem. Show your re... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"uid": "kd::d0de7555f92ba16a883860c2",
"index": "kd::d0de7555f92ba16a883860c2",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 12 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Mark is finishing up his tax forms. He notices his itemized deduction total is $1500. He's only required to put 20% of that amount on his tax form. With his other required deductions and exclusions amounting to $2000, how much will he pay in state and federal taxes?\n\nSolve th... | math | {
"ground_truth": "2300",
"style": "rule"
} | {
"uid": "kd::1b8a5c9c70fda5cf8785acf5",
"index": "kd::1b8a5c9c70fda5cf8785acf5",
"lang": "en",
"rubrics": [
{
"criterion": "Calculate the specific portion of the itemized deduction that must be reported by multiplying the total by the required percentage.",
"points": 2,
"tags": {
... |
t01_math | [
{
"role": "user",
"content": "It takes Z Henrius three times as long to wash one >= locales car hamburger|itudes as And participatory M disciplines official| superhero| girls| him, while And participatory M disciplines official| superhero| girls| him washes his car twice as fast than[I neither<|im odd|user\... | math | {
"ground_truth": "2000",
"style": "rule"
} | {
"uid": "kd::00a55b7e27550144ee2762d5",
"index": "kd::00a55b7e27550144ee2762d5",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{3000}{3} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "What will be the tenth term of the arithmetic progression 2,0,2,4,...?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Substitute n equals 10 into the formula to compute the specific value of the tenth term."
}
] | math | {
"ground_truth": "-16",
"style": "rule"
} | {
"uid": "kd::c0730ba7439d5ee691a527ef",
"index": "kd::c0730ba7439d5ee691a527ef",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 10 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Evaluate the following integral:\n$$\\int_{0}^{2\\pi}{\\frac{x^2\\sin(x)}{8+\\sin^2(x)}}dx$$\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Use the property that the integral of an odd function over a symmetric interval is zero t... | math | {
"ground_truth": "-\\frac{2\\pi^2}{3}\\ln 2",
"style": "rule"
} | {
"uid": "kd::c52d7271fb5c6b5fa054e52a",
"index": "kd::c52d7271fb5c6b5fa054e52a",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 2\\pi 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "What is the maximum number of diagonals of a cube?\n(Count $0$ as a face, and a diagonal connects two faces if they do not share an edge.)\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Verify your result by separately counting t... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"uid": "kd::99f5e22bf49ba9a76284847a",
"index": "kd::99f5e22bf49ba9a76284847a",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 12 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Icmm had 50 workers yesterday, but today they have increased the amount of workers by 10 percent. How many total amount of workers will be there after 2 days from today?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Recognize t... | math | {
"ground_truth": "55",
"style": "rule"
} | {
"uid": "kd::6f26615958c371c712ea9397",
"index": "kd::6f26615958c371c712ea9397",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 60.5 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Barbara is raising money for the upcomingEvaluate pit crew challenge. She collected 42 funds on the first two days. After three days, she had 57 pounds. What is the average daily amount of money she collected, during those last three days?\n\nSolve the problem. Show your reason... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"uid": "kd::40ed94d33825338e5577470b",
"index": "kd::40ed94d33825338e5577470b",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 15 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "각 $B$가 둔각인 둔각 삼각형 $ABC$에서, 직선 $IG$는 변 $BC$에 평행하다. 삼각형의 내심은 $I$, 중심은 $G$이다. 삼각형 $ABC$의 둘레가 144일 때, $IG$의 최대 정수 값을 구하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: 각 B 가 둔각이라는 조건을 코사인 법칙을 통해 부등식으로 변환하여 변 b 의 범위를 좁힌 뒤 최대 정수 값을 찾아라... | math | {
"ground_truth": "7",
"style": "rule"
} | {
"uid": "kd::4a2ac809b665f12278488346",
"index": "kd::4a2ac809b665f12278488346",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 \\frac{A+B+C}{3} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",... |
t01_math | [
{
"role": "user",
"content": "Find the determinant of a matrix that is similar to matrix \\( A_n \\), but with non-zero elements located on the left below the main diagonal instead of the bottom left corner.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Reco... | math | {
"ground_truth": "0",
"style": "rule"
} | {
"uid": "kd::480f05b954e5a38e6a16f82b",
"index": "kd::480f05b954e5a38e6a16f82b",
"lang": "en",
"rubrics": [
{
"criterion": "Identify that similar matrices share the same determinant value regardless of their specific arrangement.",
"points": 2,
"tags": {
"judge": false,
"i... |
t01_math | [
{
"role": "user",
"content": "F Lester bought 20 bags of chips for his party at school. Each bag costs $2.50. After paying at the cashier, F received $4.00 from the cashier back as change from his $10.00. How much, in cents, did all the chips cost?\n\nSolve the problem. Show your reasoning, then put the fin... | math | {
"ground_truth": "5000",
"style": "rule"
} | {
"uid": "kd::19fd54ce16cc4f61e1817cb8",
"index": "kd::19fd54ce16cc4f61e1817cb8",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 50 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "George buys a new car for $20,000. First, he takes $40\\%$ of the purchase price as an advance payment. Then he takes out a loan for 70\\% of his total car cost. How much did he pay in total for the car?\n\nSolve the problem. Show your reasoning, then put the final answer insid... | math | {
"ground_truth": "22000",
"style": "rule"
} | {
"uid": "kd::777a7be35f2a555b9a028a0f",
"index": "kd::777a7be35f2a555b9a028a0f",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 0.40 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ve... |
t01_math | [
{
"role": "user",
"content": "Given that \\( m \\) and \\( \\frac{2}{m} \\) are the roots of the quadratic equation \\( ax^2 + bx + 12 = 0 \\), find the value of \\( m + 2b \\).\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Substitute the calculated value of... | math | {
"ground_truth": "-70",
"style": "rule"
} | {
"uid": "kd::e6a6c2c0afaee94f7303d0f4",
"index": "kd::e6a6c2c0afaee94f7303d0f4",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{2}{m} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "Scott saw a deal at a coffee shop offering lattes on a buy 2 get 1 free promotion. He bought one plain 4 oz latte, and made 6 9 oz lattes. How many ounces of coffee did he use to make the drinks?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxe... | math | {
"ground_truth": "58",
"style": "rule"
} | {
"uid": "kd::717ba131a421af699a4663db",
"index": "kd::717ba131a421af699a4663db",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 13 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "For her birthday, her mom gave her $ 28 and her dad gave her $ 13 more. How much money does she have ?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Add the mom's gift and the calculated dad's gift together to find the total mon... | math | {
"ground_truth": "69",
"style": "rule"
} | {
"uid": "kd::bea42f6075e55d8f36b69e1d",
"index": "kd::bea42f6075e55d8f36b69e1d",
"lang": "en",
"rubrics": [
{
"criterion": "Identify the mom's gift as the base amount and interpret the dad's gift as that base plus thirteen dollars.",
"points": 2,
"tags": {
"judge": false,
... |
t01_math | [
{
"role": "user",
"content": "Find four numbers whose sum is 180 such that the ratio of the first number to the second number is equal to the ratio of the fourth number to the third number.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Select integer values ... | math | {
"ground_truth": "20, 10, 50, 100",
"style": "rule"
} | {
"uid": "kd::3fd68aeb283bd9b9b8c3da25",
"index": "kd::3fd68aeb283bd9b9b8c3da25",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{180}{3} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
t01_math | [
{
"role": "user",
"content": "A regular triangular pyramid is intersected by a plane passing through a vertex of the base and the midpoints of two lateral edges. The intersecting plane is perpendicular to one of the lateral faces. Determine the ratio of the lateral surface area of the pyramid to the area of... | math | {
"ground_truth": "\\sqrt{6}",
"style": "rule"
} | {
"uid": "kd::5525f515ae0999b632f3ff3b",
"index": "kd::5525f515ae0999b632f3ff3b",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 16 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "There are three crazy eggs for every one normal egg, cooked in a skillet. There are five normal eggs in a crate. How many eggs might be cooked despite an appalling fire?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Sum the calc... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"uid": "kd::96cbd93e34ca9eabc76e9f43",
"index": "kd::96cbd93e34ca9eabc76e9f43",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 15 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "Dan traveled 280 miles round trip air-conditioned sectionally to Laurel Point. He also traveled to Laurel Point 4 times this weekend. How many miles did he cover total for Round trip to and from the lodge?\n\nSolve the problem. Show your reasoning, then put the final answer ins... | math | {
"ground_truth": "1120",
"style": "rule"
} | {
"uid": "kd::091837e702d6e2868b109ce5",
"index": "kd::091837e702d6e2868b109ce5",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 140 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "The restaurant is selling a 100% Wild Card for half off, and you can buy ten at $10 each then what was my recipe? If it was before they made the deal of being 50% off?\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Multiply the c... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"uid": "kd::41ab3e2f9ea16f863fc555de",
"index": "kd::41ab3e2f9ea16f863fc555de",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 200 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "Solve the indicated equations: $\\sqrt {x^2+x-2}+\\sqrt {x^2+2x-3}=\\sqrt {x^2-3x+2}$.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Divide the entire equation by the common factor present in the first two radicals to simplify t... | math | {
"ground_truth": "x=1 \\text{or} x=\\frac{-3-2\\sqrt{21}}{3}",
"style": "rule"
} | {
"uid": "kd::ee04d3cc74f42b4f65d00952",
"index": "kd::ee04d3cc74f42b4f65d00952",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 5.536 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"v... |
t01_math | [
{
"role": "user",
"content": "다음 급수의 합을 계산하시오:\n\\[ 2\\sum_{i=1}^{48}\\left(\\frac{i(i+1)}{2}\\cdot\\sum_{n=1}^{i}\\frac{n(n+1)}{2}\\right) \\]\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: 각 차수의 합 공식에 N=48을 대입하기 전에 다항식의 계수를 먼저 정리하여 계산 실수를 줄여라."
}
] | math | {
"ground_truth": "398273960",
"style": "rule"
} | {
"uid": "kd::81d850a28e328bba9f8c8b21",
"index": "kd::81d850a28e328bba9f8c8b21",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 32 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"veri... |
t01_math | [
{
"role": "user",
"content": "단위 구간 위에 두 점이 무작위로 떨어질 때, 세 개의 부분 구간이 생성됩니다. 가운데 부분 구간이 오른쪽 부분 구간보다 두 배 짧을 확률을 구하시오.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\n힌트: 구간 길이의 합이 1 이라는 제약 조건을 이용해 영역의 넓이를 기하학적으로 계산하는 방법을 적용하세요."
}
] | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"uid": "kd::406922a07b1697515e1619f8",
"index": "kd::406922a07b1697515e1619f8",
"lang": "ko",
"rubrics": [
{
"criterion": "중간 결과 0.4 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
"ver... |
t01_math | [
{
"role": "user",
"content": "What is the asymptote of the function f(x) = 1/x - x? Give the vertical asymptote and the slant asymptote.\n\nSolve the problem. Show your reasoning, then put the final answer inside \\boxed{}.\n\nHint: Rewrite the function as a sum of a linear term and a term that vanishes at ... | math | {
"ground_truth": "x = 0 and y = -x",
"style": "rule"
} | {
"uid": "kd::c1b713d05c241329c39b1f06",
"index": "kd::c1b713d05c241329c39b1f06",
"lang": "en",
"rubrics": [
{
"criterion": "중간 결과 \\frac{1}{x} 에 도달",
"points": 1,
"tags": {
"judge": false,
"inject": false,
"scaffold_rank": 9,
"scaffold_kind": "generic",
... |
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