data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "A particle with charge $8.0 \\, \\mu\\text{C}$ and mass $17 \\, \\text{g}$ enters a magnetic field of magnitude $\\text{7.8 mT}$ perpendicular to its non-zero velocity. After 30 seconds, let the absolute value of the angle between its initial velocity and its current velo... | math | {
"style": "rule",
"ground_truth": "1.101"
} | {
"index": 2500,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A particular $12$-hour digital clock displays the hour and minute of a day. Unfortunately, whenever it is supposed to display a $1$, it mistakenly displays a $9$. For example, when it is 1:16 PM the clock incorrectly shows 9:96 PM. What fraction of the day will the clock show t... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 2501,
"solution": "\nTo determine the fraction of the day during which the clock displays the correct time, we need to consider both the hours and the minutes separately.\n\n#### Step 1: Analyzing the Hours\nThe clock displays the hours from 1 to 12. The clock will display the incorrect time for the enti... |
DeepScaleR | [
{
"role": "user",
"content": "A particular coin has a $\\frac{1}{3}$ chance of landing on heads (H), $\\frac{1}{3}$ chance of landing on tails (T), and $\\frac{1}{3}$ chance of landing vertically in the middle (M). When continuously flipping this coin, what is the probability of observing the continuous seq... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"index": 2502,
"solution": "For a string of coin flips $S$, let $P_{S}$ denote the probability of flipping $H M M T$ before $H M T$ if $S$ is the starting sequence of flips. We know that the desired probability, $p$, is $\\frac{1}{3} P_{H}+\\frac{1}{3} P_{M}+\\frac{1}{3} P_{T}$. Now, using conditional probability... |
DeepScaleR | [
{
"role": "user",
"content": "A particular convex polygon with seven sides has exactly one right angle. How many diagonals does this seven-sided polygon have?"
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 2503,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A particular fortune cookie lists four two-digit positive integers as your lucky numbers. The first three are 57, 13, and 72, but you got sauce on the last one and can't read it. If the sum of the digits of all four numbers equals $\\frac{1}{5}$ of the sum of all four numbers, ... | math | {
"style": "rule",
"ground_truth": "38"
} | {
"index": 2504,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A particular integer is the smallest multiple of 72, each of whose digits is either 0 or 1. How many digits does this integer have?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 2505,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A particular novel contains $40,\\!000$ words. If the author completed the novel in $80$ hours, on average how many words per hour did she write?"
}
] | math | {
"style": "rule",
"ground_truth": "500"
} | {
"index": 2506,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A particular triangle has sides of length 14 cm, 8 cm and 9 cm. In centimeters, what is the perimeter of the triangle?"
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"index": 2507,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A partition of a number \\( n \\) is a sequence of positive integers, arranged in descending order, whose sum is \\( n \\). For example, \\( n=4 \\) has 5 partitions: \\( 1+1+1+1=2+1+1=2+2=3+1=4 \\). Given two different partitions of the same number, \\( n=a_{1}+a_{2}+\\cdots+a... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 2508,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A passenger car traveling at a speed of 66 km/h arrives at its destination at 6:53, while a truck traveling at a speed of 42 km/h arrives at the same destination via the same route at 7:11. How many kilometers before the destination did the passenger car overtake the truck?"
... | math | {
"style": "rule",
"ground_truth": "34.65"
} | {
"index": 2509,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A path of length $n$ is a sequence of points $\\left(x_{1}, y_{1}\\right),\\left(x_{2}, y_{2}\\right), \\ldots,\\left(x_{n}, y_{n}\\right)$ with integer coordinates such that for all $i$ between 1 and $n-1$ inclusive, either (1) $x_{i+1}=x_{i}+1$ and $y_{i+1}=y_{i}$ (in which c... | math | {
"style": "rule",
"ground_truth": "1024"
} | {
"index": 2510,
"solution": "This is just the number of paths of length 10. The $i$th step can be either upward or rightward, so there are $2^{10}=1024$ such paths."
} |
DeepScaleR | [
{
"role": "user",
"content": "A pawn moves on a $6 \\times 6$ chessboard. It starts from the bottom-left square. At each step, it can either jump to the square directly to its right or the square directly above it. It must reach the top-right square, such that it never lies strictly above the diagonal conne... | math | {
"style": "rule",
"ground_truth": "132"
} | {
"index": 2511,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A peacock is a ten-digit positive integer that uses each digit exactly once. Compute the number of peacocks that are exactly twice another peacock."
}
] | math | {
"style": "rule",
"ground_truth": "184320"
} | {
"index": 2512,
"solution": "We begin with the following observation: Claim 1. Let $x$ be a peacock. Then, $2 x$ is a peacock if and only if: - the multiplication $x \\cdot 2$ uses five carries, - each of the pairs of digits $(0,5),(1,6),(2,7),(3,8),(4,9)$ receives exactly one carry. - The leading digit is not $5,... |
DeepScaleR | [
{
"role": "user",
"content": "A pebble is shaped as the intersection of a cube of side length 1 with the solid sphere tangent to all of the cube's edges. What is the surface area of this pebble?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{6 \\sqrt{2}-5}{2} \\pi"
} | {
"index": 2513,
"solution": "Imagine drawing the sphere and the cube. Take a cross section, with a plane parallel to two of the cube's faces, passing through the sphere's center. In this cross section, the sphere looks like a circle, and the cube looks like a square (of side length 1) inscribed in that circle. We ... |
DeepScaleR | [
{
"role": "user",
"content": "A pedestrian and a cyclist set off from point $A$ to point $B$ simultaneously. At point $B$, the cyclist turns back and meets the pedestrian 20 minutes after starting. Without stopping, the cyclist continues to point $A$, turns around, and catches up with the pedestrian 10 minu... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 2514,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pedestrian crossing signal at an intersection alternates between red and green lights, with the red light lasting for $30$ seconds. The probability that Little Ming, upon arriving at the intersection and encountering a red light, will have to wait at least $10$ seconds before... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{6}"
} | {
"index": 2515,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pedestrian departed from point \\( A \\) to point \\( B \\). After walking 8 km, a second pedestrian left point \\( A \\) following the first pedestrian. When the second pedestrian had walked 15 km, the first pedestrian was halfway to point \\( B \\), and both pedestrians arr... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 2516,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pedestrian is moving in a straight line towards a crosswalk at a constant speed of 3.6 km/h. Initially, the distance from the pedestrian to the crosswalk is 40 meters. The length of the crosswalk is 6 meters. What distance from the crosswalk will the pedestrian be after two m... | math | {
"style": "rule",
"ground_truth": "74"
} | {
"index": 2517,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pedestrian left city $A$ at noon heading towards city $B$. A cyclist left city $A$ at a later time and caught up with the pedestrian at 1 PM, then immediately turned back. After returning to city $A$, the cyclist turned around again and met the pedestrian at city $B$ at 4 PM,... | math | {
"style": "rule",
"ground_truth": "5/3"
} | {
"index": 2518,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pedestrian reported to a traffic officer the number of a car whose driver grossly violated traffic rules. This number is expressed as a four-digit number, where the unit digit is the same as the tens digit, and the hundreds digit is the same as the thousands digit. Moreover, ... | math | {
"style": "rule",
"ground_truth": "7744"
} | {
"index": 2519,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pedestrian traffic light allows pedestrians to cross the street for one minute and prohibits crossing for two minutes. Find the average waiting time for a pedestrian who approaches the intersection."
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 2520,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pedestrian walked 5.5 kilometers in 1 hour but did not reach point \\( B \\) (short by \\(2 \\pi - 5.5\\) km). Therefore, the third option is longer than the first and can be excluded.\n\nIn the first case, they need to cover a distance of 5.5 km along the alley. If they move... | math | {
"style": "rule",
"ground_truth": "11/51"
} | {
"index": 2521,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pen and its ink refill together cost $\\;\\$1.10$. The pen costs $\\;\\$1$ more than the ink refill. What is the cost of the pen in dollars?"
}
] | math | {
"style": "rule",
"ground_truth": "1.05"
} | {
"index": 2522,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pen costs $\\mathrm{Rs.}\\, 13$ and a note book costs $\\mathrm{Rs.}\\, 17$ . A school spends exactly $\\mathrm{Rs.}\\, 10000$ in the year $2017-18$ to buy $x$ pens and $y$ note books such that $x$ and $y$ are as close as possible (i.e., $|x-y|$ is minimum). ... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 2523,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A penny, nickel, dime, and quarter are simultaneously flipped. What is the expected value of the amount of the coins which come up heads? Express your answer in cents, rounded to the nearest tenth of a cent."
}
] | math | {
"style": "rule",
"ground_truth": "20.5"
} | {
"index": 2524,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pentagon $ABCDE$ is circumscribed about a circle. The angles at the vertices $A{}$, $C{}$ and $E{}$ of the pentagon are equal to $100^\\circ$. Find the measure of the angle $\\angle ACE$."
}
] | math | {
"style": "rule",
"ground_truth": "40^\\circ"
} | {
"index": 2525,
"solution": "\nTo solve for the angle \\(\\angle ACE\\) in a circumscribed pentagon \\(ABCDE\\) with angles \\( \\angle A = \\angle C = \\angle E = 100^\\circ \\), we follow these steps.\n\n**Step 1:** Use the fact that the pentagon is circumscribed.\nFor a pentagon circumscribed about a circle, th... |
DeepScaleR | [
{
"role": "user",
"content": "A pentagon is drawn by placing an isosceles right triangle on top of a square as pictured. What percent of the area of the pentagon is the area of the right triangle?\n\n[asy]\nsize(50);\ndraw((0,0)--(0,-1)--(1,-1)--(1,0)--(0,0)--(.5,.5)--(1,0));\n[/asy]"
}
] | math | {
"style": "rule",
"ground_truth": "20\\%"
} | {
"index": 2526,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pentagon is formed by cutting a triangular corner from a rectangular piece of paper. The five sides of the pentagon have lengths $13,$ $19,$ $20,$ $25$ and $31,$ in some order. Find the area of the pentagon."
}
] | math | {
"style": "rule",
"ground_truth": "745"
} | {
"index": 2527,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pentagon is formed by placing an equilateral triangle atop a square. Each side of the square is equal to the height of the equilateral triangle. What percent of the area of the pentagon is the area of the equilateral triangle?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3(\\sqrt{3} - 1)}{6} \\times 100\\%"
} | {
"index": 2528,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pentagon is formed by placing an equilateral triangle on top of a rectangle. The side length of the equilateral triangle is equal to the width of the rectangle, and the height of the rectangle is twice the side length of the triangle. What percent of the area of the pentagon ... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{\\sqrt{3} + 8} \\times 100\\%"
} | {
"index": 2529,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pentagon is formed by placing an equilateral triangle on top of a square. Calculate the percentage of the pentagon's total area that is made up by the equilateral triangle."
}
] | math | {
"style": "rule",
"ground_truth": "25.4551\\%"
} | {
"index": 2530,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pentagon is inscribed around a circle, with the lengths of its sides being whole numbers, and the lengths of the first and third sides equal to 1. Into what segments does the point of tangency divide the second side?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 2531,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pentagon is obtained by joining, in order, the points \\((0,0)\\), \\((1,2)\\), \\((3,3)\\), \\((4,1)\\), \\((2,0)\\), and back to \\((0,0)\\). The perimeter of the pentagon can be written in the form \\(a + b\\sqrt{c} + d\\sqrt{e}\\), where \\(a\\), \\(b\\), \\(c\\), \\(d\\)... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 2532,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pentagonal prism is used as the base of a new pyramid. One of the seven faces of this pentagonal prism will be chosen as the base of the pyramid. Calculate the maximum value of the sum of the exterior faces, vertices, and edges of the resulting structure after this pyramid is... | math | {
"style": "rule",
"ground_truth": "42"
} | {
"index": 2533,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A perfect power is an integer $n$ that can be represented as $a^{k}$ for some positive integers $a \\geq 1$ and $k \\geq 2$. Find the sum of all prime numbers $0<p<50$ such that $p$ is 1 less than a perfect power."
}
] | math | {
"style": "rule",
"ground_truth": "41"
} | {
"index": 2534,
"solution": "First, it is known that $a^{k}-1=(a-1)\\left(a^{k-1}+a^{k-2}+\\ldots\\right)$. This means either $a-1$ or $a^{k-1}+a^{k-2}+\\ldots+1$ must be 1 in order for $a^{k}-1$ to be prime. But this only occurs when $a$ is 2 . Thus, the only possible primes are of the form $2^{k}-1$ for some int... |
DeepScaleR | [
{
"role": "user",
"content": "A permutation $(a_1, a_2, a_3, \\dots, a_{2012})$ of $(1, 2, 3, \\dots, 2012)$ is selected at random. If $S$ is the expected value of \n\t\t\\[\n\t\t\\sum_{i = 1}^{2012} | a_i - i |,\n\t\t\\]\n\t\tthen compute the sum of the prime factors of $S$ .\n\n*Proposed by Aaron L... | math | {
"style": "rule",
"ground_truth": "2083"
} | {
"index": 2535,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A permutation $a_1,a_2,\\cdots ,a_6$ of numbers $1,2,\\cdots ,6$ can be transformed to $1,2,\\cdots,6$ by transposing two numbers exactly four times. Find the number of such permutations."
}
] | math | {
"style": "rule",
"ground_truth": "360"
} | {
"index": 2536,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A permutation $(a_1,a_2,a_3,a_4,a_5)$ of $(1,2,3,4,5)$ is heavy-tailed if $a_1 + a_2 < a_4 + a_5$. What is the number of heavy-tailed permutations?"
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"index": 2537,
"solution": "We analyze the problem by considering the position of $a_3$ and how it affects the possible values of $a_1 + a_2$ and $a_4 + a_5$. We need to ensure $a_1 + a_2 < a_4 + a_5$ for the permutation to be heavy-tailed.\n\n1. **Case 1: $a_3 = 1$.**\n - The remaining numbers are $2, 3, 4, 5$... |
DeepScaleR | [
{
"role": "user",
"content": "A permutation of \\{1,2, \\ldots, 7\\} is chosen uniformly at random. A partition of the permutation into contiguous blocks is correct if, when each block is sorted independently, the entire permutation becomes sorted. For example, the permutation $(3,4,2,1,6,5,7)$ can be parti... | math | {
"style": "rule",
"ground_truth": "\\frac{151}{105}"
} | {
"index": 2538,
"solution": "Let $\\sigma$ be a permutation on \\{1, \\ldots, n\\}. Call $m \\in\\{1, \\ldots, n\\}$ a breakpoint of $\\sigma$ if $\\{\\sigma(1), \\ldots, \\sigma(m)\\}=$ $\\{1, \\ldots, m\\}$. Notice that the maximum partition is into $k$ blocks, where $k$ is the number of breakpoints: if our brea... |
DeepScaleR | [
{
"role": "user",
"content": "A permutation of a finite set $S$ is a one-to-one function from $S$ to $S$ . A permutation $P$ of the set $\\{ 1, 2, 3, 4, 5 \\}$ is called a W-permutation if $P(1) > P(2) < P(3) > P(4) < P(5)$ . A permutation of the set $\\{1, 2, 3, 4, 5 \\}$ is selected at rando... | math | {
"style": "rule",
"ground_truth": "2/15"
} | {
"index": 2539,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A permutation of a finite set is a one-to-one function from the set to itself; for instance, one permutation of $\\{1,2,3,4\\}$ is the function $\\pi$ defined such that $\\pi(1)=1, \\pi(2)=3$, $\\pi(3)=4$, and $\\pi(4)=2$. How many permutations $\\pi$ of the set $\\{1,2, \\ldot... | math | {
"style": "rule",
"ground_truth": "945"
} | {
"index": 2540,
"solution": "For each such $\\pi$, the elements of $\\{1,2, \\ldots, 10\\}$ can be arranged into pairs $\\{i, j\\}$ such that $\\pi(i)=j ; \\pi(j)=i$. Choosing a permutation $\\pi$ is thus tantamount to choosing a partition of $\\{1,2, \\ldots, 10\\}$ into five disjoint pairs. There are 9 ways to p... |
DeepScaleR | [
{
"role": "user",
"content": "A permutation of the set of positive integers $[n] = \\{1, 2, \\ldots, n\\}$ is a sequence $(a_1, a_2, \\ldots, a_n)$ such that each element of $[n]$ appears precisely one time as a term of the sequence. For example, $(3, 5, 1, 2, 4)$ is a permutation of $[5]$ . Let $P(n)$ be t... | math | {
"style": "rule",
"ground_truth": "\\(\\boxed{4489}\\)"
} | {
"index": 2541,
"solution": "We claim that the smallest $n$ is $67^2 = \\boxed{4489}$ .\nSolution 1\nLet $S = \\{1, 4, 9, \\ldots\\}$ be the set of positive perfect squares. We claim that the relation $R = \\{(j, k)\\in [n]\\times[n]\\mid jk\\in S\\}$ is an equivalence relation on $[n]$ .\nIt is reflexive because ... |
DeepScaleR | [
{
"role": "user",
"content": "A person bequeathed an amount of money, slightly less than 1500 dollars, to be distributed as follows. His five children and the notary received amounts such that the square root of the eldest son's share, half of the second son's share, the third son's share minus 2 dollars, t... | math | {
"style": "rule",
"ground_truth": "1464"
} | {
"index": 2542,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person bought a bond for 1000 yuan with a maturity of one year. After the bond matured, he spent 440 yuan and then used the remaining money to buy the same type of bond again for another year. After the bond matured the second time, he received 624 yuan. Calculate the annual ... | math | {
"style": "rule",
"ground_truth": "4\\%"
} | {
"index": 2543,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person can commute by train or car. If he takes the train to work in the morning, he takes the car in the afternoon; if he takes the train home in the afternoon, he takes the car in the morning. Over $x$ days, this person took the train 9 times, took the car in the morning 8 ... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 2544,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person flips $2010$ coins at a time. He gains one penny every time he flips a prime number of heads, but must stop once he flips a non-prime number. If his expected amount of money gained in dollars is $\\frac{a}{b}$ , where $a$ and $b$ are relatively prime, compute $... | math | {
"style": "rule",
"ground_truth": "2017"
} | {
"index": 2545,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person flips a coin, where the probability of heads up and tails up is $\\frac{1}{2}$ each. Construct a sequence $\\left\\{a_{n}\\right\\}$ such that\n$$\na_{n}=\\left\\{\n\\begin{array}{ll}\n1, & \\text{if the } n \\text{th flip is heads;} \\\\\n-1, & \\text{if the } n \\tex... | math | {
"style": "rule",
"ground_truth": "13/128"
} | {
"index": 2546,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person forgot the last digit of a phone number and dialed randomly. Calculate the probability of connecting to the call in no more than 3 attempts."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{3}{10}"
} | {
"index": 2547,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person has $440.55$ in their wallet. They purchase goods costing $122.25$. Calculate the remaining money in the wallet. After this, calculate the amount this person would have if they received interest annually at a rate of 3% on their remaining money over a period of 1 year.... | math | {
"style": "rule",
"ground_truth": "327.85"
} | {
"index": 2548,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person has 13 pieces of a gold chain containing 80 links. Separating one link costs 1 cent, and attaching a new one - 2 cents.\n\nWhat is the minimum amount needed to form a closed chain from these pieces?\n\nRemember, larger and smaller links must alternate."
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 2549,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person has a probability of $\\frac{1}{2}$ to hit the target in each shot. What is the probability of hitting the target 3 times out of 6 shots, with exactly 2 consecutive hits? (Answer with a numerical value)"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{16}"
} | {
"index": 2550,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person has a three times higher probability of scoring a basket than missing it. Let random variable $X$ represent the number of scores in one shot. Then $P(X=1) = \\_\\_\\_\\_\\_\\_$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{16}"
} | {
"index": 2551,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person having contracted conjunctivitis infects a total of 144 people after two rounds of infection. Determine the average number of people each infected person infects in each round."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 2552,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person is waiting at the $A$ HÉV station. They get bored of waiting and start moving towards the next $B$ HÉV station. When they have traveled $1 / 3$ of the distance between $A$ and $B$, they see a train approaching $A$ station at a speed of $30 \\mathrm{~km/h}$. If they run... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 2553,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person named Jia and their four colleagues each own a car with license plates ending in 9, 0, 2, 1, and 5, respectively. To comply with the local traffic restriction rules from the 5th to the 9th day of a certain month (allowing cars with odd-ending numbers on odd days and ev... | math | {
"style": "rule",
"ground_truth": "80"
} | {
"index": 2554,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person orders 4 pairs of black socks and some pairs of blue socks. The price of each pair of black socks is twice the price of each pair of blue socks. However, the colors were reversed on the order form, causing his expenditure to increase by 50%. What is the original ratio ... | math | {
"style": "rule",
"ground_truth": "1: 4"
} | {
"index": 2555,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person receives an annuity at the end of each year for 15 years as follows: $1000 \\mathrm{K}$ annually for the first five years, $1200 \\mathrm{K}$ annually for the next five years, and $1400 \\mathrm{K}$ annually for the last five years. If they received $1400 \\mathrm{K}$ ... | math | {
"style": "rule",
"ground_truth": "807.95"
} | {
"index": 2556,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person rides a bicycle from place A to place B. If they increase their speed by 6 km/h, they can arrive 5 minutes earlier; if they decrease their speed by 5 km/h, they will be 6 minutes late. What is the distance between place A and place B in kilometers?"
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 2557,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person rolled a fair six-sided die $100$ times and obtained a $6$ $19$ times. What is the approximate probability of rolling a $6$?"
}
] | math | {
"style": "rule",
"ground_truth": "0.19"
} | {
"index": 2558,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person rolls a die twice, obtaining the numbers $m$ and $n$, which are used as the coefficients of a quadratic equation $x^2 + mx + n = 0$. The probability that the equation has real roots is ______."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{19}{36}"
} | {
"index": 2559,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person rolls two dice simultaneously and gets the scores $a$ and $b$. The eccentricity $e$ of the ellipse $\\frac{y^2}{a^2} + \\frac{x^2}{b^2} = 1$ satisfies $e \\geq \\frac{\\sqrt{3}}{2}$. Calculate the probability that this event occurs."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"index": 2560,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person starting with $64$ and making $6$ bets, wins three times and loses three times, the wins and losses occurring in random order. The chance for a win is equal to the chance for a loss. If each wager is for half the money remaining at the time of the bet, then the final r... | math | {
"style": "rule",
"ground_truth": "$37$"
} | {
"index": 2561,
"solution": "1. **Initial Amount and Bet Dynamics**: The person starts with $64$ dollars. Each bet is for half of the current amount. If the person wins a bet, the amount increases to $\\frac{3}{2}$ times the amount before the bet. If the person loses a bet, the amount decreases to $\\frac{1}{2}$ t... |
DeepScaleR | [
{
"role": "user",
"content": "A person was asked how much he paid for a hundred apples and he answered the following:\n\n- If a hundred apples cost 4 cents more, then for 1 dollar and 20 cents, he would get five apples less.\n\nHow much did 100 apples cost?"
}
] | math | {
"style": "rule",
"ground_truth": "96"
} | {
"index": 2562,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person who left home between 4 p.m. and 5 p.m. returned between 5 p.m. and 6 p.m. and found that the hands of his watch had exactly exchanged place, when did he go out ?"
}
] | math | {
"style": "rule",
"ground_truth": "4:26.8"
} | {
"index": 2563,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person's age at the time of their death was one 31st of their birth year. How old was this person in 1930?"
}
] | math | {
"style": "rule",
"ground_truth": "39"
} | {
"index": 2564,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A person's commute times (in minutes) for 5 trips were 12, 8, 10, 11, and 9, respectively. The standard deviation of this set of data is ______."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}"
} | {
"index": 2565,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pet store has 15 puppies, 6 kittens, and 8 hamsters. Alice, Bob, and Charlie each want to buy a pet. For variety, they each want a different kind of pet. How many ways can Alice, Bob, and Charlie buy pets and leave the store satisfied?"
}
] | math | {
"style": "rule",
"ground_truth": "4320"
} | {
"index": 2566,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A phone fully charges in 1 hour 20 minutes on fast charge and in 4 hours on regular charge. Fedya initially put the completely discharged phone on regular charge, then switched to fast charge once he found the proper adapter, completing the charging process. Determine the total... | math | {
"style": "rule",
"ground_truth": "144"
} | {
"index": 2567,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A phone number \\( d_{1} d_{2} d_{3}-d_{4} d_{5} d_{6} d_{7} \\) is called \"legal\" if the number \\( d_{1} d_{2} d_{3} \\) is equal to \\( d_{4} d_{5} d_{6} \\) or to \\( d_{5} d_{6} d_{7} \\). For example, \\( 234-2347 \\) is a legal phone number. Assume each \\( d_{i} \\) c... | math | {
"style": "rule",
"ground_truth": "19990"
} | {
"index": 2568,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A picture $3$ feet across is hung in the center of a wall that is $19$ feet wide. How many feet from the end of the wall is the nearest edge of the picture?"
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"index": 2569,
"solution": "1. **Identify the total width and picture width**: The wall is $19$ feet wide and the picture is $3$ feet wide.\n\n2. **Set up the equation**: The picture is centered, so the distances from each end of the wall to the nearest edge of the picture are equal. Let $x$ be the distance from ... |
DeepScaleR | [
{
"role": "user",
"content": "A piece of alloy weighing 6 kg contains copper. Another piece of alloy weighing 8 kg contains copper in a different percentage than the first piece. A certain part was separated from the first piece, and a part twice as heavy was separated from the second piece. Each of the sep... | math | {
"style": "rule",
"ground_truth": "2.4"
} | {
"index": 2570,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A piece of cheese is located at $(12,10)$ in a coordinate plane. A mouse is at $(4,-2)$ and is running up the line $y=-5x+18$. At the point $(a,b)$ the mouse starts getting farther from the cheese rather than closer to it. What is $a + b$?"
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 2571,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A piece of graph paper is folded once so that (0,2) is matched with (4,0), and (7,3) is matched with $(m,n)$. Find $m+n$."
}
] | math | {
"style": "rule",
"ground_truth": "6.8"
} | {
"index": 2572,
"solution": "\n1. **Identify the line of fold**: The line of fold is the perpendicular bisector of the segment connecting $(0,2)$ and $(4,0)$. The midpoint of this segment is calculated as follows:\n \\[\n \\left(\\frac{0+4}{2}, \\frac{2+0}{2}\\right) = (2,1)\n \\]\n The slope of the line c... |
DeepScaleR | [
{
"role": "user",
"content": "A piece of iron wire with a length of $80cm$ is randomly cut into three segments. Calculate the probability that each segment has a length of no less than $20cm$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{16}"
} | {
"index": 2573,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A piece of paper containing six joined squares labeled as shown in the diagram is folded along the edges of the squares to form a cube. The label of the face opposite the face labeled $\\text{X}$ is"
}
] | math | {
"style": "rule",
"ground_truth": "Y"
} | {
"index": 2574,
"solution": "To determine the face opposite to the face labeled $\\text{X}$ on a cube formed by folding a flat arrangement of six squares, we need to identify which faces are adjacent to $\\text{X}$ and which are not. The face opposite to $\\text{X}$ will be the one that does not share any edge wit... |
DeepScaleR | [
{
"role": "user",
"content": "A piece of paper with a thickness of $0.1$ millimeters is folded once, resulting in a thickness of $2 \\times 0.1$ millimeters. Continuing to fold it $2$ times, $3$ times, $4$ times, and so on, determine the total thickness after folding the paper $20$ times and express it as t... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"index": 2575,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A piece of platinum, which has a density of $2.15 \\cdot 10^{4} \\mathrm{kg} / \\mathrm{m}^{3}$, is connected to a piece of cork wood (density $2.4 \\cdot 10^{2} \\mathrm{kg} / \\mathrm{m}^{3}$). The density of the combined system is $4.8 \\cdot 10^{2} \\mathrm{kg} / \\mathrm{m... | math | {
"style": "rule",
"ground_truth": "85"
} | {
"index": 2576,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A piece of string fits exactly once around the perimeter of a rectangle whose area is 180. The ratio of the length to the width of the rectangle is 3:2. Rounded to the nearest whole number, what is the area of the largest circle that can be formed from this piece of string?"
... | math | {
"style": "rule",
"ground_truth": "239"
} | {
"index": 2577,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A piece of string fits exactly once around the perimeter of a rectangle with a length of 16 and a width of 10. Rounded to the nearest whole number, what is the area of the largest circle that can be formed from the piece of string?"
}
] | math | {
"style": "rule",
"ground_truth": "215"
} | {
"index": 2578,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A piece of string fits exactly once around the perimeter of a square whose area is 144. Rounded to the nearest whole number, what is the area of the largest circle that can be formed from the piece of string?"
}
] | math | {
"style": "rule",
"ground_truth": "183"
} | {
"index": 2579,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A piece of string is cut in two at a point selected at random. The probability that the longer piece is at least x times as large as the shorter piece is"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{x+1}"
} | {
"index": 2580,
"solution": "Let's consider a string of unit length (length = 1) for simplicity. We cut the string at a point $C$ chosen uniformly at random along the string. Let $C$ be the length of the shorter piece after the cut, and $1 - C$ be the length of the longer piece. We need to find the probability tha... |
DeepScaleR | [
{
"role": "user",
"content": "A piece of wood of uniform density in the shape of a right triangle with base length $3$ inches and hypotenuse $5$ inches weighs $12$ ounces. Another piece of the same type of wood, with the same thickness, also in the shape of a right triangle, has a base length of $5$ inches ... | math | {
"style": "rule",
"ground_truth": "24.5"
} | {
"index": 2581,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pipe with inside diameter 10'' is to carry water from a reservoir to a small town in an arid land. Neglecting the friction and turbulence of the water against the inside of the pipes, what is the minimum number of 2''-inside-diameter pipes of the same length needed to carry t... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 2582,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pirate finds three chests on the wrecked ship S.S. Triumph, recorded in base 7. The chests contain $3214_7$ dollars worth of silver, $1652_7$ dollars worth of precious stones, $2431_7$ dollars worth of pearls, and $654_7$ dollars worth of ancient coins. Calculate the total va... | math | {
"style": "rule",
"ground_truth": "3049"
} | {
"index": 2583,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pirate is counting the loot he has stolen from S.S. AOPS, on which everything is counted in base 5. A treasure chest contains $3124_{5}$ dollars worth of jewelry, $3122_{5}$ dollars worth of gold coins, and $124_{5}$ dollars worth of rubbing alcohol. What is the total dolla... | math | {
"style": "rule",
"ground_truth": "865"
} | {
"index": 2584,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pirate is searching for buried treasure on 6 islands. On each island, there is a $\\frac{1}{4}$ chance that the island has buried treasure and no traps, a $\\frac{1}{12}$ chance that the island has traps but no treasure, and a $\\frac{2}{3}$ chance that the island has neither... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{54}"
} | {
"index": 2585,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pirate is tallying his newly plundered wealth from the vessel G.S. Legends, where all values are counted in base 8. The treasure chest includes $5267_{8}$ dollars worth of silks, $6712_{8}$ dollars worth of precious stones, and $327_{8}$ dollars worth of spices. What is the t... | math | {
"style": "rule",
"ground_truth": "6488"
} | {
"index": 2586,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pizza is cut into 10 pieces. Two of the pieces are each \\(\\frac{1}{24}\\) of the whole pizza, four are each \\(\\frac{1}{12}\\), two are each \\(\\frac{1}{8}\\), and two are each \\(\\frac{1}{6}\\). A group of \\(n\\) friends share the pizza by distributing all of these pie... | math | {
"style": "rule",
"ground_truth": "39"
} | {
"index": 2587,
"solution": "Each of the \\(n\\) friends is to receive \\(\\frac{1}{n}\\) of the pizza. Since there are two pieces that are each \\(\\frac{1}{6}\\) of the pizza and these pieces cannot be cut, then each friend receives at least \\(\\frac{1}{6}\\) of the pizza. This means that there cannot be more t... |
DeepScaleR | [
{
"role": "user",
"content": "A pizza parlor has six different toppings. How many different one- and two-topping pizzas can you order?"
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"index": 2588,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A pizza parlor offers six toppings. What is the greatest number of four-topping pizzas that can be made such that no two pizzas have the same topping combination?"
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 2589,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A plan is to transport 1240 tons of goods A and 880 tons of goods B using a fleet of trucks to a certain location. The fleet consists of two different types of truck carriages, A and B, with a total of 40 carriages. The cost of using each type A carriage is 6000 yuan, and the c... | math | {
"style": "rule",
"ground_truth": "26.8"
} | {
"index": 2590,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A plane $P$ slices through a cube of volume 1 with a cross-section in the shape of a regular hexagon. This cube also has an inscribed sphere, whose intersection with $P$ is a circle. What is the area of the region inside the regular hexagon but outside the circle?"
}
] | math | {
"style": "rule",
"ground_truth": "(3 \\sqrt{3}-\\pi) / 4"
} | {
"index": 2591,
"solution": "One can show that the hexagon must have as its vertices the midpoints of six edges of the cube, as illustrated; for example, this readily follows from the fact that opposite sides of the hexagons and the medians between them are parallel. We then conclude that the side of the hexagon i... |
DeepScaleR | [
{
"role": "user",
"content": "A plane contains $40$ lines, no $2$ of which are parallel. Suppose that there are $3$ points where exactly $3$ lines intersect, $4$ points where exactly $4$ lines intersect, $5$ points where exactly $5$ lines intersect, $6$ points where exactly $6$ lines intersect, and no point... | math | {
"style": "rule",
"ground_truth": "607"
} | {
"index": 2592,
"solution": "In this solution, let $\\boldsymbol{n}$-line points be the points where exactly $n$ lines intersect. We wish to find the number of $2$-line points.\n There are $\\binom{40}{2}=780$ pairs of lines. Among them:\nThe $3$-line points account for $3\\cdot\\binom32=9$ pairs of lines.\nThe $4... |
DeepScaleR | [
{
"role": "user",
"content": "A plane flew straight against a wind between two towns in 84 minutes and returned with that wind in 9 minutes less than it would take in still air. The number of minutes (2 answers) for the return trip was"
}
] | math | {
"style": "rule",
"ground_truth": "63 or 12"
} | {
"index": 2593,
"solution": "1. **Define Variables:**\n Let $d$ be the distance between the two towns, $p$ be the speed of the plane in still air, and $w$ be the speed of the wind.\n\n2. **Equation for the trip against the wind:**\n The time taken to fly against the wind is given as 84 minutes. Therefore, the ... |
DeepScaleR | [
{
"role": "user",
"content": "A plane flies between two cities. With the tailwind, it takes 5 hours and 30 minutes, and against the wind, it takes 6 hours. Given that the wind speed is 24 kilometers per hour, and assuming the plane's flying speed is $x$ kilometers per hour, then the speed of the plane with ... | math | {
"style": "rule",
"ground_truth": "528"
} | {
"index": 2594,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A plane flies from city A to city B against a wind in 120 minutes. On the return trip with the wind, it takes 10 minutes less than it would in still air. Determine the time in minutes for the return trip."
}
] | math | {
"style": "rule",
"ground_truth": "110"
} | {
"index": 2595,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A plane has no vertex of a regular dodecahedron on it,try to find out how many edges at most may the plane intersect the regular dodecahedron?"
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 2596,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A plane intersects a right circular cylinder of radius $1$ forming an ellipse. If the major axis of the ellipse of $50\\%$ longer than the minor axis, the length of the major axis is\n$\\textbf{(A)}\\ 1\\qquad \\textbf{(B)}\\ \\frac{3}{2}\\qquad \\textbf{(C)}\\ 2\\qquad \\textb... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"index": 2597,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A plane intersects a right circular cylinder of radius $2$ forming an ellipse. If the major axis of the ellipse is $30\\%$ longer than the minor axis, what is the length of the major axis?"
}
] | math | {
"style": "rule",
"ground_truth": "5.2"
} | {
"index": 2598,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A plane intersects a right circular cylinder of radius $2$ forming an ellipse. If the major axis of the ellipse is $60\\%$ longer than the minor axis, find the length of the major axis."
}
] | math | {
"style": "rule",
"ground_truth": "6.4"
} | {
"index": 2599,
"solution": ""
} |
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