data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "A box contains a collection of triangular, square, and rectangular tiles. There are 32 tiles in the box, consisting of 114 edges in total. Each rectangle has 5 edges due to a small notch cut on one side. Determine the number of square tiles in the box."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 900,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains a total of 400 tickets that come in five colours: blue, green, red, yellow and orange. The ratio of blue to green to red tickets is $1: 2: 4$. The ratio of green to yellow to orange tickets is $1: 3: 6$. What is the smallest number of tickets that must be drawn t... | math | {
"style": "rule",
"ground_truth": "196"
} | {
"index": 901,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains chips, each of which is red, white, or blue. The number of blue chips is at least half the number of white chips, and at most one third the number of red chips. The number which are white or blue is at least $55$. The minimum number of red chips is"
}
] | math | {
"style": "rule",
"ground_truth": "57"
} | {
"index": 902,
"solution": "Let the number of white chips be denoted as $w$, the number of blue chips as $b$, and the number of red chips as $r$. According to the problem, we have the following conditions:\n1. $b \\geq \\frac{1}{2} w$\n2. $b \\leq \\frac{1}{3} r$\n3. $w + b \\geq 55$\n\nWe aim to find the minimum ... |
DeepScaleR | [
{
"role": "user",
"content": "A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards are selected randomly without replacement from the box. What is the probability that 4 is the largest value selected?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{10}"
} | {
"index": 903,
"solution": "To find the probability that 4 is the largest value selected, we need to consider two scenarios:\n1. The number 5 is not selected.\n2. The numbers selected are all less than or equal to 4.\n\n#### Step 1: Calculate the probability of not selecting 5.\nThe probability that the first card... |
DeepScaleR | [
{
"role": "user",
"content": "A box contains four balls, each with a unique number from 1 to 4, and all balls are identical in shape and size.\n(1) If two balls are randomly drawn from the box, what is the probability that the sum of their numbers is greater than 5?\n(2) If one ball is drawn from the box, i... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{8}"
} | {
"index": 904,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains gold coins. If the coins are equally divided among six people, four coins are left over. If the coins are equally divided among five people, three coins are left over. If the box holds the smallest number of coins that meets these two conditions, how many coins a... | math | {
"style": "rule",
"ground_truth": "0"
} | {
"index": 905,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains one hundred multicolored balls: 28 red, 20 green, 13 yellow, 19 blue, 11 white, and 9 black. What is the minimum number of balls that must be drawn from the box, without looking, to ensure that at least 15 balls of one color are among them?"
}
] | math | {
"style": "rule",
"ground_truth": "76"
} | {
"index": 906,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains seven cards, each with a different integer from 1 to 7 written on it. Avani takes three cards from the box and then Niamh takes two cards, leaving two cards in the box. Avani looks at her cards and then tells Niamh \"I know the sum of the numbers on your cards is... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 907,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains seven cards, each with a different integer from 1 to 7 written on it. Avani takes three cards from the box and then Niamh takes two cards, leaving two cards in the box. Avani looks at her cards and then tells Niamh \"I know the sum of the numbers on your cards is... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 908,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains six cards. Three of the cards are black on both sides, one card is black on one side and red on the other, and two of the cards are red on both sides. You pick a card uniformly at random from the box and look at a random side. Given that the side you see is red... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{5}"
} | {
"index": 909,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains three balls, each of a different color. Every minute, Randall randomly draws a ball from the box, notes its color, and then returns it to the box. Consider the following two conditions: (1) Some ball has been drawn at least three times (not necessarily consecutiv... | math | {
"style": "rule",
"ground_truth": "\\frac{13}{27}"
} | {
"index": 910,
"solution": "At any time, we describe the current state by the number of times each ball is drawn, sorted in nonincreasing order. For example, if the red ball has been drawn twice and green ball once, then the state would be $(2,1,0)$. Given state $S$, let $P_{S}$ be the probability that the state w... |
DeepScaleR | [
{
"role": "user",
"content": "A box contains tiles, numbered 1, 2, 3,..., 49, 50. Only tiles which are marked with a number congruent to $2 \\pmod{5}$ are blue. One tile is chosen randomly from the box. What is the probability that the tile is blue?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{5}"
} | {
"index": 911,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains twelve balls, each of a different color. Every minute, Randall randomly draws a ball from the box, notes its color, and then returns it to the box. Consider the following two conditions: (1) Some ball has been drawn at least twelve times (not necessarily consecut... | math | {
"style": "rule",
"ground_truth": "0.02236412255 \\ldots"
} | {
"index": 912,
"solution": "Below is a python implementation to compute the probability, using the same method as the solution to the easier version (with three balls). ``` from fractions import Fraction N = 12 probs = [{} for i in range ((N-1)*(N-1)+2)] prob1 = Fraction() prob2 = Fraction() init = tuple(O for i i... |
DeepScaleR | [
{
"role": "user",
"content": "A box of 100 personalized pencils costs $\\$30$. How many dollars does it cost to buy 2500 pencils?"
}
] | math | {
"style": "rule",
"ground_truth": "\\$750"
} | {
"index": 913,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box of 25 chocolate candies costs $\\$6$. How many dollars does it cost to buy 600 chocolate candies?"
}
] | math | {
"style": "rule",
"ground_truth": "144"
} | {
"index": 914,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box of chocolates in the shape of a cuboid was full of chocolates arranged in rows and columns. Míša ate some of them, and the remaining chocolates were rearranged to fill three entire rows completely, except for one space. Míša ate the remaining chocolates from another incom... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 915,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box with a volume of 16 $\\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\\text{cm}^3$ hold?"
}
] | math | {
"style": "rule",
"ground_truth": "150"
} | {
"index": 916,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A boy has the following seven coins in his pocket: $2$ pennies, $2$ nickels, $2$ dimes, and $1$ quarter. He takes out two coins, records the sum of their values, and then puts them back with the other coins. He continues to take out two coins, record the sum of their values, an... | math | {
"style": "rule",
"ground_truth": "9"
} | {
"index": 917,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A boy is riding a scooter from one bus stop to another and looking in the mirror to see if a bus appears behind him. As soon as the boy notices the bus, he can change the direction of his movement. What is the maximum distance between the bus stops so that the boy is guaranteed... | math | {
"style": "rule",
"ground_truth": "1.5"
} | {
"index": 918,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A boy named Vasya wrote down the nonzero coefficients of a tenth-degree polynomial \\( P(x) \\) in his notebook. He then calculated the derivative of the resulting polynomial and wrote down its nonzero coefficients, and continued this process until he arrived at a constant, whi... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 919,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A boy presses his thumb along a vertical rod that rests on a rough horizontal surface. Then he gradually tilts the rod, keeping the component of the force along the rod constant, which is applied to its end. When the tilt angle of the rod to the horizontal is $\\alpha=80^{\\cir... | math | {
"style": "rule",
"ground_truth": "0.17"
} | {
"index": 920,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A boy wrote the first twenty natural numbers on a piece of paper. He didn't like how one of them was written, so he crossed it out. Among the remaining 19 numbers, there is one number that equals the arithmetic mean of these 19 numbers. Which number did he cross out? If the pro... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 921,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A brand of orange juice is available in shop $A$ and shop $B$ at an original price of $\\$2.00$ per bottle. Shop $A$ provides a \"buy 4 get 1 free\" promotion and shop $B$ provides a $15\\%$ discount if one buys 4 bottles or more. Find the minimum cost (in cents) if one wants t... | math | {
"style": "rule",
"ground_truth": "2160"
} | {
"index": 922,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bridge is built by suspending a plank of wood between two triangular wedges with equal heights, as in the following diagram: [asy]\nimport olympiad;\nimport math;\n\n// Draw triangles\npair A = (0, 1);\npair B = (-cos(1.3962), 0);\npair C = (cos(1.3962), 0);\npair D = (2, 1);... | math | {
"style": "rule",
"ground_truth": "155^\\circ"
} | {
"index": 923,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bridge needs to be constructed over a river with a required elevation of 800 feet from one side to the other. Determine the additional bridge length required if the gradient is reduced from 2% to 1.5%."
}
] | math | {
"style": "rule",
"ground_truth": "13333.33"
} | {
"index": 924,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A broken line consists of $31$ segments. It has no self intersections, and its start and end points are distinct. All segments are extended to become straight lines. Find the least possible number of straight lines."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 925,
"solution": "\nLet us consider a broken line made up of 31 segments with no self-intersections, where the start and end points are distinct. Each segment of the broken line can be extended indefinitely to form a straight line. The problem asks us to find the least possible number of distinct straigh... |
DeepScaleR | [
{
"role": "user",
"content": "A bug crawls along a number line, starting at $-2$. It crawls to $-6$, then turns around and crawls to $5$. How many units does the bug crawl altogether?"
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 926,
"solution": "1. **Calculate the distance from $-2$ to $-6$:**\n The distance on a number line is the absolute difference between the two points. Thus, the distance from $-2$ to $-6$ is:\n \\[\n |-6 - (-2)| = |-6 + 2| = |-4| = 4 \\text{ units}\n \\]\n\n2. **Calculate the distance from $-6$ to... |
DeepScaleR | [
{
"role": "user",
"content": "A bug is on a corner of a cube. A healthy path for the bug is a path along the edges of the cube that starts and ends where the bug is located, uses no edge multiple times, and uses at most two of the edges adjacent to any particular face. Find the number of healthy paths."
}... | math | {
"style": "rule",
"ground_truth": "6"
} | {
"index": 927,
"solution": "There are 6 symmetric ways to choose the first two edges on the path. After these are chosen, all subsequent edges are determined, until the starting corner is reached once again."
} |
DeepScaleR | [
{
"role": "user",
"content": "A bug is on one exterior vertex of solid $S$, a $3 \\times 3 \\times 3$ cube that has its center $1 \\times 1 \\times 1$ cube removed, and wishes to travel to the opposite exterior vertex. Let $O$ denote the outer surface of $S$ (formed by the surface of the $3 \\times 3 \\time... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{29}}{3 \\sqrt{5}} \\text{ OR } \\frac{\\sqrt{145}}{15}"
} | {
"index": 928,
"solution": "By $\\left(^{*}\\right)$, the shortest route in $O$ has length $2 \\sqrt{1.5^{2}+3^{2}}=3 \\sqrt{5}$. By $\\left({ }^{* *}\\right)$, the shortest route overall (in $S$ ) has length $2 \\sqrt{1.5^{2}+1^{2}+2^{2}}=\\sqrt{3^{2}+2^{2}+4^{2}}=\\sqrt{29}$. Therefore the desired ratio is $\\fr... |
DeepScaleR | [
{
"role": "user",
"content": "A bug is on the edge of a ceiling of a circular room with a radius of 65 feet. The bug walks straight across the ceiling to the opposite edge, passing through the center of the circle. It next walks straight to another point on the edge of the circle but not back through the ce... | math | {
"style": "rule",
"ground_truth": "313"
} | {
"index": 929,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bug moves in the coordinate plane, starting at $(0,0)$. On the first turn, the bug moves one unit up, down, left, or right, each with equal probability. On subsequent turns the bug moves one unit up, down, left, or right, choosing with equal probability among the three direct... | math | {
"style": "rule",
"ground_truth": "1/54"
} | {
"index": 930,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bug starts at a vertex of a square. On each move, it randomly selects one of the three vertices where it is not currently located and crawls along a side of the square to that vertex. Given that the probability that the bug moves to its starting vertex on its eighth move is \... | math | {
"style": "rule",
"ground_truth": "2734"
} | {
"index": 931,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bug starts at a vertex of a square. On each move, it randomly selects one of the three vertices where it is not currently located, and crawls along a side of the square to that vertex. Determine the probability that the bug returns to its starting vertex on its eighth move an... | math | {
"style": "rule",
"ground_truth": "2734"
} | {
"index": 932,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bug starts at a vertex of an equilateral triangle. On each move, it randomly selects one of the two vertices where it is not currently located, and crawls along a side of the triangle to that vertex. Given that the probability that the bug moves to its starting vertex on its ... | math | {
"style": "rule",
"ground_truth": "683"
} | {
"index": 933,
"solution": "This method does not rigorously get the answer, but it works. As the bug makes more and more moves, the probability of it going back to the origin approaches closer and closer to 1/3. Therefore, after 10 moves, the probability gets close to $341.33/1024$. We can either round up or down.... |
DeepScaleR | [
{
"role": "user",
"content": "A bug starts at one vertex of a cube and moves along the edges of the cube according to the following rule. At each vertex the bug will choose to travel along one of the three edges emanating from that vertex. Each edge has equal probability of being chosen, and all choices are... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{729}"
} | {
"index": 934,
"solution": "1. **Understanding the Problem**: A bug starts at one vertex of a cube and moves along the edges. At each vertex, it can choose any of the three connected edges with equal probability. We need to find the probability that after seven moves, the bug visits every vertex exactly once.\n\n2... |
DeepScaleR | [
{
"role": "user",
"content": "A bug travels from A to B along the segments in the hexagonal lattice pictured below. The segments marked with an arrow can be traveled only in the direction of the arrow, and the bug never travels the same segment more than once. How many different paths are there?"
}
] | math | {
"style": "rule",
"ground_truth": "2400"
} | {
"index": 935,
"solution": "1. **Identify the number of ways to reach the red arrows:**\n - There is only one way to reach any of the red arrows from point A, as each red arrow has a unique path leading directly from A.\n\n2. **Calculate the number of ways to reach the blue arrows from the red arrows:**\n - Fr... |
DeepScaleR | [
{
"role": "user",
"content": "A bug travels in the coordinate plane, moving only along the lines that are parallel to the $x$-axis or $y$-axis. Let $A = (-3, 2)$ and $B = (3, -2)$. Consider all possible paths of the bug from $A$ to $B$ of length at most $20$. How many points with integer coordinates lie on ... | math | {
"style": "rule",
"ground_truth": "195"
} | {
"index": 936,
"solution": "To solve this problem, we need to find all integer-coordinate points $(x, y)$ that a bug can reach on its path from $A = (-3, 2)$ to $B = (3, -2)$, given that the maximum allowable path length is 20 units. The bug moves only along lines parallel to the $x$-axis or $y$-axis.\n\n1. **Calc... |
DeepScaleR | [
{
"role": "user",
"content": "A bug walks all day and sleeps all night. On the first day, it starts at point $O$, faces east, and walks a distance of $5$ units due east. Each night the bug rotates $60^\\circ$ counterclockwise. Each day it walks in this new direction half as far as it walked the previous day... | math | {
"style": "rule",
"ground_truth": "103"
} | {
"index": 937,
"solution": "The ant goes in the opposite direction every $3$ moves, going $(1/2)^3=1/8$ the distance backwards. Using geometric series, he travels $1-1/8+1/64-1/512...=(7/8)(1+1/64+1/4096...)=(7/8)(64/63)=8/9$ the distance of the first three moves over infinity moves. Now, we use coordinates meanin... |
DeepScaleR | [
{
"role": "user",
"content": "A builder has two identical bricks. She places them side by side in three different ways, resulting in shapes with surface areas of 72, 96, and 102. What is the surface area of one original brick?"
}
] | math | {
"style": "rule",
"ground_truth": "54"
} | {
"index": 938,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A builder has two identical bricks. She places them side by side in three different ways, resulting in shapes with surface areas of 72, 96, and 102. What is the surface area of one original brick?\nA) 36\nB) 48\nC) 52\nD) 54\nE) 60"
}
] | math | {
"style": "rule",
"ground_truth": "54"
} | {
"index": 939,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A building contractor needs to pay his $108$ workers $\\$ 200 $ each. He is carrying $ 122 $ one hundred dollar bills and $ 188 $ fifty dollar bills. Only $ 45 $ workers get paid with two $ \\ $100$ bills. Find the number of workers who get paid with four $\\$ 50$ bills."
... | math | {
"style": "rule",
"ground_truth": "31"
} | {
"index": 940,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A building has seven rooms numbered 1 through 7 on one floor, with various doors connecting these rooms. The doors can be either one-way or two-way. Additionally, there is a two-way door between room 1 and the outside, and there is a treasure in room 7. Design the arrangement o... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 941,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A building has three different staircases, all starting at the base of the building and ending at the top. One staircase has 104 steps, another has 117 steps, and the other has 156 steps. Whenever the steps of the three staircases are at the same height, there is a floor. How m... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 942,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bullet was fired perpendicular to a moving express train with a speed of \\( c = 60 \\frac{\\text{km}}{\\text{hr}} \\). The bullet pierced a windowpane on both sides of the car. How are the two holes positioned relative to each other if the bullet's speed was \\( c' = 40 \\fr... | math | {
"style": "rule",
"ground_truth": "1.667"
} | {
"index": 943,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bullet with a mass of \\( m = 10 \\) g, flying horizontally with a speed of \\( v_{1} = 400 \\) m/s, passes through a massive board and emerges from it with a speed of \\( v_{2} = 100 \\) m/s. Find the amount of work done on the bullet by the resistive force of the board."
... | math | {
"style": "rule",
"ground_truth": "750"
} | {
"index": 944,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bundle of wire was used in the following sequence:\n- The first time, more than half of the total length was used, plus an additional 3 meters.\n- The second time, half of the remaining length was used, minus 10 meters.\n- The third time, 15 meters were used.\n- Finally, 7 me... | math | {
"style": "rule",
"ground_truth": "54"
} | {
"index": 945,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A burger at Ricky C's now weighs 180 grams, of which 45 grams are filler. What percent of the burger is not filler? Additionally, what percent of the burger is filler?"
}
] | math | {
"style": "rule",
"ground_truth": "25\\%"
} | {
"index": 946,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A burger at Ricky C's weighs 120 grams, of which 30 grams are filler. What percent of the burger is not filler?"
}
] | math | {
"style": "rule",
"ground_truth": "75\\%"
} | {
"index": 947,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bus arrives randomly between 3:30 pm and 4:30 pm, waits for 40 minutes, and then departs. If Sara also arrives randomly between 3:30 pm and 4:30 pm, what is the probability that the bus will still be there when she arrives?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"index": 948,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bus arrives randomly sometime between 1:00 and 2:30, waits for 20 minutes, and then leaves. If Laura also arrives randomly between 1:00 and 2:30, what is the probability that the bus will be there when Laura arrives?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{16}{81}"
} | {
"index": 949,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bus arrives randomly sometime between 2:00 and 3:00 and waits for 15 minutes before leaving. If Carla arrives randomly between 2:00 and 3:00, what is the probability that the bus will still be there when Carla arrives?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7}{32}"
} | {
"index": 950,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bus at a certain station departs punctually at 7:00 and 7:30 in the morning. Student Xiao Ming arrives at the station to catch the bus between 6:50 and 7:30, and his arrival time is random. The probability that he waits for less than 10 minutes for the bus is ______."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 951,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bus can hold a maximum of 38 students. What is the minimum number of buses needed to transport 411 students?"
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 952,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bus ticket costs 1 yuan each. Xiaoming and 6 other children are lining up to buy tickets. Each of the 6 children has only 1 yuan, while Xiaoming has a 5-yuan note. The seller has no change. In how many ways can they line up so that the seller can give Xiaoming change when he ... | math | {
"style": "rule",
"ground_truth": "10800"
} | {
"index": 953,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bus ticket is numbered with six digits: from 000000 to 999999. You buy one ticket. What is the probability that you will get a ticket whose digits are in ascending (or descending) order?"
}
] | math | {
"style": "rule",
"ground_truth": "0.00042"
} | {
"index": 954,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bus traveling a 100 km route is equipped with a computer that forecasts the remaining time to arrival at the final destination. This time is calculated based on the assumption that the average speed of the bus on the remaining part of the route will be the same as it was on t... | math | {
"style": "rule",
"ground_truth": "85"
} | {
"index": 955,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bus with programmers departed from Novosibirsk to Pavlodar. After traveling 70 km, another car with Pavel Viktorovich left Novosibirsk on the same route and caught up with the bus in Karasuk. After that, Pavel traveled another 40 km, while the bus traveled only 20 km in the s... | math | {
"style": "rule",
"ground_truth": "140"
} | {
"index": 956,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bus, a truck, and a car are driving in the same direction on a straight road at constant speeds. At a certain moment, the bus is in front, the car is at the back, and the truck is exactly in the middle between the bus and the car. After 10 minutes, the car catches up with the... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 957,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A buyer took goods worth 10 rubles from a seller and gave 25 rubles. The seller did not have change, so he exchanged money with a neighbor. After they finished the transaction and the buyer left, the neighbor discovered that the 25 rubles were counterfeit. The seller returned 2... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 958,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A cafe has 3 tables and 5 individual counter seats. People enter in groups of size between 1 and 4, inclusive, and groups never share a table. A group of more than 1 will always try to sit at a table, but will sit in counter seats if no tables are available. Conversely, a group... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 959,
"solution": "We first show that $M+N \\geq 16$. Consider the point right before the last table is occupied. We have two cases: first suppose there exists at least one open counter seat. Then, every table must contribute at least 3 to the value of $M+N$, because no groups of 1 will have taken a table... |
DeepScaleR | [
{
"role": "user",
"content": "A cake has a shape of triangle with sides $19,20$ and $21$ . It is allowed to cut it it with a line into two pieces and put them on a round plate such that pieces don't overlap each other and don't stick out of the plate. What is the minimal diameter of the plate?"
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"index": 960,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A calculator has a squaring key $\\boxed{x^2}$ which replaces the current number displayed with its square. For example, if the display is $\\boxed{000003}$ and the $\\boxed{x^2}$ key is depressed, then the display becomes $\\boxed{000009}$. If the display reads $\\boxed{0000... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"index": 961,
"solution": "We start with the number $2$ displayed on the calculator. Each time we press the $\\boxed{x^2}$ key, the displayed number is replaced by its square. We need to determine how many times we must press the key until the displayed number exceeds $500$.\n\n1. **Initial Display**: $2$\n2. **F... |
DeepScaleR | [
{
"role": "user",
"content": "A calculator has digits from 0 to 9 and signs of two operations. Initially, the display shows the number 0. You can press any keys. The calculator performs operations in the sequence of keystrokes. If an operation sign is pressed several times in a row, the calculator remembers... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"index": 962,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A can is in the shape of a right circular cylinder. The circumference of the base of the can is 12 inches, and the height of the can is 5 inches. A spiral strip is painted on the can in such a way that it winds around the can exactly once as it reaches from the bottom of the ca... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 963,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A can of soup can feed $3$ adults or $5$ children. If there are $5$ cans of soup and $15$ children are fed, then how many adults would the remaining soup feed?"
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"index": 964,
"solution": "1. **Determine the number of cans needed to feed 15 children**: \n Given that one can of soup can feed 5 children, we calculate the number of cans needed to feed 15 children as follows:\n \\[\n \\text{Number of cans} = \\frac{15 \\text{ children}}{5 \\text{ children per can}} = 3 ... |
DeepScaleR | [
{
"role": "user",
"content": "A candy company makes 5 colors of jellybeans, which come in equal proportions. If I grab a random sample of 5 jellybeans, what is the probability that I get exactly 2 distinct colors?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{12}{125}"
} | {
"index": 965,
"solution": "There are $\\binom{5}{2}=10$ possible pairs of colors. Each pair of colors contributes $2^{5}-2=30$ sequences of beans that use both colors. Thus, the answer is $10 \\cdot 30 / 5^{5}=12 / 125$."
} |
DeepScaleR | [
{
"role": "user",
"content": "A cao has 6 legs, 3 on each side. A walking pattern for the cao is defined as an ordered sequence of raising and lowering each of the legs exactly once (altogether 12 actions), starting and ending with all legs on the ground. The pattern is safe if at any point, he has at least... | math | {
"style": "rule",
"ground_truth": "1416528"
} | {
"index": 966,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A capacitor with a capacitance of $C_{1} = 20 \\mu$F is charged to a voltage $U_{1} = 20$ V. A second capacitor with a capacitance of $C_{2} = 5 \\mu$F is charged to a voltage $U_{2} = 5$ V. The capacitors are connected with opposite-charged plates. Determine the voltage that w... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 967,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A capricious mathematician writes a book with pages numbered from $2$ to $400$ . The pages are to be read in the following order. Take the last unread page ( $400$ ), then read (in the usual order) all pages which are not relatively prime to it and which have not been read b... | math | {
"style": "rule",
"ground_truth": "397"
} | {
"index": 968,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A car and a truck start traveling towards each other simultaneously from points $A$ and $B$, respectively. It is known that the car's speed is twice the speed of the truck. The car arrives at point $C$ at 8:30, and the truck arrives at point $C$ at 15:00 on the same day. Both v... | math | {
"style": "rule",
"ground_truth": "10:40"
} | {
"index": 969,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A car is averaging 50 miles per hour. If the car maintains this speed, how many minutes less would a 450-mile trip take than a 475-mile trip?"
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 970,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A car is braking to a complete stop. It is known that its speed at the midpoint of the distance was 100 km/h. Determine its initial speed."
}
] | math | {
"style": "rule",
"ground_truth": "141.4"
} | {
"index": 971,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A car left the city for the village, and simultaneously, a cyclist left the village for the city. When the car and the cyclist met, the car immediately turned around and went back to the city. As a result, the cyclist arrived in the city 35 minutes later than the car. How many ... | math | {
"style": "rule",
"ground_truth": "55"
} | {
"index": 972,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A car license plate contains three letters and three digits, for example, A123BE. The allowable letters are А, В, Е, К, М, Н, О, Р, С, Т, У, Х (a total of 12 letters) and all digits except the combination 000. Katya considers a plate number lucky if the second letter is a conso... | math | {
"style": "rule",
"ground_truth": "288000"
} | {
"index": 973,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A car license plate contains three letters and three digits, for example, A123BE. The allowed letters are А, В, Е, К, М, Н, О, Р, С, Т, У, Х (a total of 12 letters) and all digits except the combination 000. Kira considers a license plate lucky if the second letter is a vowel, ... | math | {
"style": "rule",
"ground_truth": "359999"
} | {
"index": 974,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A car license plate contains three letters and three digits, for example, A123BE. The allowed letters are А, В, Е, К, М, Н, О, Р, С, Т, У, Х (a total of 12 letters), and all digits except for the combination 000. Tanya considers a license plate happy if the first letter is a co... | math | {
"style": "rule",
"ground_truth": "384000"
} | {
"index": 975,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A car travels 192 miles on 6 gallons of gas. How far can it travel on 8 gallons of gas?"
}
] | math | {
"style": "rule",
"ground_truth": "256"
} | {
"index": 976,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A car travels 40 kph for 20 kilometers, 50 kph for 25 kilometers, 60 kph for 45 minutes and 48 kph for 15 minutes. What is the average speed of the car, in kph?"
}
] | math | {
"style": "rule",
"ground_truth": "51"
} | {
"index": 977,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A car travels due east at $\\frac 23$ mile per minute on a long, straight road. At the same time, a circular storm, whose radius is $51$ miles, moves southeast at $\\frac 12\\sqrt{2}$ mile per minute. At time $t=0$, the center of the storm is $110$ miles due north of the car. A... | math | {
"style": "rule",
"ground_truth": "198"
} | {
"index": 978,
"solution": "We set up a coordinate system, with the starting point of the car at the origin. At time $t$, the car is at $\\left(\\frac 23t,0\\right)$ and the center of the storm is at $\\left(\\frac{t}{2}, 110 - \\frac{t}{2}\\right)$. Using the distance formula,\n\\begin{eqnarray*} \\sqrt{\\left(\\... |
DeepScaleR | [
{
"role": "user",
"content": "A car travels due east at a speed of $\\frac{5}{4}$ miles per minute on a straight road. Simultaneously, a circular storm with a 51-mile radius moves south at $\\frac{1}{2}$ mile per minute. Initially, the center of the storm is 110 miles due north of the car. Calculate the ave... | math | {
"style": "rule",
"ground_truth": "\\frac{880}{29}"
} | {
"index": 979,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A car travels the 120 miles from $A$ to $B$ at 60 miles per hour, and then returns to $A$ on the same road. If the average rate of the round trip is 45 miles per hour, what is the rate, in miles per hour, of the car traveling back from $B$ to $A$?"
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 980,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A car's clock is running at a constant speed but is inaccurate. One day, when the driver begins shopping, he notices both the car clock and his wristwatch (which is accurate) show 12:00 noon. After shopping, the wristwatch reads 12:30, and the car clock reads 12:35. Later that ... | math | {
"style": "rule",
"ground_truth": "6:00"
} | {
"index": 981,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A card is chosen at random from a standard deck of 52 cards, and then it is replaced and another card is chosen. What is the probability that at least one of the cards is a diamond or an ace?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{88}{169}"
} | {
"index": 982,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A card is chosen at random from a standard deck of 52 cards, and then it is replaced and another card is chosen. What is the probability that at least one of the cards is a heart, a spade, or a king?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{133}{169}"
} | {
"index": 983,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A card is chosen at random from a standard deck of 54 cards, including 2 jokers, and then it is replaced, and another card is chosen. What is the probability that at least one of the cards is a diamond, an ace, or a face card?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{533}{729}"
} | {
"index": 984,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A card is secretly removed from a standard deck of 52 cards. Then two cards are dealt at random from the now 51-card deck. What is the probability that both cards drawn are from the same suit and the second card is a face card?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{50}"
} | {
"index": 985,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A cardboard box in the shape of a rectangular parallelopiped is to be enclosed in a cylindrical container with a hemispherical lid. If the total height of the container from the base to the top of the lid is $60$ centimetres and its base has radius $30$ centimetres, find th... | math | {
"style": "rule",
"ground_truth": "108000"
} | {
"index": 986,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A cart rolls down a hill, travelling $5$ inches the first second and accelerating so that during each successive $1$-second time interval, it travels $7$ inches more than during the previous $1$-second interval. The cart takes $30$ seconds to reach the bottom of the hill. How f... | math | {
"style": "rule",
"ground_truth": "3195"
} | {
"index": 987,
"solution": "1. **Identify the sequence type**: The problem describes a sequence where the distance traveled each second increases by a constant amount. This is an arithmetic sequence.\n\n2. **Determine the first term and common difference**: \n - The first term $a_1 = 5$ inches (distance traveled... |
DeepScaleR | [
{
"role": "user",
"content": "A carton contains milk that is $2\\%$ fat, an amount that is $40\\%$ less fat than the amount contained in a carton of whole milk. What is the percentage of fat in whole milk?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{10}{3}"
} | {
"index": 988,
"solution": "1. **Understanding the Problem:**\n The problem states that a carton of milk contains 2% fat, which is 40% less than the fat content in a carton of whole milk. We need to find the percentage of fat in the whole milk.\n\n2. **Setting Up the Equation:**\n Let $x$ be the percentage of ... |
DeepScaleR | [
{
"role": "user",
"content": "A cashier from Aeroflot has to deliver tickets to five groups of tourists. Three of these groups live in the hotels \"Druzhba\", \"Rossiya\", and \"Minsk\". The fourth group's address will be given by tourists from \"Rossiya\", and the fifth group's address will be given by tou... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 989,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A cashier, upon checking the account before leaving work, finds that the cash is 153 yuan less than the account book. She knows the actual amount collected cannot be wrong, so it must be due to a decimal point error during bookkeeping. What is the actual amount of the cash that... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"index": 990,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A cat has found $432_{9}$ methods in which to extend each of her nine lives. How many methods are there in base 10?"
}
] | math | {
"style": "rule",
"ground_truth": "353"
} | {
"index": 991,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A cat is going up a stairwell with ten stairs. The cat can jump either two or three stairs at each step, or walk the last step if necessary. How many different ways can the cat go from the bottom to the top?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 992,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A caterpillar is climbing a 20-meter pole. During the day, it climbs 5 meters, and during the night, it slides down 4 meters. How long will it take for the caterpillar to reach the top of the pole?"
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 993,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A cauldron has the shape of a paraboloid of revolution. The radius of its base is \\( R = 3 \\) meters, and the depth is \\( H = 5 \\) meters. The cauldron is filled with a liquid, the specific weight of which is \\( 0.8 \\Gamma / \\text{cm}^3 \\). Calculate the work required t... | math | {
"style": "rule",
"ground_truth": "294300\\pi"
} | {
"index": 994,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A cell phone plan costs $20$ dollars each month, plus $5$ cents per text message sent, plus $10$ cents for each minute used over $30$ hours. In January Michelle sent $100$ text messages and talked for $30.5$ hours. How much did she have to pay?"
}
] | math | {
"style": "rule",
"ground_truth": "28.00"
} | {
"index": 995,
"solution": "1. **Calculate the base cost of the plan:**\n The base price of Michelle's cell phone plan is $20$ dollars.\n\n2. **Calculate the cost for text messages:**\n Michelle sent $100$ text messages, and each text message costs $5$ cents. Therefore, the total cost for text messages is:\n ... |
DeepScaleR | [
{
"role": "user",
"content": "A certain TV station randomly selected $100$ viewers to evaluate a TV program in order to understand the evaluation of the same TV program by viewers of different genders. It is known that the ratio of the number of \"male\" to \"female\" viewers selected is $9:11$. The evaluat... | math | {
"style": "rule",
"ground_truth": "212.5"
} | {
"index": 996,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain agency has 18 elderly, 12 middle-aged, and 6 young individuals. When drawing a sample of size X using systematic sampling and stratified sampling, there is no need to discard any individuals. However, if the sample size is increased by 1, then using systematic samplin... | math | {
"style": "rule",
"ground_truth": "X = 6"
} | {
"index": 997,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain bookstore currently has $7700$ yuan in funds, planning to use all of it to purchase a total of $20$ sets of three types of books, A, B, and C. Among them, type A books cost $500$ yuan per set, type B books cost $400$ yuan per set, and type C books cost $250$ yuan per ... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 998,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A certain brand of computers has a warranty period of $1$ year. Based on a large amount of repair record data, the maximum number of repairs for this brand of computers within one year is $3$ times, with $15\\%$ needing $1$ repair, $6\\%$ needing $2$ repairs, and $4\\%$ needing... | math | {
"style": "rule",
"ground_truth": "0.9"
} | {
"index": 999,
"solution": ""
} |
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