data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "A basketball team has 15 available players. Initially, 5 players start the game, and the other 10 are available as substitutes. The coach can make up to 4 substitutions during the game, under the same rules as the soccer game—no reentry for substituted players and each substitu... | math | {
"style": "rule",
"ground_truth": "51"
} | {
"index": 800,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A basketball team has 16 players, including a set of triplets: Alice, Betty, and Cindy, as well as a set of twins: Donna and Elly. In how many ways can we choose 7 starters if the only restriction is that not all three triplets or both twins can be in the starting lineup togeth... | math | {
"style": "rule",
"ground_truth": "8778"
} | {
"index": 801,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A basketball team has 18 players, including two sets of twins: Ben & Jerry and Tom & Tim. In how many ways can we choose 5 starters if at least one member from each set of twins must be included in the starting lineup?"
}
] | math | {
"style": "rule",
"ground_truth": "1834"
} | {
"index": 802,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A basketball team has 20 players. The coach needs to choose a starting lineup consisting of one point guard and 7 other players (these players are interchangeable). How many different starting lineups can the coach choose?"
}
] | math | {
"style": "rule",
"ground_truth": "1007760"
} | {
"index": 803,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A batch of disaster relief supplies is loaded into 26 trucks. The trucks travel at a constant speed of \\( v \\) kilometers per hour directly to the disaster area. If the distance between the two locations is 400 kilometers and the distance between every two trucks must be at l... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 804,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A batch of fragile goods totaling $10$ items is transported to a certain place by two trucks, A and B. Truck A carries $2$ first-class items and $2$ second-class items, while truck B carries $4$ first-class items and $2$ second-class items. Upon arrival at the destination, it w... | math | {
"style": "rule",
"ground_truth": "\\frac{29}{48}"
} | {
"index": 805,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A batch of tablets from four different brands was delivered to a computer store. Among them, Lenovo, Samsung, and Huawei tablets made up less than a third of the total, with Samsung tablets being 6 more than Lenovo tablets. All remaining tablets are Apple iPads, and there are t... | math | {
"style": "rule",
"ground_truth": "94"
} | {
"index": 806,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A battery of three guns fired a volley, and two shells hit the target. Find the probability that the first gun hit the target, given that the probabilities of hitting the target by the first, second, and third guns are $p_{1}=0,4$, $p_{2}=0,3$, and $p_{3}=0,5$, respectively."
... | math | {
"style": "rule",
"ground_truth": "20/29"
} | {
"index": 807,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A beam of light is emitted from point $P(1,2,3)$, reflected by the $Oxy$ plane, and then absorbed at point $Q(4,4,4)$. The distance traveled by the light beam is ______."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{62}"
} | {
"index": 808,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A beam of light strikes $\\overline{BC}\\,$ at point $C\\,$ with angle of incidence $\\alpha=19.94^\\circ\\,$ and reflects with an equal angle of reflection as shown. The light beam continues its path, reflecting off line segments $\\overline{AB}\\,$ and $\\overline{BC}\\,$ acc... | math | {
"style": "rule",
"ground_truth": "71"
} | {
"index": 809,
"solution": "At each point of reflection, we pretend instead that the light continues to travel straight. [asy] pathpen = linewidth(0.7); size(250); real alpha = 28, beta = 36; pair B = MP(\"B\",(0,0),NW), C = MP(\"C\",D((1,0))), A = MP(\"A\",expi(alpha * pi/180),N); path r = C + .4 * expi(beta * pi... |
DeepScaleR | [
{
"role": "user",
"content": "A bear is in the center of the left down corner of a $100*100$ square .we call a cycle in this grid a bear cycle if it visits each square exactly ones and gets back to the place it started.Removing a row or column with compose the bear cycle into number of pathes.Find the min... | math | {
"style": "rule",
"ground_truth": "5000"
} | {
"index": 810,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A beaver walks from $(0,0)$ to $(4,4)$ in the plane, walking one unit in the positive $x$ direction or one unit in the positive $y$ direction at each step. Moreover, he never goes to a point $(x, y)$ with $y>x$. How many different paths can he walk?"
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 811,
"solution": "$C(4)=14$."
} |
DeepScaleR | [
{
"role": "user",
"content": "A bee starts flying from point $P_0$. She flies $1$ inch due east to point $P_1$. For $j \\ge 1$, once the bee reaches point $P_j$, she turns $30^{\\circ}$ counterclockwise and then flies $j+1$ inches straight to point $P_{j+1}$. When the bee reaches $P_{2015},$ how far from $P... | math | {
"style": "rule",
"ground_truth": "1008 \\sqrt{6} + 1008 \\sqrt{2}"
} | {
"index": 812,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A belt is installed on two pulleys with radii of 14 inches and 4 inches respectively. The belt is taut and does not intersect itself. If the distance between the points where the belt touches the two pulleys is 24 inches, find the distance between the centers of the two pulleys... | math | {
"style": "rule",
"ground_truth": "26"
} | {
"index": 813,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A belt is installed on two pulleys with radii of 14 inches and 4 inches respectively. The belt is taut and does not intersect itself. If the distance between the points where the belt touches the two pulleys is 24 inches, what is the distance (in inches) between the centers of ... | math | {
"style": "rule",
"ground_truth": "26"
} | {
"index": 814,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A belt is placed without slack around two non-crossing circular pulleys which have radii of $15$ inches and $5$ inches respectively. The distance between the points where the belt contacts the pulleys is $30$ inches. Determine the distance between the centers of the two pulleys... | math | {
"style": "rule",
"ground_truth": "10\\sqrt{10}"
} | {
"index": 815,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A best-of-9 series is to be played between two teams; that is, the first team to win 5 games is the winner. The Mathletes have a chance of $2 / 3$ of winning any given game. What is the probability that exactly 7 games will need to be played to determine a winner?"
}
] | math | {
"style": "rule",
"ground_truth": "20/81"
} | {
"index": 816,
"solution": "If the Mathletes are to win, they must win exactly 5 out of the 7 games. One of the 5 games they win must be the 7 th game, because otherwise they would win the tournament before 7 games are completed. Thus, in the first 6 games, the Mathletes must win 4 games and lose 2. The probabilit... |
DeepScaleR | [
{
"role": "user",
"content": "A biased coin has a probability of $\\frac{3}{4}$ of landing heads and $\\frac{1}{4}$ of landing tails on each toss. The outcomes of the tosses are independent. The probability of winning Game C, where the player tosses the coin four times and wins if either all four outcomes a... | math | {
"style": "rule",
"ground_truth": "\\frac{61}{256}"
} | {
"index": 817,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A biased coin lands heads with a probability of $\\frac{2}{3}$ and tails with $\\frac{1}{3}$. A player can choose between Game C and Game D. In Game C, the player tosses the coin five times and wins if either the first three or the last three outcomes are all the same. In Game ... | math | {
"style": "rule",
"ground_truth": "\\frac{29}{81}"
} | {
"index": 818,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A biased coin with the probability of landing heads as 1/3 is flipped 12 times. What is the probability of getting exactly 9 heads in the 12 flips?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1760}{531441}"
} | {
"index": 819,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bicycle costs 389 yuan, and an electric fan costs 189 yuan. Dad wants to buy a bicycle and an electric fan. He will need approximately \\_\\_\\_\\_\\_\\_ yuan."
}
] | math | {
"style": "rule",
"ground_truth": "600"
} | {
"index": 820,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bicycle factory plans to produce a batch of bicycles of the same model, planning to produce $220$ bicycles per day. However, due to various reasons, the actual daily production will differ from the planned quantity. The table below shows the production situation of the worker... | math | {
"style": "rule",
"ground_truth": "155080"
} | {
"index": 821,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bicycle trip is 30 km long. Ari rides at an average speed of 20 km/h. Bri rides at an average speed of 15 km/h. If Ari and Bri begin at the same time, how many minutes after Ari finishes the trip will Bri finish?"
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 822,
"solution": "Riding at 15 km/h, Bri finishes the 30 km in $\\frac{30 \\text{ km}}{15 \\text{ km/h}} = 2 \\text{ h}$. Riding at 20 km/h, Ari finishes the 30 km in $\\frac{30 \\text{ km}}{20 \\text{ km/h}} = 1.5 \\text{ h}$. Therefore, Bri finishes 0.5 h after Ari, which is 30 minutes."
} |
DeepScaleR | [
{
"role": "user",
"content": "A big $L$ is formed as shown. What is its area?"
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"index": 823,
"solution": "1. **Identify the dimensions of the big rectangle**: The problem states that the shape is a big \"L\" formed within a rectangle. Assume the dimensions of the big rectangle are $8$ units by $5$ units based on the typical dimensions used in such problems.\n\n2. **Calculate the area of the... |
DeepScaleR | [
{
"role": "user",
"content": "A bin contains 10 black balls and 9 white balls. 4 balls are drawn at random. What is the probability of drawing 3 balls of one color and 1 ball of another color?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{160}{323}"
} | {
"index": 824,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bin has 5 green balls and $k$ purple balls in it, where $k$ is an unknown positive integer. A ball is drawn at random from the bin. If a green ball is drawn, the player wins 2 dollars, but if a purple ball is drawn, the player loses 2 dollars. If the expected amount won fo... | math | {
"style": "rule",
"ground_truth": "k=3"
} | {
"index": 825,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bin has 8 black balls and 7 white balls. 3 of the balls are drawn at random. What is the probability of drawing 2 of one color and 1 of the other color?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{4}{5}"
} | {
"index": 826,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A binary operation $\\diamondsuit$ has the properties that $a\\,\\diamondsuit\\, (b\\,\\diamondsuit \\,c) = (a\\,\\diamondsuit \\,b)\\cdot c$ and that $a\\,\\diamondsuit \\,a=1$ for all nonzero real numbers $a, b,$ and $c$. (Here $\\cdot$ represents multiplication). Find the so... | math | {
"style": "rule",
"ground_truth": "\\frac{25}{84}"
} | {
"index": 827,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A binary string of length $n$ is a sequence of $n$ digits, each of which is 0 or 1 . The distance between two binary strings of the same length is the number of positions in which they disagree; for example, the distance between the strings 01101011 and 00101110 is 3 since they... | math | {
"style": "rule",
"ground_truth": "\\begin{tabular}{ll} 00000000 & 00110101 \\ 11001010 & 10011110 \\ 11100001 & 01101011 \\ 11010100 & 01100110 \\ 10111001 & 10010011 \\ 01111100 & 11001101 \\ 00111010 & 10101100 \\ 01010111 & 11110010 \\ 00001111 & 01011001 \\ 10100111 & 11111111 \\ \\end{tabular}"
} | {
"index": 828,
"solution": "The maximum possible number of such strings is 20 . An example of a set attaining this bound is \\begin{tabular}{ll} 00000000 & 00110101 \\\\ 11001010 & 10011110 \\\\ 11100001 & 01101011 \\\\ 11010100 & 01100110 \\\\ 10111001 & 10010011 \\\\ 01111100 & 11001101 \\\\ 00111010 & 10101100 ... |
DeepScaleR | [
{
"role": "user",
"content": "A biologist found a pond with frogs. When classifying them by their mass, he noticed the following:\n\n*The $50$ lightest frogs represented $30\\%$ of the total mass of all the frogs in the pond, while the $44$ heaviest frogs represented $27\\%$ of the total mass.*As fa... | math | {
"style": "rule",
"ground_truth": "165"
} | {
"index": 829,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A biologist sequentially placed 150 beetles into ten jars. Each subsequent jar contains more beetles than the previous one. The number of beetles in the first jar is at least half the number of beetles in the tenth jar. How many beetles are in the sixth jar?"
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 830,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A biologist sequentially placed 150 beetles into ten jars. In each subsequent jar, he placed more beetles than in the previous one. The number of beetles in the first jar is at least half of the number of beetles in the tenth jar. How many beetles are in the sixth jar?"
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 831,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A biologist sequentially placed 150 beetles into ten jars. In each subsequent jar, he placed more beetles than in the previous one. The number of beetles in the first jar is no less than half the number of beetles in the tenth jar. How many beetles are in the sixth jar?"
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 832,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A biologist wants to calculate the number of fish in a lake. On May 1 she catches a random sample of 60 fish, tags them, and releases them. On September 1 she catches a random sample of 70 fish and finds that 3 of them are tagged. To calculate the number of fish in the lake on ... | math | {
"style": "rule",
"ground_truth": "840"
} | {
"index": 833,
"solution": "First, we notice that there are 45 tags left, after 25% of the original fish have went away/died. Then, some $x$ percent of fish have been added such that $\\frac{x}{x+75} = 40 \\%$, or $\\frac{2}{5}$. Solving for $x$, we get that $x = 50$, so the total number of fish in September is $1... |
DeepScaleR | [
{
"role": "user",
"content": "A biologist wishes to estimate the fish population in a protected area. Initially, on March 1st, she captures and tags 80 fish, then releases them back into the water. Four months later, on July 1st, she captures another 90 fish for a follow-up study, finding that 4 of these ar... | math | {
"style": "rule",
"ground_truth": "900"
} | {
"index": 834,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bird discovered $543_{8}$ different ways to build a nest in each of its eight tree homes. How many ways are there in base 10?"
}
] | math | {
"style": "rule",
"ground_truth": "355"
} | {
"index": 835,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bivalent metal element is used in a chemical reaction. When 3.5g of the metal is added into 50g of a dilute hydrochloric acid solution with a mass percentage of 18.25%, there is some metal leftover after the reaction finishes. When 2.5g of the metal is added into the same mas... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 836,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A black and white chocolate bar consists of individual pieces arranged in $n$ horizontal rows and $m$ vertical columns, painted in a checkerboard pattern. Ian ate all the black pieces, and Max ate all the white pieces. What is the sum of $m + n$ if it is known that Ian ate $8 \... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 837,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A blackboard contains 68 pairs of nonzero integers. Suppose that for each positive integer $k$ at most one of the pairs $(k, k)$ and $(-k, -k)$ is written on the blackboard. A student erases some of the 136 integers, subject to the condition that no two erased integers may ad... | math | {
"style": "rule",
"ground_truth": "\\[\n43\n\\]"
} | {
"index": 838,
"solution": "Answer: 43\n \nAttainability: Consider 8 distinct positive numbers. Let there be 5 pairs for each of the numbers including 2 clones of that number. Let there also be 28 pairs that include the negatives of those numbers such that each negative associates with another negative once and ex... |
DeepScaleR | [
{
"role": "user",
"content": "A blind box refers to a toy box where consumers cannot know the specific product style in advance. A certain brand has launched two blind box sets. Set $A$ contains $4$ different items, including a small rabbit toy. Set $B$ contains $2$ different items, with a $50\\%$ chance of... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"index": 839,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A block of cheese in the shape of a rectangular solid measures $10$ cm by $13$ cm by $14$ cm. Ten slices are cut from the cheese. Each slice has a width of $1$ cm and is cut parallel to one face of the cheese. The individual slices are not necessarily parallel to each other. Wh... | math | {
"style": "rule",
"ground_truth": "729"
} | {
"index": 840,
"solution": "Let the lengths of the three sides of the rectangular solid after the cutting be $a,b,c$, so that the desired volume is $abc$. Note that each cut reduces one of the dimensions by one, so that after ten cuts, $a+b+c = 10 + 13 + 14 - 10 = 27$. By AM-GM, $\\frac{a+b+c}{3} = 9 \\ge \\sqrt[3... |
DeepScaleR | [
{
"role": "user",
"content": "A block of iron solidifies from molten iron, and its volume reduces by $\\frac{1}{34}$. Then, if this block of iron melts back into molten iron (with no loss in volume), by how much does its volume increase?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{33}"
} | {
"index": 841,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A block of wood has the shape of a right circular cylinder with a radius of $8$ and a height of $10$. The entire surface of the block is painted red. Points $P$ and $Q$ are chosen on the edge of one of the circular faces such that the arc $\\overarc{PQ}$ measures $180^\\text{o}... | math | {
"style": "rule",
"ground_truth": "193"
} | {
"index": 842,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A block of wood has the shape of a right circular cylinder with radius $6$ and height $8$, and its entire surface has been painted blue. Points $A$ and $B$ are chosen on the edge of one of the circular faces of the cylinder so that $\\overarc{AB}$ on that face measures $120^\\t... | math | {
"style": "rule",
"ground_truth": "53"
} | {
"index": 843,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A block of wood has the shape of a right circular cylinder with radius $6$ and height $8$, and its entire surface has been painted blue. Points $A$ and $B$ are chosen on the edge of one of the circular faces of the cylinder so that $\\overarc{AB}$ on that face measures $120^\\t... | math | {
"style": "rule",
"ground_truth": "53"
} | {
"index": 844,
"solution": "Label the points where the plane intersects the top face of the cylinder as $C$ and $D$, and the center of the cylinder as $O$, such that $C,O,$ and $A$ are collinear. Let $T$ be the center of the bottom face, and $M$ the midpoint of $\\overline{AB}$. Then $OT=4$, $TM=3$ (because of the... |
DeepScaleR | [
{
"role": "user",
"content": "A block wall 100 feet long and 7 feet high will be constructed using blocks that are 1 foot high and either 2 feet long or 1 foot long (no blocks may be cut). The vertical joins in the blocks must be staggered as shown, and the wall must be even on the ends. What is the smalles... | math | {
"style": "rule",
"ground_truth": "353"
} | {
"index": 845,
"solution": "1. **Determine the number of rows**: Since each block is 1 foot high and the wall is 7 feet high, there will be 7 rows of blocks.\n\n2. **Analyze the pattern of the blocks**: The problem specifies that the vertical joins in the blocks must be staggered. This means that the arrangement o... |
DeepScaleR | [
{
"role": "user",
"content": "A board game spinner is divided into four regions labeled $A$, $B$, $C$, and $D$. The probability of the arrow stopping on region $A$ is $\\frac{3}{8}$, the probability of it stopping in $B$ is $\\frac{1}{4}$, and the probability of it stopping in region $C$ is equal to the pr... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{16}"
} | {
"index": 846,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A board game spinner is divided into three parts labeled $A$, $B$ and $C$. The probability of the spinner landing on $A$ is $\\frac{1}{3}$ and the probability of the spinner landing on $B$ is $\\frac{5}{12}$. What is the probability of the spinner landing on $C$? Express your... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"index": 847,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A board game spinner is divided into three regions labeled $A$, $B$ and $C$. The probability of the arrow stopping on region $A$ is $\\frac{1}{2}$ and on region $B$ is $\\frac{1}{5}$. What is the probability of the arrow stopping on region $C$? Express your answer as a commo... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{10}"
} | {
"index": 848,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A board game spinner is divided into three regions labeled $A$, $B$ and $C$. The probability of the arrow stopping on region $A$ is $\\frac{1}{3}$ and on region $B$ is $\\frac{1}{2}$. What is the probability of the arrow stopping on region $C$? Express your answer as a commo... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"index": 849,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A board of size \\(2022 \\times 2022\\) is given. Lisa and Varya take turns painting \\(2 \\times 2\\) squares on the board with red and blue colors. They agreed that each cell can be painted no more than once in blue and no more than once in red. Cells that are painted blue an... | math | {
"style": "rule",
"ground_truth": "2021 \\cdot 2020"
} | {
"index": 850,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A boat has a speed of $15$ mph in still water. In a stream that has a current of $5$ mph it travels a certain distance downstream and returns. The ratio of the average speed for the round trip to the speed in still water is:"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{8}{9}"
} | {
"index": 851,
"solution": "1. **Identify speeds and distances:**\n - Speed of the boat in still water: $15$ mph.\n - Speed of the current: $5$ mph.\n - Downstream speed (boat speed + current speed): $15 + 5 = 20$ mph.\n - Upstream speed (boat speed - current speed): $15 - 5 = 10$ mph.\n\n2. **Assume a dis... |
DeepScaleR | [
{
"role": "user",
"content": "A book has 136 pages. Each page has the same number of words, and each page has no more than 100 words on it. The number of words in the book is congruent to 184, modulo 203. How many words are on each page?"
}
] | math | {
"style": "rule",
"ground_truth": "73"
} | {
"index": 852,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A book has a total of 100 pages, numbered sequentially from 1, 2, 3, 4…100. The digit “2” appears in the page numbers a total of \\_\\_\\_\\_\\_\\_ times."
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 853,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A book is published in three volumes, the pages being numbered from $1$ onwards. The page numbers are continued from the first volume to the second volume to the third. The number of pages in the second volume is $50$ more than that in the first volume, and the number pages... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"index": 854,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A book of one hundred pages has its pages numbered from 1 to 100. How many pages in this book have the digit 5 in their numbering? (Note: one sheet has two pages.)"
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 855,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A book of one hundred pages has its pages numbered from 1 to 100. How many pages in this book have the digit 5 in their numbering? (Note: one sheet has two pages.)\n(a) 13\n(b) 14\n(c) 15\n(d) 16\n(e) 17"
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 856,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A book that is to be recorded onto compact discs takes $412$ minutes to read aloud. Each disc can hold up to $56$ minutes of reading. Assume that the smallest possible number of discs is used and that each disc contains the same length of reading. How many minutes of reading wi... | math | {
"style": "rule",
"ground_truth": "51.5"
} | {
"index": 857,
"solution": "1. **Calculate the number of discs needed if each disc is fully utilized:** \n Given that each disc can hold up to $56$ minutes and the total reading time is $412$ minutes, the number of discs required if each disc is fully utilized is calculated by dividing the total minutes by the ... |
DeepScaleR | [
{
"role": "user",
"content": "A book with 53 pages numbered 1 to 53 has its pages renumbered in reverse, from 53 to 1. For how many pages do the new page number and old page number share the same units digit?"
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 858,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bookstore has a sale on days of the month that are multiples of 5 (such as June 5, June 10...). A shoe store has a sale every 6 days. The shoe store has a sale on July 3. How many times in July do the two stores have sales on the same date?"
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 859,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bookstore is deciding what price it should charge for a certain book. After research, the store finds that if the book's price is $p$ dollars (where $p \\le 26$), then the number of books sold per month is $130-5p$. What price should the store charge to maximize its revenue?"... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 860,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bored student walks down a hall that contains a row of closed lockers, numbered $1$ to $1024$. He opens the locker numbered 1, and then alternates between skipping and opening each locker thereafter. When he reaches the end of the hall, the student turns around and starts bac... | math | {
"style": "rule",
"ground_truth": "342"
} | {
"index": 861,
"solution": "List all the numbers from $1$ through $1024$, then do the process yourself!!! It will take about 25 minutes (if you don't start to see the pattern), but that's okay, eventually, you will get $\\boxed{342}$.\n (Note: If you try to do this, first look through all the problems! -Guy)"
} |
DeepScaleR | [
{
"role": "user",
"content": "A boss and two engineers are to meet at a park. Each of them arrives at a random time between 1:00 PM and 3:00 PM. The boss leaves instantly if not both engineers are present upon his arrival. Each engineer will wait for up to 1.5 hours for the other before leaving. What is the... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"index": 862,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A boss plans a business meeting at Starbucks with the two engineers below him. However, he fails to set a time, and all three arrive at Starbucks at a random time between 2:00 and 4:00 p.m. When the boss shows up, if both engineers are not already there, he storms out and cance... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{24}"
} | {
"index": 863,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A boss schedules a meeting at a cafe with two of his staff, planning to arrive randomly between 1:00 PM and 4:00 PM. Each staff member also arrives randomly within the same timeframe. If the boss arrives and any staff member isn't there, he leaves immediately. Each staff member... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"index": 864,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bot is held in orbit by the gravitational force of attraction to the planet, which creates a centripetal acceleration equal to $4 \\pi^{2}(2 R) / T^{2}$, where $R$ is the radius of the planet and $T$ is the period of revolution of the bot. From Newton's second law, we have:\n... | math | {
"style": "rule",
"ground_truth": "6000"
} | {
"index": 865,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bottle of cola costs 2 yuan, and two empty bottles can be exchanged for one more bottle of cola. With 30 yuan, what is the maximum number of bottles of cola that you can drink?"
}
] | math | {
"style": "rule",
"ground_truth": "29"
} | {
"index": 866,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bottled water company has designed a new cup for its dispenser. The cup will be a right circular cone with a three-inch radius. How tall will the cup need to be to hold 93 cubic inches of water? Express your answer to the nearest whole number."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 867,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A boulevard has 25 houses on each side, for a total of 50 houses. The addresses on the east side of the boulevard follow an arithmetic sequence, as do the addresses on the west side. On the east side, the addresses start at 5 and increase by 7 (i.e., 5, 12, 19, etc.), while on ... | math | {
"style": "rule",
"ground_truth": "113"
} | {
"index": 868,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bouncy ball is dropped from a height of 100 meters. After each bounce, it reaches a height that is half of the previous one. What is the total distance the ball has traveled when it hits the ground for the 10th time? (Round the answer to the nearest whole number)"
}
] | math | {
"style": "rule",
"ground_truth": "300"
} | {
"index": 869,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bowl contained 320 grams of pure white sugar. Mixture \\( Y \\) was formed by taking \\( x \\) grams of the white sugar out of the bowl, adding \\( x \\) grams of brown sugar to the bowl, and then mixing uniformly. In Mixture \\( Y \\), the ratio of the mass of the white suga... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"index": 870,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bowl contains 10 jellybeans (four red, one blue and five white). If you pick three jellybeans from the bowl at random and without replacement, what is the probability that exactly two will be red? Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{10}"
} | {
"index": 871,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bowling ball cannot weigh more than 16 pounds and must have a diameter of $8 \\frac{1}{2}$ inches. How many square inches are in the surface area of a bowling ball before the finger holes are drilled? Express your answer as a common fraction in terms of $\\pi$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{289\\pi}{4}"
} | {
"index": 872,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bowling ball is a solid ball with a spherical surface and diameter 30 cm. To custom fit a bowling ball for each bowler, three holes are drilled in the ball. Bowler Kris has holes drilled that are 8 cm deep and have diameters of 2 cm, 2 cm, and 3 cm. Assuming the three holes a... | math | {
"style": "rule",
"ground_truth": "4466\\pi"
} | {
"index": 873,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A bowling ball must have a diameter of 9 inches. Calculate both the surface area and the volume of the bowling ball before the finger holes are drilled. Express your answers as common fractions in terms of \\(\\pi\\)."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{729\\pi}{6}"
} | {
"index": 874,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box $2$ centimeters high, $3$ centimeters wide, and $5$ centimeters long can hold $40$ grams of clay. A second box with twice the height, three times the width, and the same length as the first box can hold $n$ grams of clay. What is $n$?"
}
] | math | {
"style": "rule",
"ground_truth": "200"
} | {
"index": 875,
"solution": "1. **Calculate the volume of the first box**: \n The volume $V$ of a rectangular prism is calculated by the formula:\n \\[\n V = \\text{height} \\times \\text{width} \\times \\text{length}\n \\]\n For the first box, the dimensions are given as height = $2$ cm, width = $3$ cm,... |
DeepScaleR | [
{
"role": "user",
"content": "A box contains $11$ balls, numbered $1, 2, 3, \\dots 11$. If $6$ balls are drawn simultaneously at random, what is the probability that the sum of the numbers on the balls drawn is odd?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{118}{231}"
} | {
"index": 876,
"solution": "To solve this problem, we need to calculate the probability that the sum of the numbers on the six balls drawn is odd. We start by noting that there are 6 odd-numbered balls (1, 3, 5, 7, 9, 11) and 5 even-numbered balls (2, 4, 6, 8, 10) in the box.\n\nThe sum of the numbers on the balls... |
DeepScaleR | [
{
"role": "user",
"content": "A box contains $12$ ping-pong balls, of which $9$ are new and $3$ are old. Three balls are randomly drawn from the box for use, and then returned to the box. Let $X$ denote the number of old balls in the box after this process. What is the value of $P(X = 4)$?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{27}{220}"
} | {
"index": 877,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains $2$ pennies, $4$ nickels, and $6$ dimes. Six coins are drawn without replacement, with each coin having an equal probability of being chosen. What is the probability that the value of coins drawn is at least $50$ cents?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{127}{924}"
} | {
"index": 878,
"solution": "To solve this problem, we need to calculate the probability that the value of the coins drawn is at least 50 cents. We will first determine the total number of ways to draw 6 coins from the 12 available, and then find the number of successful outcomes where the total value is at least 5... |
DeepScaleR | [
{
"role": "user",
"content": "A box contains $28$ red balls, $20$ green balls, $19$ yellow balls, $13$ blue balls, $11$ white balls, and $9$ black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least $15$ balls of a single color will be dr... | math | {
"style": "rule",
"ground_truth": "76"
} | {
"index": 879,
"solution": "To solve this problem, we need to determine the minimum number of balls that must be drawn to ensure that at least 15 balls of one color are drawn. We will consider the worst-case scenario where we draw the maximum number of balls possible without reaching 15 balls of any single color.\... |
DeepScaleR | [
{
"role": "user",
"content": "A box contains $3$ cards labeled with $1$, $2$, and $3$ respectively. A card is randomly drawn from the box, its number recorded, and then returned to the box. This process is repeated. The probability that at least one of the numbers drawn is even is _______."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{9}"
} | {
"index": 880,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains $3$ pennies, $5$ nickels, $7$ dimes, and $4$ quarters. Eight coins are drawn without replacement, with each coin having an equal probability of being chosen. What is the probability that the value of coins drawn is at least $1.00$ (100 cents)?\nA) $\\frac{325}{75... | math | {
"style": "rule",
"ground_truth": "\\frac{2345}{75582}"
} | {
"index": 881,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains $3$ shiny pennies and $4$ dull pennies. One by one, pennies are drawn at random from the box and not replaced. If the probability is $a/b$ that it will take more than four draws until the third shiny penny appears and $a/b$ is in lowest terms, then $a+b=$"
}
] | math | {
"style": "rule",
"ground_truth": "66"
} | {
"index": 882,
"solution": "1. **Identify the Total Number of Combinations**:\n The box contains 3 shiny pennies (denoted as 1) and 4 dull pennies (denoted as 0). The total number of ways to arrange these pennies is given by the binomial coefficient $\\binom{7}{3}$, which counts the number of ways to choose 3 po... |
DeepScaleR | [
{
"role": "user",
"content": "A box contains $5$ chips, numbered $1$, $2$, $3$, $4$, and $5$. Chips are drawn randomly one at a time without replacement until the sum of the values drawn exceeds $4$. What is the probability that $3$ draws are required?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{5}"
} | {
"index": 883,
"solution": "To solve this problem, we need to determine the probability that exactly three draws are required for the sum of the values drawn to exceed $4$. This means that the sum of the values of the first two chips drawn must be $4$ or less, and the sum of the values of the first three chips dra... |
DeepScaleR | [
{
"role": "user",
"content": "A box contains $6$ balls, of which $3$ are yellow, $2$ are blue, and $1$ is red. Three balls are drawn from the box.\n\n$(1)$ If the $3$ yellow balls are numbered as $A$, $B$, $C$, the $2$ blue balls are numbered as $d$, $e$, and the $1$ red ball is numbered as $x$, use $(a,b,c... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{5}"
} | {
"index": 884,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains 2 red marbles, 2 green marbles, and 2 yellow marbles. Carol takes 2 marbles from the box at random; then Claudia takes 2 of the remaining marbles at random; and then Cheryl takes the last 2 marbles. What is the probability that Cheryl gets 2 marbles of the same c... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{5}"
} | {
"index": 885,
"solution": "To solve this problem, we need to calculate the probability that Cheryl gets 2 marbles of the same color. We can use the principle of symmetry and consider the probability of any specific outcome for Cheryl, as the draws are random and independent of the order in which the participants ... |
DeepScaleR | [
{
"role": "user",
"content": "A box contains 4 cards, each with one of the following functions defined on \\\\(R\\\\): \\\\(f_{1}(x)={x}^{3}\\\\), \\\\(f_{2}(x)=|x|\\\\), \\\\(f_{3}(x)=\\sin x\\\\), \\\\(f_{4}(x)=\\cos x\\\\). Now, if we randomly pick 2 cards from the box and multiply the functions on the c... | math | {
"style": "rule",
"ground_truth": "\\dfrac{2}{3}"
} | {
"index": 886,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains 4 labels marked with the numbers $1$, $2$, $3$, and $4$. Two labels are randomly selected according to the following conditions. Find the probability that the numbers on the two labels are consecutive integers:\n1. The selection is made without replacement;\n2. T... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{16}"
} | {
"index": 887,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains 4 white balls and 4 black balls. I draw them out of the box, one at a time. What is the probability that all of my draws alternate colors?"
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{1}{35}"
} | {
"index": 888,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains 5 balls of the same size, including 3 white balls and 2 red balls. Two balls are drawn from the box. \n$(1)$ Find the probability of drawing 1 white ball and 1 red ball. \n$(2)$ Let $X$ represent the number of white balls drawn out of the 2 balls. Find the dist... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"index": 889,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains 5 black ties, 7 gold ties, and 8 pink ties. What is the probability that Stephen randomly chooses a pink tie?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{5}"
} | {
"index": 890,
"solution": "There are \\(5+7+8=20\\) ties in the box, 8 of which are pink. When Stephen removes a tie at random, the probability of choosing a pink tie is \\(\\frac{8}{20}\\) which is equivalent to \\(\\frac{2}{5}\\)."
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains 5 white balls and 3 black balls. What is the probability that when drawing the balls one at a time, all draws alternate in color starting with a white ball?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{56}"
} | {
"index": 891,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains 5 white balls and 5 black balls. I draw them out of the box, one at a time. What is the probability that all of my draws alternate colors, starting and ending with the same color?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{126}"
} | {
"index": 892,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains 5 white balls and 6 black balls. A ball is drawn out of the box at random. What is the probability that the ball is white?"
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{5}{11}"
} | {
"index": 893,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains 5 white balls and 6 black balls. Five balls are drawn out of the box at random. What is the probability that they all are white?"
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{1}{462}"
} | {
"index": 894,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains 5 white balls and 6 black balls. Two balls are drawn out of the box at random. What is the probability that they both are white?"
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{2}{11}"
} | {
"index": 895,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains 5 white balls and 6 black balls. I draw them out of the box, one at a time. What is the probability that all of my draws alternate in color starting with a black ball?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{462}"
} | {
"index": 896,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains 5 white balls and 6 black balls. You draw them out of the box, one at a time. What is the probability that the first four draws alternate in colors, starting with a black ball?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{33}"
} | {
"index": 897,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains 6 cards numbered 1, 2, ..., 6. A card is randomly drawn from the box, and its number is denoted as $a$. The box is then adjusted to retain only the cards with numbers greater than $a$. A second draw is made, and the probability that the first draw is an odd numbe... | math | {
"style": "rule",
"ground_truth": "\\frac{17}{45}"
} | {
"index": 898,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A box contains a collection of triangular and square tiles. There are $25$ tiles in the box, containing $84$ edges total. How many square tiles are there in the box?"
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"index": 899,
"solution": "1. **Define Variables:**\n Let $a$ be the number of triangular tiles and $b$ be the number of square tiles in the box.\n\n2. **Set Up Equations:**\n - Each triangle has 3 edges, and each square has 4 edges.\n - The total number of tiles is given by the equation:\n \\[\n a ... |
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