data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "To a natural number \\( N \\), the largest divisor of \\( N \\) that is less than \\( N \\) was added, resulting in a power of ten. Find all such \\( N \\)."
}
] | math | {
"style": "rule",
"ground_truth": "75"
} | {
"index": 35800,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To actively create a \"demonstration school for the prevention and control of myopia in children and adolescents in the city\" and cultivate students' good eye habits, a certain school conducted a competition on correct eye knowledge this semester. $20$ student answer sheets we... | math | {
"style": "rule",
"ground_truth": "1755"
} | {
"index": 35801,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To address the threat of AIDS to humanity, now three research institutes, designated as Institute A, Institute B, and Institute C, are independently developing an AIDS vaccine. The probabilities of successfully developing a vaccine are respectively $\\frac{1}{2}$, $\\frac{1}{3}... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 35802,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To arrange 5 volunteers and 2 elderly people in a row, where the 2 elderly people are adjacent but not at the ends, calculate the total number of different arrangements."
}
] | math | {
"style": "rule",
"ground_truth": "960"
} | {
"index": 35803,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To arrange a class schedule for one day with the subjects Chinese, Mathematics, Politics, English, Physical Education, and Art, where Mathematics must be in the morning and Physical Education in the afternoon, determine the total number of different arrangements."
}
] | math | {
"style": "rule",
"ground_truth": "192"
} | {
"index": 35804,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To assess the shooting level of a university shooting club, an analysis group used stratified sampling to select the shooting scores of $6$ senior members and $2$ new members for analysis. After calculation, the sample mean of the shooting scores of the $6$ senior members is $8... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{2}"
} | {
"index": 35805,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To bake $12$ cookies, I use $2$ quarts of milk. There are $2$ pints in a quart. How many pints of milk do I need to bake $3$ cookies?"
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 35806,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To be able to walk to the center $C$ of a circular fountain, a repair crew places a 16-foot plank from $A$ to $B$ and then a 10-foot plank from $D$ to $C$, where $D$ is the midpoint of $\\overline{AB}$ . What is the area of the circular base of the fountain? Express your answer... | math | {
"style": "rule",
"ground_truth": "164 \\pi \\mbox{ square feet}"
} | {
"index": 35807,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To be continuous at $x = -1$, the value of $\\frac{x^3 + 1}{x^2 - 1}$ is taken to be:"
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{3}{2}"
} | {
"index": 35808,
"solution": "1. **Identify the point of discontinuity**: We start by noting that the function $\\frac{x^3 + 1}{x^2 - 1}$ is undefined at $x = -1$ and $x = 1$ because the denominator becomes zero at these points. To find the value that makes the function continuous at $x = -1$, we need to simplify ... |
DeepScaleR | [
{
"role": "user",
"content": "To be eligible for an algebra class a student must have an average of at least $83\\%$ over all four quarters in his or her pre-algebra class. If Fisher had an $82\\%$, $77\\%$, and $75\\%$ in the first three quarters, what is the minimum score he must earn in the 4th quarter t... | math | {
"style": "rule",
"ground_truth": "98\\%"
} | {
"index": 35809,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To calculate $31^2$, Emily mentally figures the value $30^2$ and adds 61. Emily subtracts a number from $30^2$ to calculate $29^2$. What number does she subtract?"
}
] | math | {
"style": "rule",
"ground_truth": "59"
} | {
"index": 35810,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To calculate $41^2$, David mentally figures the value $40^2$ and adds 81. David subtracts a number from $40^2$ to calculate $39^2$. What number does he subtract?"
}
] | math | {
"style": "rule",
"ground_truth": "79"
} | {
"index": 35811,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To calculate $41^2$, Tom mentally computes $40^2$ and adds a number. To find $39^2$, Tom subtracts a number from $40^2$. What number does he add to calculate $41^2$ and subtract to calculate $39^2$?"
}
] | math | {
"style": "rule",
"ground_truth": "79"
} | {
"index": 35812,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To celebrate 2019, Faraz gets four sandwiches shaped in the digits 2, 0, 1, and 9 at lunch. However, the four digits get reordered (but not flipped or rotated) on his plate and he notices that they form a 4-digit multiple of 7. What is the greatest possible number that could ha... | math | {
"style": "rule",
"ground_truth": "1092"
} | {
"index": 35813,
"solution": "Note that 2 and 9 are equivalent $\\bmod 7$. So we will replace the 9 with a 2 for now. Since 7 is a divisor of 21, a four digit multiple of 7 consisting of $2,0,1$, and 2 cannot have a 2 followed by a 1 (otherwise we could subtract a multiple of 21 to obtain a number of the form $2 \... |
DeepScaleR | [
{
"role": "user",
"content": "To celebrate her birthday, Ana is going to prepare pear and apple pies. In the market, an apple weighs $300 \\text{ g}$ and a pear weighs $200 \\text{ g}$. Ana's bag can hold a maximum weight of $7 \\text{ kg}$. What is the maximum number of fruits she can buy to make pies with... | math | {
"style": "rule",
"ground_truth": "34"
} | {
"index": 35814,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To complete the grid below, each of the digits 1 through 4 must occur once\nin each row and once in each column. What number will occupy the lower\nright-hand square?\n\\[\\begin{tabular}{|c|c|c|c|}\\hline 1 & & 2 &\\ \\hline 2 & 3 & &\\ \\hline & &&4\\ \\hline & &&\\ \\hline\\... | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 35815,
"solution": "We are given a 4x4 grid where each digit from 1 through 4 must appear exactly once in each row and once in each column. The initial grid is:\n\n\\[\n\\begin{array}{|c|c|c|c|}\n\\hline\n1 & & 2 & \\\\\n\\hline\n2 & 3 & & \\\\\n\\hline\n & & & 4 \\\\\n\\hline\n & & & ... |
DeepScaleR | [
{
"role": "user",
"content": "To control her blood pressure, Jill's grandmother takes one half of a pill every other day. If one supply of medicine contains $60$ pills, then the supply of medicine would last approximately"
}
] | math | {
"style": "rule",
"ground_truth": "8\\text{ months}"
} | {
"index": 35816,
"solution": "1. **Determine the rate of consumption**: Jill's grandmother takes one half of a pill every other day. This means that in two days, she consumes one half of a pill.\n\n2. **Calculate the number of days per pill**: Since she takes half a pill every two days, she will take a full pill e... |
DeepScaleR | [
{
"role": "user",
"content": "To determine the minimum time required for the concentration of the drug in the air to drop below 0.25 milligrams per cubic meter, solve the equation y = 0.25 for t using the function y=\\begin{cases} 10t & (0 \\leqslant t \\leqslant 0.1), \\\\ {\\left( \\frac{1}{16} \\right)}^... | math | {
"style": "rule",
"ground_truth": "0.6"
} | {
"index": 35817,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To encourage residents to conserve water, a city charges residents for domestic water use in a tiered pricing system. The table below shows partial information on the tiered pricing for domestic water use for residents in the city, each with their own water meter:\n\n| Water Sa... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"index": 35818,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To enhance and beautify the city, all seven streetlights on a road are to be changed to colored lights. If there are three colors available for the colored lights - red, yellow, and blue - and the installation requires that no two adjacent streetlights are of the same color, wi... | math | {
"style": "rule",
"ground_truth": "114"
} | {
"index": 35819,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To enhance students' physical fitness, our school has set up sports interest classes for seventh graders. Among them, the basketball interest class has $x$ students, the number of students in the soccer interest class is $2$ less than twice the number of students in the basketb... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"index": 35820,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To ensure the safety of property during the Spring Festival holiday, an office needs to arrange for one person to be on duty each day for seven days. Given that there are 4 people in the office, and each person needs to work for either one or two days, the number of different d... | math | {
"style": "rule",
"ground_truth": "2520"
} | {
"index": 35821,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To estimate the consumption of disposable wooden chopsticks, in 1999, a sample of 10 restaurants from a total of 600 high, medium, and low-grade restaurants in a certain county was taken. The daily consumption of disposable chopstick boxes in these restaurants was as follows: ... | math | {
"style": "rule",
"ground_truth": "7260"
} | {
"index": 35822,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To examine the effectiveness of a certain influenza vaccine, a laboratory randomly selected 100 healthy mice for an experiment and obtained the following contingency table:\n\n| | Infection | Not Infected |\n|----------|-----------|--------------|\n| Injected | 10 ... | math | {
"style": "rule",
"ground_truth": "0.05"
} | {
"index": 35823,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To express 20 as a sum of different powers of 2, we would write $20 = 2^4 + 2^2$. The sum of the exponents of these powers is $4 + 2 = 6$. If 400 were expressed as a sum of at least two distinct powers of 2, what would be the least possible sum of the exponents of these powers?... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"index": 35824,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To express 20 as a sum of distinct powers of 2, we would write $20 = 2^4 + 2^2$. The sum of the exponents of these powers is $4 + 2 = 6$. If 1562 were expressed as a sum of distinct powers of 2, what would be the least possible sum of the exponents of these powers?"
}
] | math | {
"style": "rule",
"ground_truth": "27"
} | {
"index": 35825,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To factorize the quadratic trinomial $x^{2}+4x-5$, we can first add $4$ to $x^{2}+4x$ to make it a perfect square trinomial. Then, subtract $4$ so that the value of the entire expression remains unchanged. Therefore, we have: $x^{2}+4x-5=x^{2}+4x+4-4-5=\\left(x+2\\right)^{2}-9=... | math | {
"style": "rule",
"ground_truth": "-24"
} | {
"index": 35826,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To implement the \"double reduction\" policy and promote intangible cultural heritage, a certain school plans to organize extracurricular interest classes for students to visit the following projects: $A$ (Xiu Shui pottery art), $B$ (Xiu Shui tea-picking opera), $C$ (Jiujiang m... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"index": 35827,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To investigate a non-luminous black planet in distant space, Xiao Feitian drives a high-speed spaceship equipped with a powerful light, traveling straight towards the black planet at a speed of 100,000 km/s. When Xiao Feitian had just been traveling for 100 seconds, the spacesh... | math | {
"style": "rule",
"ground_truth": "2000"
} | {
"index": 35828,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To investigate the growth inhibitory effect of a certain drug on mice, $40$ mice were divided into two groups, a control group (without the drug) and an experimental group (with the drug).<br/>$(1)$ Suppose the number of mice in the control group among two mice is $X$, find the... | math | {
"style": "rule",
"ground_truth": "95\\%"
} | {
"index": 35829,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To investigate the height of high school students, a stratified sampling method is used to draw a sample of 100 students from three grades. 24 students are sampled from grade 10, 26 from grade 11. If there are 600 students in grade 12, then the total number of students in the s... | math | {
"style": "rule",
"ground_truth": "1200"
} | {
"index": 35830,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To make a rectangular frame with lengths of 3cm, 4cm, and 5cm, the total length of wire needed is cm. If paper is then glued around the outside (seams not considered), the total area of paper needed is cm<sup>2</sup>."
}
] | math | {
"style": "rule",
"ground_truth": "94"
} | {
"index": 35831,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To make lemonade, I use a ratio of $7$ parts water to $1$ part lemon juice. If I want to make a gallon of lemonade, and there are four quarts in a gallon, how many quarts of water do I need? Write your answer as a proper or improper fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7}{2}"
} | {
"index": 35832,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To make pizza dough, Luca mixes 50 mL of milk for every 250 mL of flour. How many mL of milk does he mix with 750 mL of flour?"
}
] | math | {
"style": "rule",
"ground_truth": "150"
} | {
"index": 35833,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To measure the height of tower AB on the opposite bank of a river, a point C is chosen on the bank such that the base of the tower A is exactly to the west of point C. At this point, the elevation angle to the top of the tower B is measured to be 45°. Then, moving from point C ... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 35834,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To meet market demand, a clothing supermarket purchased a short-sleeved $T$-shirt at the beginning of June. The cost price of each shirt is $80$ yuan, and the supermarket stipulates that the selling price of each shirt must not be less than $90$ yuan. According to a survey, whe... | math | {
"style": "rule",
"ground_truth": "12000"
} | {
"index": 35835,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To meet market demand, a supermarket purchased a brand of zongzi before the arrival of the Dragon Boat Festival on May 5th. The cost of each box is $40. The supermarket stipulates that the selling price of each box must not be less than $45. Based on past sales experience, it w... | math | {
"style": "rule",
"ground_truth": "440"
} | {
"index": 35836,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To meet the shopping needs of customers during the \"May Day\" period, a fruit supermarket purchased cherries and cantaloupes from the fruit production base for $9160$ yuan, totaling $560$ kilograms. The purchase price of cherries is $35$ yuan per kilogram, and the purchase pri... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"index": 35837,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To monitor the skier's movements, the coach divided the track into three sections of equal length. It was found that the skier's average speeds on these three separate sections were different. The time required for the skier to cover the first and second sections together was 4... | math | {
"style": "rule",
"ground_truth": "58.5"
} | {
"index": 35838,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To obtain the graph of the function $$y=2\\sin(x+ \\frac {\\pi}{6})\\cos(x+ \\frac {\\pi}{6})$$, determine the horizontal shift required to transform the graph of the function $y=\\sin 2x$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac {\\pi}{6}"
} | {
"index": 35839,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To obtain the graph of the function $y=2\\cos \\left(2x-\\frac{\\pi }{6}\\right)$, all points on the graph of the function $y=2\\sin 2x$ need to be translated $\\frac{\\pi }{6}$ units to the left."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi }{6}"
} | {
"index": 35840,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To obtain the graph of the function $y=\\cos \\left( \\frac{1}{2}x+ \\frac{\\pi}{6}\\right)$, determine the necessary horizontal shift of the graph of the function $y=\\cos \\frac{1}{2}x$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{6}"
} | {
"index": 35841,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To obtain the graph of the function $y=\\sin\\left(2x+\\frac{\\pi}{3}\\right)$, find the transformation required to obtain the graph of the function $y=\\cos\\left(2x-\\frac{\\pi}{3}\\right)$."
}
] | math | {
"style": "rule",
"ground_truth": "\\left(\\frac{\\pi}{12}\\right)"
} | {
"index": 35842,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To open the safe, you need to enter a code — a number consisting of seven digits: twos and threes. The safe will open if there are more twos than threes, and the code is divisible by both 3 and 4. Create a code that opens the safe."
}
] | math | {
"style": "rule",
"ground_truth": "2222232"
} | {
"index": 35843,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To popularize knowledge of fire safety, a certain school organized a competition on related knowledge. The competition is divided into two rounds, and each participant must participate in both rounds. If a participant wins in both rounds, they are considered to have won the com... | math | {
"style": "rule",
"ground_truth": "\\frac{223}{300}"
} | {
"index": 35844,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To prepare a certain dye, it is necessary to add three types of organic dyes, two types of inorganic dyes, and two types of additives. The addition order of the organic dyes cannot be adjacent. Now, to study the impact of all different addition orders on the dyeing effect, the ... | math | {
"style": "rule",
"ground_truth": "1440"
} | {
"index": 35845,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To prepare for her half-marathon, Mary ran a total of $2847_9$ miles. How many miles (in base ten) did Mary run?"
}
] | math | {
"style": "rule",
"ground_truth": "2149"
} | {
"index": 35846,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To prevent the spread of the novel coronavirus, individuals need to maintain a safe distance of at least one meter between each other. In a certain meeting room with four rows and four columns of seats, the distance between adjacent seats is more than one meter. During the epid... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 35847,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To promote her school's annual Kite Olympics, Genevieve makes a small kite and a large kite for a bulletin board display. For her small kite, Genevieve draws the kite on a grid with the points one inch apart, as shown below.\n\n[asy]\nfor ( int x = 0; x <= 6; ++x )\n{\n\nfor ( ... | math | {
"style": "rule",
"ground_truth": "21"
} | {
"index": 35848,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To protect the ecological environment, a mountainous area in our city has started to implement the policy of returning farmland to forest since 2005. It is known that at the end of 2004, the forest coverage area of this mountainous area was $a$ acres. \n(1) Assuming the annual... | math | {
"style": "rule",
"ground_truth": "7.2\\%"
} | {
"index": 35849,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To qualify for the competition, wrestler Vladimir must have three matches and win at least two of them consecutively. His opponents are Andrei (A) and Boris (B). Vladimir can choose to schedule the matches in the order ABA or BAB. The probability of Vladimir losing one match to... | math | {
"style": "rule",
"ground_truth": "0.742"
} | {
"index": 35850,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To reach the Solovyov family's dacha from the station, one must first travel 3 km on the highway and then 2 km on a path. Upon arriving at the station, the mother called her son Vasya at the dacha and asked him to meet her on his bicycle. They started moving towards each other ... | math | {
"style": "rule",
"ground_truth": "800"
} | {
"index": 35851,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To rebuild homes after an earthquake for disaster relief, in order to repair a road damaged during the earthquake, if Team A alone takes 3 months to complete the work, costing $12,000 per month; if Team B alone takes 6 months to complete the work, costing $5,000 per month. How ... | math | {
"style": "rule",
"ground_truth": "34,000"
} | {
"index": 35852,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To set up for a Fourth of July party, David is making a string of red, white, and blue balloons. He places them according to the following rules: - No red balloon is adjacent to another red balloon. - White balloons appear in groups of exactly two, and groups of white balloons ... | math | {
"style": "rule",
"ground_truth": "99"
} | {
"index": 35853,
"solution": "It is possible to achieve 99 red balloons with the arrangement $$\\text { WWBBBWW } \\underbrace{\\text { RBBBWWRBBBWW ...RBBBWW, }}_{99 \\text { RBBBWW's }}$$ which contains $99 \\cdot 6+7=601$ balloons. Now assume that one can construct a chain with 98 or fewer red balloons. Then th... |
DeepScaleR | [
{
"role": "user",
"content": "To shift the graph of the function $y=\\sin \\left(2x- \\frac{\\pi}{4}\\right)$ to the graph of the function $y = \\sin(2x)$, determine the horizontal shift required."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{8}"
} | {
"index": 35854,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To solve the problem, we need to find the value of $\\log_{4}{\\frac{1}{8}}$.\nA) $-\\frac{1}{2}$\nB) $-\\frac{3}{2}$\nC) $\\frac{1}{2}$\nD) $\\frac{3}{2}$"
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{3}{2}"
} | {
"index": 35855,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To stabilize housing prices, a local government decided to build a batch of affordable housing for the community. The plan is to purchase a piece of land for 16 million yuan and build a residential community with 10 buildings on it. Each building has the same number of floors, ... | math | {
"style": "rule",
"ground_truth": "1225"
} | {
"index": 35856,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To stabilize housing prices, a local government decided to build a batch of affordable housing for the community. The plan is to purchase a piece of land for 16 million yuan and build a residential community with 10 buildings on it. Each building has the same number of floors, ... | math | {
"style": "rule",
"ground_truth": "1225"
} | {
"index": 35857,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To survive the coming Cambridge winter, Chim Tu doesn't wear one T-shirt, but instead wears up to FOUR T-shirts, all in different colors. An outfit consists of three or more T-shirts, put on one on top of the other in some order, such that two outfits are distinct if the sets o... | math | {
"style": "rule",
"ground_truth": "144"
} | {
"index": 35858,
"solution": "We note that there are 4 choices for Chim Tu's innermost T-shirt, 3 choices for the next, and 2 choices for the next. At this point, he has exactly 1 T-shirt left, and 2 choices: either he puts that one on as well or he discards it. Thus, he has a total of $4 \\times 3 \\times 2 \\tim... |
DeepScaleR | [
{
"role": "user",
"content": "To take quizzes, each of 30 students in a class is paired with another student. If the pairing is done randomly, what is the probability that Margo is paired with her best friend, Irma? Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{29}"
} | {
"index": 35859,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To test the quality of a certain product, it was decided to use the random number table method to draw 5 samples from 300 products for inspection. The products are numbered from 000, 001, 002, ..., to 299. The following are the 7th and 8th rows of the random number table. If we... | math | {
"style": "rule",
"ground_truth": "057"
} | {
"index": 35860,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To test whether an integer, $n$, is prime, it is enough to be sure that none of the primes less than or equal to the square root of $n$ divide $n$. If you want to check that a number between 900 and 950 is prime with this rule, what is the largest prime divisor you need to test... | math | {
"style": "rule",
"ground_truth": "29"
} | {
"index": 35861,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To the eight-digit number 20222023, append one digit to the left and one digit to the right so that the resulting ten-digit number is divisible by 72. Determine all possible solutions."
}
] | math | {
"style": "rule",
"ground_truth": "3202220232"
} | {
"index": 35862,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To transmit a positive integer less than 1000, the Networked Number Node offers two options.\n\nOption 1. Pay $\\$$d to send each digit d. Therefore, 987 would cost $\\$$9 + $\\$$8 + $\\$$7 = $\\$$24 to transmit.\n\nOption 2. Encode integer into binary (base 2) first, and then ... | math | {
"style": "rule",
"ground_truth": "503"
} | {
"index": 35863,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To walk 2 km, ride 3 km by bicycle, and drive 20 km by car, Uncle Vanya needs 1 hour and 6 minutes. If he needs to walk 5 km, ride 8 km by bicycle, and drive 30 km by car, it takes him 2 hours and 24 minutes. How much time will Uncle Vanya need to walk 4 km, ride 5 km by bicycl... | math | {
"style": "rule",
"ground_truth": "174"
} | {
"index": 35864,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "To welcome the 2008 Olympic Games, a craft factory plans to produce the Olympic logo \"China Seal\" and the Olympic mascot \"Fuwa\". The factory mainly uses two types of materials, A and B. It is known that producing a set of the Olympic logo requires 4 boxes of material A and ... | math | {
"style": "rule",
"ground_truth": "2400"
} | {
"index": 35865,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Today is 17.02.2008. Natasha noticed that in this date, the sum of the first four digits is equal to the sum of the last four digits. When will this coincidence happen for the last time this year?"
}
] | math | {
"style": "rule",
"ground_truth": "25.12.2008"
} | {
"index": 35866,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Today is December 19, 2010. What is the integer part of the sum $\\frac{2010}{1000}+\\frac{1219}{100}+\\frac{27}{10}$?"
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 35867,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Today our cat gave birth to kittens! It is known that the two lightest kittens together weigh 80 g, the four heaviest kittens together weigh 200 g, and the total weight of all the kittens is 500 g. How many kittens did the cat give birth to?"
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 35868,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Today, Ivan the Confessor prefers continuous functions $f:[0,1]\\to\\mathbb{R}$ satisfying $f(x)+f(y)\\geq |x-y|$ for all pairs $x,y\\in [0,1]$. Find the minimum of $\\int_0^1 f$ over all preferred functions.\n\n("
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"index": 35869,
"solution": "\nWe are given a continuous function \\( f: [0, 1] \\to \\mathbb{R} \\) that satisfies the inequality \\( f(x) + f(y) \\geq |x-y| \\) for all \\( x, y \\in [0, 1] \\). Our goal is to find the minimum value of the integral \\(\\int_0^1 f(x) \\, dx\\).\n\n### Step-by-Step Analysis:\n\n1... |
DeepScaleR | [
{
"role": "user",
"content": "Today, Ivan the Confessor prefers continuous functions \\(f:[0,1] \\rightarrow \\mathbb{R}\\) satisfying \\(f(x)+f(y) \\geq|x-y|\\) for all pairs \\(x, y \\in[0,1]\\). Find the minimum of \\(\\int_{0}^{1} f\\) over all preferred functions."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"index": 35870,
"solution": "The minimum of \\(\\int_{0}^{1} f\\) is \\(\\frac{1}{4}\\). Applying the condition with \\(0 \\leq x \\leq \\frac{1}{2}, y=x+\\frac{1}{2}\\) we get $$f(x)+f\\left(x+\\frac{1}{2}\\right) \\geq \\frac{1}{2}.$$ By integrating, $$\\int_{0}^{1} f(x) \\mathrm{d} x=\\int_{0}^{1 / 2}\\left(f(... |
DeepScaleR | [
{
"role": "user",
"content": "Tom adds up all the even integers from 2 to 600, inclusive. Lara adds up all the integers from 1 to 200, inclusive. What is Tom's sum divided by Lara's sum?"
}
] | math | {
"style": "rule",
"ground_truth": "4.5"
} | {
"index": 35871,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Tom has a red marble, a green marble, a blue marble, and three identical yellow marbles. How many different groups of two marbles can Tom choose?"
}
] | math | {
"style": "rule",
"ground_truth": "7"
} | {
"index": 35872,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Tom has a scientific calculator. Unfortunately, all keys are broken except for one row: 1, 2, 3, + and -.\nTom presses a sequence of $5$ random keystrokes; at each stroke, each key is equally likely to be pressed. The calculator then evaluates the entire expression, yielding... | math | {
"style": "rule",
"ground_truth": "1866"
} | {
"index": 35873,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Tom has twelve slips of paper which he wants to put into five cups labeled $A$, $B$, $C$, $D$, $E$. He wants the sum of the numbers on the slips in each cup to be an integer. Furthermore, he wants the five integers to be consecutive and increasing from $A$ to $E$. The numbers o... | math | {
"style": "rule",
"ground_truth": "D"
} | {
"index": 35874,
"solution": "1. **Calculate the total sum of the numbers on the slips**:\n The numbers on the slips are $2, 2, 2, 2.5, 2.5, 3, 3, 3, 3, 3.5, 4,$ and $4.5$. Their total sum is:\n \\[\n 2+2+2+2.5+2.5+3+3+3+3+3.5+4+4.5 = 35\n \\]\n\n2. **Determine the sums for each cup**:\n Since Tom wants ... |
DeepScaleR | [
{
"role": "user",
"content": "Tom is searching for the $6$ books he needs in a random pile of $30$ books. What is the expected number of books must he examine before finding all $6$ books he needs?"
}
] | math | {
"style": "rule",
"ground_truth": "14.7"
} | {
"index": 35875,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Tom's age is $T$ years, which is also the sum of the ages of his three children. His age $N$ years ago was twice the sum of their ages then. What is $T/N$?"
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"index": 35876,
"solution": "1. **Define the variables and set up the equation:**\n - Let $T$ be Tom's current age.\n - Let $N$ be the number of years ago when Tom's age was twice the sum of his children's ages.\n - The sum of the ages of Tom's three children is also $T$.\n\n2. **Calculate the ages $N$ year... |
DeepScaleR | [
{
"role": "user",
"content": "Tom's algebra notebook consists of 50 pages, 25 sheets of paper. Specifically, page 1 and page 2 are the front and back of the first sheet of paper, page 3 and page 4 are the front and back of the second sheet of paper, and so on. One day, Tom left the notebook on the table whi... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 35877,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Tom's favorite number is between $100$ and $150$. It is a multiple of $13$, but not a multiple of $3$. The sum of its digits is a multiple of $4$. What is Tom's favorite number?"
}
] | math | {
"style": "rule",
"ground_truth": "143"
} | {
"index": 35878,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Tom's graduating class has 288 students. At the graduation ceremony, the students will sit in rows with the same number of students in each row. If there must be at least 10 rows and at least 15 students in each row, then there can be $x$ students in each row. What is the sum o... | math | {
"style": "rule",
"ground_truth": "58"
} | {
"index": 35879,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Tom, Dick and Harry started out on a $100$-mile journey. Tom and Harry went by automobile at the rate of $25$ mph, while Dick walked at the rate of $5$ mph. After a certain distance, Harry got off and walked on at $5$ mph, while Tom went back for Dick and got him to the destina... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"index": 35880,
"solution": "1. **Define Variables:**\n Let $d_1$ be the distance Harry traveled by car, and $d_2$ be the distance Tom backtracked to pick up Dick. Let $T$ be the total time for the trip.\n\n2. **Set Up Equations:**\n - **Harry's journey:** He travels $d_1$ miles by car and then walks the rema... |
DeepScaleR | [
{
"role": "user",
"content": "Tom, Dick, and Harry are playing a game. Starting at the same time, each of them flips a fair coin repeatedly until he gets his first head, at which point he stops. What is the probability that all three flip their coins the same number of times?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{7}"
} | {
"index": 35881,
"solution": "1. **Understanding the Problem**: Tom, Dick, and Harry each flip a fair coin repeatedly until they get a head. We need to find the probability that all three stop flipping their coins after the same number of flips.\n\n2. **Modeling the Coin Flips**: The probability that a single pers... |
DeepScaleR | [
{
"role": "user",
"content": "Tom, Dick, and Harry each flip a fair coin repeatedly until they get their first tail. Calculate the probability that all three flip their coins an even number of times and they all get their first tail on the same flip."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{63}"
} | {
"index": 35882,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Tom, Dorothy, and Sammy went on a vacation and agreed to split the costs evenly. During their trip Tom paid $105, Dorothy paid $125, and Sammy paid $175. In order to share costs equally, Tom gave Sammy $t$ dollars, and Dorothy gave Sammy $d$ dollars. What is $t-d$?"
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 35883,
"solution": "1. **Calculate the total amount spent and the individual shares:**\n - Total amount spent by Tom, Dorothy, and Sammy:\n \\[\n 105 + 125 + 175 = 405 \\text{ dollars}\n \\]\n - Since they agreed to split the costs evenly, each person's share is:\n \\[\n \\frac{40... |
DeepScaleR | [
{
"role": "user",
"content": "Tom, Dorothy, and Sammy went on a vacation and agreed to split the costs evenly. During their trip Tom paid $105, Dorothy paid $125, and Sammy paid $175. In order to share costs equally, find the difference between the amount of money Tom gave Sammy and the amount of money Doro... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 35884,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Tom, Dorothy, and Sammy went on a vacation and agreed to split the costs evenly. During their trip Tom paid $105, Dorothy paid $125, and Sammy paid $175. In order to share the costs equally, Tom gave Sammy $t$ dollars, and Dorothy gave Sammy $d$ dollars. What is $t-d$?"
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 35885,
"solution": "1. **Calculate the total amount paid by all three:**\n Tom paid $105, Dorothy paid $125, and Sammy paid $175. Therefore, the total amount paid is:\n \\[\n 105 + 125 + 175 = 405\n \\]\n\n2. **Determine the amount each should have paid:**\n Since they agreed to split the costs... |
DeepScaleR | [
{
"role": "user",
"content": "Tom, John, and Lily each shot six arrows at a target. Arrows hitting anywhere within the same ring scored the same number of points. Tom scored 46 points and John scored 34 points. How many points did Lily score?"
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 35886,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Tom, Sara, and Jim split $\\$1200$ among themselves to be used in investments. Each starts with a different amount. At the end of one year, they have a total of $\\$1800$. Sara triples her money by the end of the year, Jim doubles his money, whereas Tom loses $\\$200$. What was... | math | {
"style": "rule",
"ground_truth": "400"
} | {
"index": 35887,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Tommy takes a 25-question true-false test. He answers each question correctly with independent probability $\\frac{1}{2}$ . Tommy earns bonus points for correct streaks: the first question in a streak is worth 1 point, the second question is worth 2 points, and so on. For in... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"index": 35888,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Toner Drum and Celery Hilton are both running for president. A total of $129$ million people cast their vote in a random order, with exactly $63$ million and $66$ million voting for Toner Drum and Celery Hilton, respectively. The Combinatorial News Network displays the fa... | math | {
"style": "rule",
"ground_truth": "1/43"
} | {
"index": 35889,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Tony will paint 16 right, cylindrical columns. The top face and bottom face of each column will be covered, so those parts will not be painted. Each column is 18 feet tall and has a diameter of 10 feet. One gallon of paint will cover 350 square feet. If paint is sold only in... | math | {
"style": "rule",
"ground_truth": "26"
} | {
"index": 35890,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Tony works $2$ hours a day and is paid $\\$0.50$ per hour for each full year of his age. During a six month period Tony worked $50$ days and earned $\\$630$. How old was Tony at the end of the six month period?"
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 35891,
"solution": "1. **Understanding the payment structure**: Tony earns $0.50$ per hour for each full year of his age. Since he works $2$ hours a day, his daily earnings are $2 \\times 0.50 \\times \\text{age} = \\text{age}$ dollars per day.\n\n2. **Setting up the equation**: Tony worked $50$ days and... |
DeepScaleR | [
{
"role": "user",
"content": "Toothpicks are used to make a grid that is $60$ toothpicks long and $32$ toothpicks wide. How many toothpicks are used altogether?"
}
] | math | {
"style": "rule",
"ground_truth": "3932"
} | {
"index": 35892,
"solution": "To determine the total number of toothpicks used in constructing a grid that is $60$ toothpicks long and $32$ toothpicks wide, we need to consider both the vertical and horizontal toothpicks.\n\n1. **Vertical Toothpicks:**\n - Each vertical line extends from the top to the bottom of... |
DeepScaleR | [
{
"role": "user",
"content": "Toothpicks of equal length are used to build a rectangular grid as shown. If the grid is 20 toothpicks high and 10 toothpicks wide, then the number of toothpicks used is"
}
] | math | {
"style": "rule",
"ground_truth": "430"
} | {
"index": 35893,
"solution": "To determine the number of toothpicks used to build a rectangular grid that is 20 toothpicks high and 10 toothpicks wide, we need to consider both the horizontal and vertical toothpicks.\n\n1. **Counting Horizontal Toothpicks:**\n - The grid is 20 toothpicks high, which means there ... |
DeepScaleR | [
{
"role": "user",
"content": "Topsoil costs $\\$6$ per cubic foot. What is the cost, in dollars, of 5 cubic yards of topsoil?"
}
] | math | {
"style": "rule",
"ground_truth": "810"
} | {
"index": 35894,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Tori's mathematics test had 75 problems: 10 arithmetic, 30 algebra, and 35 geometry problems. Although she answered $70\\%$ of the arithmetic, $40\\%$ of the algebra, and $60\\%$ of the geometry problems correctly, she did not pass the test because she got less than $60\\%$ of ... | math | {
"style": "rule",
"ground_truth": "5"
} | {
"index": 35895,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Toss a fair coin, with the probability of landing heads or tails being $\\frac {1}{2}$ each. Construct the sequence $\\{a_n\\}$ such that\n$$\na_n= \n\\begin{cases} \n1 & \\text{if the } n\\text{-th toss is heads,} \\\\ \n-1 & \\text{if the } n\\text{-th toss is tails.}\n\\end{... | math | {
"style": "rule",
"ground_truth": "\\frac {13}{128}"
} | {
"index": 35896,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Toward the end of a game of Fish, the 2 through 7 of spades, inclusive, remain in the hands of three distinguishable players: \\mathrm{DBR}, \\mathrm{RB}, and DB , such that each player has at least one card. If it is known that DBR either has more than one card or has an even-... | math | {
"style": "rule",
"ground_truth": "450"
} | {
"index": 35897,
"solution": "First, we count the number of distributions where each player has at least 1 card. The possible distributions are: - Case 1: $4 / 1 / 1$ : There are 3 choices for who gets 4 cards, 6 choices for the card that one of the single-card players holds, and 5 choices for the card the other s... |
DeepScaleR | [
{
"role": "user",
"content": "Tracy had a bag of candies, and none of the candies could be broken into pieces. She ate $\\frac{1}{3}$ of them and then gave $\\frac{1}{4}$ of what remained to her friend Rachel. Tracy and her mom then each ate 15 candies from what Tracy had left. Finally, Tracy's brother took... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"index": 35898,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Train 109 T departs from Beijing at 19:33 and arrives in Shanghai the next day at 10:26; train 1461 departs from Beijing at 11:58 and arrives in Shanghai the next day at 8:01. How many minutes are the running times of these two trains different?"
}
] | math | {
"style": "rule",
"ground_truth": "310"
} | {
"index": 35899,
"solution": ""
} |
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