data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "ABCDE is a regular pentagon. The star ACEBD has an area of 1. AC and BE meet at P, BD and CE meet at Q. Find the area of APQD."
}
] | math | {
"style": "rule",
"ground_truth": "1/2"
} | {
"index": 4200,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "ABCDEF is a six-digit number. All its digits are different and arranged in ascending order from left to right. This number is a perfect square.\n\nDetermine what this number is."
}
] | math | {
"style": "rule",
"ground_truth": "134689"
} | {
"index": 4201,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "ABCDEF is a six-digit number. All of its digits are different and arranged in ascending order from left to right. This number is a perfect square.\n\nDetermine what this number is."
}
] | math | {
"style": "rule",
"ground_truth": "134689"
} | {
"index": 4202,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Aaron has 144 identical cubes, each with edge length 1 cm. He uses all of the cubes to construct a solid rectangular prism, which he places on a flat table. If the perimeter of the base of the prism is 20 cm, what is the sum of all possible heights of the prism?"
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"index": 4203,
"solution": "Suppose that the base of the prism is $b \\mathrm{~cm}$ by $w \\mathrm{~cm}$ and the height of the prism is $h \\mathrm{~cm}$. Since Aaron has 144 cubes with edge length 1 cm, then the volume of the prism is $144 \\mathrm{~cm}^{3}$, and so $bwh = 144$. Since the perimeter of the base i... |
DeepScaleR | [
{
"role": "user",
"content": "Aaron takes a square sheet of paper, with one corner labeled $A$ . Point $P$ is chosen at random inside of the square and Aaron folds the paper so that points $A$ and $P$ coincide. He cuts the sheet along the crease and discards the piece containing $A$ . Let $p$ be t... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 4204,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Aaron the ant walks on the coordinate plane according to the following rules. He starts at the origin $p_0=(0,0)$ facing to the east and walks one unit, arriving at $p_1=(1,0)$. For $n=1,2,3,\\dots$, right after arriving at the point $p_n$, if Aaron can turn $90^\\circ$ left an... | math | {
"style": "rule",
"ground_truth": "(13,-22)"
} | {
"index": 4205,
"solution": "1. **Identify the pattern of movement**: Aaron the ant starts at the origin and moves in a spiral pattern. He moves east, then north, west, south, and this cycle repeats with increasing steps.\n\n2. **Determine the number of steps in each direction**: \n - First, he moves 1 step east... |
DeepScaleR | [
{
"role": "user",
"content": "Abbot writes the letter $A$ on the board. Every minute, he replaces every occurrence of $A$ with $A B$ and every occurrence of $B$ with $B A$, hence creating a string that is twice as long. After 10 minutes, there are $2^{10}=1024$ letters on the board. How many adjacent pairs ... | math | {
"style": "rule",
"ground_truth": "341"
} | {
"index": 4206,
"solution": "Let $a_{n}$ denote the number of adjacent pairs of letters that are the same after $n$ minutes, and $b_{n}$ the number of adjacent pairs that are different. Lemma 1. $a_{n}=b_{n-1}$ for all $n \\geq 0$. Proof. Any adjacent pair of identical letters $X X$ at stage $n$ either came from t... |
DeepScaleR | [
{
"role": "user",
"content": "Abby, Bart, Cindy and Damon weigh themselves in pairs. Together Abby and Bart weigh 260 pounds, Bart and Cindy weigh 245 pounds, and Cindy and Damon weigh 270 pounds. How many pounds do Abby and Damon weigh together?"
}
] | math | {
"style": "rule",
"ground_truth": "285"
} | {
"index": 4207,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Abby, Bernardo, Carl, and Debra play a game in which each of them starts with four coins. The game consists of four rounds. In each round, four balls are placed in an urn---one green, one red, and two white. The players each draw a ball at random without replacement. Whoever ge... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{192}"
} | {
"index": 4208,
"solution": "1. **Understanding the Game and Initial Setup**:\n - Each player starts with 4 coins.\n - In each round, one player gives a coin to another based on the draw of colored balls (green and red).\n - The goal is to find the probability that after four rounds, each player still has ex... |
DeepScaleR | [
{
"role": "user",
"content": "Abby, Bernardo, Carl, and Debra play a revised game where each starts with five coins and there are five rounds. In each round, five balls are placed in an urn—two green, two red, and one blue. Each player draws a ball at random without replacement. If a player draws a green ba... | math | {
"style": "rule",
"ground_truth": "\\frac{64}{15625}"
} | {
"index": 4209,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Abby, Bridget, and four of their classmates will be seated in two rows of three for a group picture, as shown.\n\\begin{tabular}{ccc} X & X & X \\\\ X & X & X \\end{tabular}\nIf the seating positions are assigned randomly, what is the probability that Abby and Bridget are adjac... | math | {
"style": "rule",
"ground_truth": "\\frac{7}{15}"
} | {
"index": 4210,
"solution": "1. **Total Arrangements**: First, we calculate the total number of ways to arrange 6 kids (including Abby and Bridget) in 6 seats. This is simply the number of permutations of 6 items, which is $6!$.\n\n2. **Adjacent Arrangements**: We need to count the number of ways Abby and Bridget ... |
DeepScaleR | [
{
"role": "user",
"content": "Abe can paint the room in 15 hours, Bea can paint 50 percent faster than Abe, and Coe can paint twice as fast as Abe. Abe begins to paint the room and works alone for the first hour and a half. Then Bea joins Abe, and they work together until half the room is painted. Then Coe ... | math | {
"style": "rule",
"ground_truth": "334"
} | {
"index": 4211,
"solution": "From the given information, we can see that Abe can paint $\\frac{1}{15}$ of the room in an hour, Bea can paint $\\frac{1}{15}\\times\\frac{3}{2} = \\frac{1}{10}$ of the room in an hour, and Coe can paint the room in $\\frac{1}{15}\\times 2 = \\frac{2}{15}$ of the room in an hour. Afte... |
DeepScaleR | [
{
"role": "user",
"content": "Abe holds 1 green and 1 red jelly bean in his hand. Bob holds 1 green, 1 yellow, and 2 red jelly beans in his hand. Each randomly picks a jelly bean to show the other. What is the probability that the colors match?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{8}"
} | {
"index": 4212,
"solution": "1. **Identify the possible outcomes for matching colors**: Abe and Bob can either both show a green jelly bean or both show a red jelly bean. These are the only two scenarios where their jelly bean colors match.\n\n2. **Calculate the probability of both showing a green jelly bean**:\n ... |
DeepScaleR | [
{
"role": "user",
"content": "Abe, Bobby, Charles, Devin and Edwin are the participants in a race. How many different 1st-2nd-3rd place outcomes are possible if there are no ties? Two different outcomes to include are Bobby-Devin-Edwin and Devin-Bobby-Edwin."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 4213,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Abigail chooses an integer at random from the set $\\{2,4,6,8,10\\}$. Bill chooses an integer at random from the set $\\{2,4,6,8,10\\}$. Charlie chooses an integer at random from the set $\\{2,4,6,8,10\\}$. What is the probability that the product of their three integers is not... | math | {
"style": "rule",
"ground_truth": "\\frac{98}{125}"
} | {
"index": 4214,
"solution": "For the product of the three integers to be a power of 2, it can have no prime factors other than 2. In each of the three sets, there are 3 powers of 2 (namely, 2,4 and 8) and 2 integers that are not a power of 2 (namely, 6 and 10). The probability that each chooses a power of 2 is $\\... |
DeepScaleR | [
{
"role": "user",
"content": "Abigail, Beatrice, and Carson combine their eggs to sell them at the market. If Abigail has 37 eggs, Beatrice has 49 eggs, and Carson has 14 eggs, and if eggs can only be sold in cartons of 12, how many eggs will be left over if all cartons are sold?"
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"index": 4215,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "About 40% of students in a certain school are nearsighted, and about 30% of the students in the school use their phones for more than 2 hours per day, with a nearsighted rate of about 50% among these students. If a student who uses their phone for no more than 2 hours per day i... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{14}"
} | {
"index": 4216,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Absent-Minded Scientist had a sore knee. The doctor prescribed him 10 pills for his knee: taking one pill daily. These pills are effective in $90\\%$ of cases, and in $2\\%$ of cases, there is a side effect - absence of absent-mindedness, if it existed.\n\nAnother doctor prescr... | math | {
"style": "rule",
"ground_truth": "0.69"
} | {
"index": 4217,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "According to Moor's Law, the number of shoes in Moor's room doubles every year. In 2013, Moor's room starts out having exactly one pair of shoes. If shoes always come in unique, matching pairs, what is the earliest year when Moor has the ability to wear at least 500 mismatche... | math | {
"style": "rule",
"ground_truth": "2018"
} | {
"index": 4218,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "According to census statistics, the probability of a woman of childbearing age giving birth to a boy or a girl is equal. If a second child is allowed, calculate the probability that a woman of childbearing age will have two girls."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac {1}{4}"
} | {
"index": 4219,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "According to national regulations, only adults aged between 18 and 70 are eligible to apply for a motor vehicle driver's license. A sixth-grade student, Li Ming, says, \"My dad has a driver's license. His age equals the product of the month and day of his birth, and that produc... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"index": 4220,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "According to statistical data, the daily output of a factory does not exceed 200,000 pieces, and the daily defect rate $p$ is approximately related to the daily output $x$ (in 10,000 pieces) by the following relationship:\n$$\np= \\begin{cases} \n\\frac{x^{2}+60}{540} & (0<x\\l... | math | {
"style": "rule",
"ground_truth": "\\frac{100}{9}"
} | {
"index": 4221,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "According to the Shannon formula $C=W\\log_{2}(1+\\frac{S}{N})$, if the bandwidth $W$ is not changed, but the signal-to-noise ratio $\\frac{S}{N}$ is increased from $1000$ to $12000$, then find the approximate percentage increase in the value of $C$."
}
] | math | {
"style": "rule",
"ground_truth": "36\\%"
} | {
"index": 4222,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "According to the chart shown, what was the average daily high temperature in Addington from September 15th, 2008 through September 19th, 2008, inclusive? Express your answer as a decimal to the nearest tenth. [asy]\nsize(300);\ndefaultpen(linewidth(.7pt)+fontsize(6pt));\n\nint[... | math | {
"style": "rule",
"ground_truth": "54.4"
} | {
"index": 4223,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "According to the classification standard of the Air Pollution Index (API) for city air quality, when the air pollution index is not greater than 100, the air quality is good. The environmental monitoring department of a city randomly selected the air pollution index for 5 days ... | math | {
"style": "rule",
"ground_truth": "440"
} | {
"index": 4224,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "According to the data shown, how much cheaper, in cents, is the cheaper store's price for Camera $X$ compared to the more expensive? \\begin{tabular}{|l|l|}\n\\hline\n\\textbf{Store}& \\textbf{Sale Price for Camera $X$} \\\\ \\hline\nSuper Savers & $\\$9$~off the list price~$\\... | math | {
"style": "rule",
"ground_truth": "99"
} | {
"index": 4225,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "According to the definition of the Richter scale, the relationship between the relative energy $E$ released by an earthquake and the earthquake magnitude $n$ is: $E=10^n$. What is the multiple of the relative energy released by a magnitude 9 earthquake compared to a magnitude 7... | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 4226,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "According to the graph, what is the average monthly balance, in dollars, of David's savings account during the four-month period shown? [asy]\ndraw((0,0)--(13,0)--(13,8)--(0,8)--cycle,linewidth(1));\ndraw((0,2)--(13,2),linewidth(1));\ndraw((0,4)--(13,4),linewidth(1));\ndraw((0,... | math | {
"style": "rule",
"ground_truth": "\\$150"
} | {
"index": 4227,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "According to the latest revision of the \"Regulations on the Application and Use of Motor Vehicle Driving Licenses\" by the Ministry of Public Security: each driving license applicant must pass the \"Subject One\" (theoretical subject) and \"Comprehensive Subject\" (combination... | math | {
"style": "rule",
"ground_truth": "0.9988"
} | {
"index": 4228,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "According to the notice from the Ministry of Industry and Information Technology on the comprehensive promotion of China's characteristic enterprise new apprenticeship system and the strengthening of skills training, our region clearly promotes the new apprenticeship system tra... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{10}"
} | {
"index": 4229,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "According to the standard convention for exponentiation, \n\\[2^{2^{2^{2}}} = 2^{(2^{(2^2)})} = 2^{16} = 65536.\\]\nIf the order in which the exponentiations are performed is changed, how many other values are possible?"
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 4230,
"solution": "To solve this problem, we need to evaluate the expression $2^{2^{2^{2}}}$ with different parenthesizations and determine how many distinct values can be obtained.\n\nThe expression $2^{2^{2^{2}}}$ can be parenthesized in the following ways:\n1. $2^{(2^{(2^2)})}$\n2. $2^{((2^2)^2)}$\n3.... |
DeepScaleR | [
{
"role": "user",
"content": "According to the table below, how many dollars are in the median value of the 59 salaries paid to this company's employees?\n\n\\begin{tabular}{|c|c|c|}\n\\hline\n\\textbf{Position Title}&\\textbf{\\# with Title}&\\textbf{Salary}\\\\\\hline\nPresident&1&$\\$130{,}000$\\\\\\hlin... | math | {
"style": "rule",
"ground_truth": "\\$23{,}000"
} | {
"index": 4231,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Ace runs with constant speed and Flash runs $x$ times as fast, $x>1$. Flash gives Ace a head start of $y$ yards, and, at a given signal, they start off in the same direction. Then the number of yards Flash must run to catch Ace is:"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{xy}{x-1}"
} | {
"index": 4232,
"solution": "1. **Setup the problem**: Let $v$ be the speed of Ace. Then the speed of Flash is $xv$, where $x > 1$. Ace has a head start of $y$ yards.\n\n2. **Determine the time for Flash to catch Ace**: Let $t$ be the time it takes for Flash to catch up to Ace. In this time, Ace runs a distance of... |
DeepScaleR | [
{
"role": "user",
"content": "Acme Corporation has released a new version of its vowel soup where each vowel (A, E, I, O, U) appears six times, and additionally, each bowl contains one wildcard character that can represent any vowel. How many six-letter \"words\" can be formed from a bowl of this new Acme E... | math | {
"style": "rule",
"ground_truth": "46656"
} | {
"index": 4233,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Acme Corporation has released an alphabet soup in which each of the vowels (A, E, I, O, U) of the English alphabet appears five times (and the consonants do not appear at all). How many five-letter words can be formed from a bowl of Acme Vowel Soup? (Note: The words do not have... | math | {
"style": "rule",
"ground_truth": "3125"
} | {
"index": 4234,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Acme T-Shirt Company charges a $\\$50$ set-up fee plus $\\$9$ for each shirt printed. Beta T-shirt Company has no set up fee, but charges $\\$14$ per shirt. What is the minimum number of shirts for which a customer saves money by using Acme?"
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 4235,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Acute angles \\( A \\) and \\( B \\) of a triangle satisfy the equation \\( \\tan A - \\frac{1}{\\sin 2A} = \\tan B \\) and \\( \\cos^2 \\frac{B}{2} = \\frac{\\sqrt{6}}{3} \\). Determine the value of \\( \\sin 2A \\)."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2\\sqrt{6} - 3}{3}"
} | {
"index": 4236,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Acute triangle $A B C$ has circumcenter $O$. The bisector of $\\angle A B C$ and the altitude from $C$ to side $A B$ intersect at $X$. Suppose that there is a circle passing through $B, O, X$, and $C$. If $\\angle B A C=n^{\\circ}$, where $n$ is a positive integer, compute the ... | math | {
"style": "rule",
"ground_truth": "67"
} | {
"index": 4237,
"solution": "We have $\\angle X B C=B / 2$ and $\\angle X C B=90^{\\circ}-B$. Thus, $\\angle B X C=90^{\\circ}+B / 2$. We have $\\angle B O C=2 A$, so $$90^{\\circ}+B / 2=2 A$$ This gives $B=4 A-180^{\\circ}$, which gives $C=360^{\\circ}-5 A$. In order for $0^{\\circ}<B<90^{\\circ}$, we need $45^{\... |
DeepScaleR | [
{
"role": "user",
"content": "Acute-angled $\\triangle ABC$ is inscribed in a circle with center at $O$. The measures of arcs are $\\stackrel \\frown {AB} = 80^\\circ$ and $\\stackrel \\frown {BC} = 100^\\circ$. A point $E$ is taken in minor arc $AC$ such that $OE$ is perpendicular to $AC$. Find the ratio o... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 4238,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Acute-angled $\\triangle ABC$ is inscribed in a circle with center at $O$; $\\stackrel \\frown {AB} = 100^\\circ$ and $\\stackrel \\frown {BC} = 80^\\circ$.\nA point $E$ is taken in minor arc $AC$ such that $OE$ is perpendicular to $AC$. The task is to determine the ratio of th... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 4239,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Acute-angled $\\triangle ABC$ is inscribed in a circle with center at $O$; $\\stackrel \\frown {AB} = 120^\\circ$ and $\\stackrel \\frown {BC} = 72^\\circ$.\nA point $E$ is taken in minor arc $AC$ such that $OE$ is perpendicular to $AC$. Then the ratio of the magnitudes of $\\a... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"index": 4240,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Adam and Bettie are playing a game. They take turns generating a random number between $0$ and $127$ inclusive. The numbers they generate are scored as follows: $\\bullet$ If the number is zero, it receives no points. $\\bullet$ If the number is odd, it receives one more ... | math | {
"style": "rule",
"ground_truth": "429"
} | {
"index": 4241,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Adam and Sarah start on bicycle trips from the same point at the same time. Adam travels north at 10 mph and Sarah travels west at 5 mph. After how many hours are they 85 miles apart?"
}
] | math | {
"style": "rule",
"ground_truth": "7.6"
} | {
"index": 4242,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Adam and Simon start on bicycle trips from the same point at the same time. Adam travels east at 8mph and Simon travels south at 6mph. After how many hours are they 60 miles apart?"
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"index": 4243,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Adam and Simon start on bicycle trips from the same point at the same time. Adam travels north at 10 mph and Simon travels west at 12 mph. How many hours will it take for them to be 130 miles apart?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{65}{\\sqrt{61}}"
} | {
"index": 4244,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Adam filled a $3 \\times 3$ table with the numbers from 1 to 9 as follows:\n\n| 7 | 6 | 4 |\n| :--- | :--- | :--- |\n| 1 | 2 | 8 |\n| 9 | 3 | 5 |\n\nFor this arrangement, the sum of the numbers along every side of the table remains the same. Adam found that the numbers can be a... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 4245,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Adam has $15$ of a certain type of rare coin and is interested in knowing how much this collection is worth. He discovers that $5$ of these coins are worth $12$ dollars in total. Assuming that the value of each coin is the same, how many dollars is his entire collection worth?... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 4246,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Adam, Bendeguz, Cathy, and Dennis all see a positive integer $n$ . Adam says, \" $n$ leaves a remainder of $2$ when divided by $3$ .\" Bendeguz says, \"For some $k$ , $n$ is the sum of the first $k$ positive integers.\" Cathy says, \"Let $s$ be the largest perfect s... | math | {
"style": "rule",
"ground_truth": "210"
} | {
"index": 4247,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Adam, Benin, Chiang, Deshawn, Esther, and Fiona have internet accounts. Some, but not all, of them are internet friends with each other, and none of them has an internet friend outside this group. Each of them has the same number of internet friends. In how many different wa... | math | {
"style": "rule",
"ground_truth": "170"
} | {
"index": 4248,
"solution": "1. **Understanding the Problem:**\n - We have 6 individuals: Adam, Benin, Chiang, Deshawn, Esther, and Fiona.\n - Each individual has the same number of internet friends within this group.\n - The number of friends each person has ranges from 1 to 4, as no one can be friends with... |
DeepScaleR | [
{
"role": "user",
"content": "Adam, Benin, Chiang, Deshawn, Esther, and Fiona have internet accounts. Some, but not all, of them are internet friends with each other, and none of them has an internet friend outside this group. Each of them has the same number of internet friends. In how many different ways ... | math | {
"style": "rule",
"ground_truth": "170"
} | {
"index": 4249,
"solution": "1. **Understanding the Problem:**\n - We have 6 individuals: Adam, Benin, Chiang, Deshawn, Esther, and Fiona.\n - Each individual has the same number of internet friends within this group.\n - We need to determine the number of ways this can happen, considering different possible... |
DeepScaleR | [
{
"role": "user",
"content": "Adams plans a profit of $10$ % on the selling price of an article and his expenses are $15$ % of sales. The rate of markup on an article that sells for $ $5.00$ is:"
}
] | math | {
"style": "rule",
"ground_truth": "33\\frac {1}{3}\\%"
} | {
"index": 4250,
"solution": "1. **Define Variables:**\n Let $C$ be the cost of the product and $S$ be the selling price. According to the problem, Adams plans a profit of 10% on the selling price, and his expenses are 15% of the selling price.\n\n2. **Express the Relationships:**\n The profit is 10% of the sel... |
DeepScaleR | [
{
"role": "user",
"content": "Add $-45.367$, $108.2$, and $23.7654$, then round your answer to the nearest tenth."
}
] | math | {
"style": "rule",
"ground_truth": "86.6"
} | {
"index": 4251,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $101_2 + 11_2 + 1100_2 + 11101_2.$ Express your answer in base $2.$"
}
] | math | {
"style": "rule",
"ground_truth": "110001_2"
} | {
"index": 4252,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $10_7 + 163_7.$ Express your answer in base 7."
}
] | math | {
"style": "rule",
"ground_truth": "203_7"
} | {
"index": 4253,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $123.4567$ to $98.764$ and round your answer to the nearest hundredth. Then, subtract $0.02$ from the rounded result."
}
] | math | {
"style": "rule",
"ground_truth": "222.20"
} | {
"index": 4254,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $12_8 + 157_8.$ Express your answer in base 8."
}
] | math | {
"style": "rule",
"ground_truth": "171_8"
} | {
"index": 4255,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $175_{9} + 714_{9} + 61_9$. Express your answer in base $9$."
}
] | math | {
"style": "rule",
"ground_truth": "1061_{9}"
} | {
"index": 4256,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $1_3 + 12_3 + 212_3 + 2121_3.$ Express your answer in base 3."
}
] | math | {
"style": "rule",
"ground_truth": "10200_3"
} | {
"index": 4257,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $2175_{9} + 1714_{9} + 406_9$. Express your answer in base $9$."
}
] | math | {
"style": "rule",
"ground_truth": "4406_{9}"
} | {
"index": 4258,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $254_{9} + 627_{9} + 503_{9}$. Express your answer in base 9."
}
] | math | {
"style": "rule",
"ground_truth": "1485_{9}"
} | {
"index": 4259,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $256_{7} + 463_{7} + 132_7$. Express your answer in base $7$."
}
] | math | {
"style": "rule",
"ground_truth": "1214_{7}"
} | {
"index": 4260,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $26_7 + 245_7.$ Express your answer in base 7."
}
] | math | {
"style": "rule",
"ground_truth": "304_7"
} | {
"index": 4261,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $36_7 + 274_7.$ Express your answer in base 7."
}
] | math | {
"style": "rule",
"ground_truth": "343_7"
} | {
"index": 4262,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $45.23$ to $78.569$ and round your answer to the nearest tenth."
}
] | math | {
"style": "rule",
"ground_truth": "123.8"
} | {
"index": 4263,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $452_8$ and $167_8$ in base $8$, then subtract $53_8$ from the result."
}
] | math | {
"style": "rule",
"ground_truth": "570_8"
} | {
"index": 4264,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $46.913$ to $58.27$ and round your answer to the nearest hundredth."
}
] | math | {
"style": "rule",
"ground_truth": "105.18"
} | {
"index": 4265,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $49.213$ to $27.569$, and round your answer to the nearest whole number."
}
] | math | {
"style": "rule",
"ground_truth": "77"
} | {
"index": 4266,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $4_6 + 14_6.$ Express your answer in base $6.$"
}
] | math | {
"style": "rule",
"ground_truth": "22_6"
} | {
"index": 4267,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $5.467$ and $3.92$ as a decimal."
}
] | math | {
"style": "rule",
"ground_truth": "9.387"
} | {
"index": 4268,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $518_{12} + 276_{12}$. Express your answer in base 12, using $A$ for $10$ and $B$ for $11$ if necessary."
}
] | math | {
"style": "rule",
"ground_truth": "792_{12}"
} | {
"index": 4269,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $537_{8} + 246_{8}$. Express your answer in base $8$, and then convert your answer to base $16$, using alphabetic representation for numbers $10$ to $15$ (e.g., $A$ for $10$, $B$ for $11$, etc.)."
}
] | math | {
"style": "rule",
"ground_truth": "205_{16}"
} | {
"index": 4270,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $5_7 + 16_7.$ Express your answer in base $7.$"
}
] | math | {
"style": "rule",
"ground_truth": "24_7"
} | {
"index": 4271,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $704_{12} + 159_{12}$. Express your answer in base $12$, using $A$ for $10$ and $B$ for $11$ if necessary."
}
] | math | {
"style": "rule",
"ground_truth": "861_{12}"
} | {
"index": 4272,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $7A3_{16} + 1F4_{16}$. Express your answer in base 16, using A for 10, B for 11, ..., F for 15."
}
] | math | {
"style": "rule",
"ground_truth": "997_{16}"
} | {
"index": 4273,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $81.76$ to $34.587$ and round your answer to the nearest tenth."
}
] | math | {
"style": "rule",
"ground_truth": "116.3"
} | {
"index": 4274,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $91.234$ to $42.7689$ and round your answer to the nearest hundredth."
}
] | math | {
"style": "rule",
"ground_truth": "134.00"
} | {
"index": 4275,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $956_{12} + 273_{12}$. Express your answer in base $12$, using $A$ for $10$ and $B$ for $11$ if necessary."
}
] | math | {
"style": "rule",
"ground_truth": "1009_{12}"
} | {
"index": 4276,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add $A85_{12}$ and $2B4_{12}$. Express your answer in base $12$, using $A$ for $10$ and $B$ for $11$ if necessary."
}
] | math | {
"style": "rule",
"ground_truth": "1179_{12}"
} | {
"index": 4277,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add 22 and 62."
}
] | math | {
"style": "rule",
"ground_truth": "84"
} | {
"index": 4278,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add 24.567 to 38.924, then multiply the sum by 2.5, and round the result to the nearest hundredth."
}
] | math | {
"style": "rule",
"ground_truth": "158.73"
} | {
"index": 4279,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add 3 digits after 325 to make a six-digit number such that it is divisible by 3, 4, and 5, and make this number as small as possible. What is the new six-digit number?"
}
] | math | {
"style": "rule",
"ground_truth": "325020"
} | {
"index": 4280,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add 47.2189 to 34.0076 and round to the nearest hundredth."
}
] | math | {
"style": "rule",
"ground_truth": "81.23"
} | {
"index": 4281,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add 53.463 to 12.9873 and round to the nearest thousandth."
}
] | math | {
"style": "rule",
"ground_truth": "66.450"
} | {
"index": 4282,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add 74.6893 to 23.152 and round to the nearest hundredth."
}
] | math | {
"style": "rule",
"ground_truth": "97.84"
} | {
"index": 4283,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add 75.892 to 34.5167 and then multiply the sum by 2. Round the final result to the nearest thousandth."
}
] | math | {
"style": "rule",
"ground_truth": "220.817"
} | {
"index": 4284,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add 76.893 to 34.2176 and round to the nearest tenth."
}
] | math | {
"style": "rule",
"ground_truth": "111.1"
} | {
"index": 4285,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add 78.1563 to 24.3981 and round to the nearest hundredth."
}
] | math | {
"style": "rule",
"ground_truth": "102.55"
} | {
"index": 4286,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add 78.621 to 34.0568 and round to the nearest thousandth."
}
] | math | {
"style": "rule",
"ground_truth": "112.678"
} | {
"index": 4287,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add \\(53_8 + 27_8\\). Express your answer in base \\(8\\)."
}
] | math | {
"style": "rule",
"ground_truth": "102_8"
} | {
"index": 4288,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add the following two numbers: $800,000,000,000 + 299,999,999,999$.\nA) $1,000,000,000,000$\nB) $1,099,999,999,999$\nC) $1,100,000,000,000$\nD) $900,000,000,000$\nE) $2,099,999,999,999$"
}
] | math | {
"style": "rule",
"ground_truth": "1,099,999,999,999"
} | {
"index": 4289,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add the square of the smallest area from squares of size $1 \\times 1, 2 \\times 2,$ and $3 \\times 3,$ such that the number of squares of each size is the same."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 4290,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add together all natural numbers less than 1980 for which the sum of their digits is even!"
}
] | math | {
"style": "rule",
"ground_truth": "979605"
} | {
"index": 4291,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Add together the numbers $7.56$ and $4.29$. Write the result as a decimal."
}
] | math | {
"style": "rule",
"ground_truth": "11.85"
} | {
"index": 4292,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Adding two dots above the decimal 0.142857 makes it a repeating decimal. The 2020th digit after the decimal point is 5. What is the repeating cycle? $\\quad$ ."
}
] | math | {
"style": "rule",
"ground_truth": "142857"
} | {
"index": 4293,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Addison's age is three times Brenda's age. Janet is six years older than Brenda. Addison and Janet are twins. How old is Brenda?"
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"index": 4294,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Adia writes a list in increasing order of the integers between 1 and 100, inclusive, that cannot be written as the product of two consecutive positive integers. What is the 40th integer in her list?"
}
] | math | {
"style": "rule",
"ground_truth": "46"
} | {
"index": 4295,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Adjacent sides of Figure 1 are perpendicular. Four sides of Figure 1 are removed to form Figure 2. What is the total length, in units, of the segments in Figure 2?\n\n[asy]\ndraw((0,0)--(4,0)--(4,6)--(3,6)--(3,3)--(1,3)--(1,8)--(0,8)--cycle);\ndraw((7,8)--(7,0)--(11,0)--(11,6)-... | math | {
"style": "rule",
"ground_truth": "19"
} | {
"index": 4296,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Admiral Ackbar needs to send a 5-character message through hyperspace to the Rebels. Each character is a lowercase letter, and the same letter may appear more than once in a message. When the message is beamed through hyperspace, the characters come out in a random order. Ackba... | math | {
"style": "rule",
"ground_truth": "26"
} | {
"index": 4297,
"solution": "If there is more than one distinct letter sent in the message, then there will be at most a $1/5$ chance of transmitting the right message. So the message must consist of one letter repeated five times, so there are 26 possible messages."
} |
DeepScaleR | [
{
"role": "user",
"content": "Adnan is trying to remember his four-digit PIN. He is sure it contains the digits 5, 3, 7, and 0 but can't recall the order in which they appear. How many different arrangements are possible for his PIN?"
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 4298,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Adults made up $\\frac5{12}$ of the crowd of people at a concert. After a bus carrying $50$ more people arrived, adults made up $\\frac{11}{25}$ of the people at the concert. Find the minimum number of adults who could have been at the concert after the bus arrived."
}
] | math | {
"style": "rule",
"ground_truth": "154"
} | {
"index": 4299,
"solution": "Let $x$ be the number of people at the party before the bus arrives. We know that $x\\equiv 0\\pmod {12}$, as $\\frac{5}{12}$ of people at the party before the bus arrives are adults. Similarly, we know that $x + 50 \\equiv 0 \\pmod{25}$, as $\\frac{11}{25}$ of the people at the party ... |
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