data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "At the end of $1997$, Jason was one-third as old as his grandmother. The sum of the years in which they were born was $3852$. How old will Jason be at the end of $2004$?\nA) $41.5$\nB) $42.5$\nC) $43.5$\nD) $44.5$"
}
] | math | {
"style": "rule",
"ground_truth": "42.5"
} | {
"index": 5300,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the end of $1997$, the desert area in a certain region was $9\\times 10^{5}hm^{2}$ (note: $hm^{2}$ is the unit of area, representing hectares). Geologists started continuous observations from $1998$ to understand the changes in the desert area of this region. The observation... | math | {
"style": "rule",
"ground_truth": "2021"
} | {
"index": 5301,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the end of 1994, Walter was half as old as his grandmother. The sum of the years in which they were born was 3838. How old will Walter be at the end of 1999?"
}
] | math | {
"style": "rule",
"ground_truth": "55"
} | {
"index": 5302,
"solution": "1. **Assign variables to ages**: Let Walter's age in 1994 be $x$. Then, his grandmother's age in 1994 is $2x$ because Walter is half as old as his grandmother.\n\n2. **Set up the equation for their birth years**: Walter was born in $1994 - x$ and his grandmother was born in $1994 - 2x$... |
DeepScaleR | [
{
"role": "user",
"content": "At the end of a game, each of the five members of a basketball team shake hands with each of the five members of the other team, and all of the players shake hands with the two referees. How many handshakes occur?"
}
] | math | {
"style": "rule",
"ground_truth": "45"
} | {
"index": 5303,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the end of a professional bowling tournament, the top 5 bowlers have a playoff. First #5 bowls #4. The loser receives $5$th prize and the winner bowls #3 in another game. The loser of this game receives $4$th prize and the winner bowls #2. The loser of this game receives $3$... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 5304,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the end of a professional bowling tournament, the top 6 bowlers have a playoff. First #6 bowls #5. The loser receives $6^{th}$ prize and the winner bowls #4 in another game. The loser of this game receives $5^{th}$ prize and the winner bowls #3. The loser of this game receiv... | math | {
"style": "rule",
"ground_truth": "32"
} | {
"index": 5305,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the end of the day, a bakery had $\\frac{6}{7}$ of a pie left over. Louie, Duey and Huey split the pie, with each taking home the same amount of leftover pie. How much pie did Louie take home?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{7}"
} | {
"index": 5306,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the end of the school year, teachers of the third grade met with the parents of some of their students; exactly 31 people were present at this meeting. The Latin teacher was asked questions by 16 parents, the French teacher by 17 parents, the English teacher by 18 parents, a... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"index": 5307,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the end of the year 2000, Steve had $\\$100$ and Wayne had $\\$10000$. At the end of each following year, Steve had twice as much money as he did at the end of the previous year and Wayne had half as much money as he did at the end of the previous year. At the end of which y... | math | {
"style": "rule",
"ground_truth": "2004"
} | {
"index": 5308,
"solution": "We make a table of the total amount of money that each of Steve and Wayne have at the end of each year. After the year 2000, each entry in Steve's column is found by doubling the previous entry and each entry in Wayne's column is found by dividing the previous entry by 2. We stop when ... |
DeepScaleR | [
{
"role": "user",
"content": "At the end of the year, the Math Club decided to hold an election for which 5 equal officer positions were available. However, 16 candidates were nominated, of whom 7 were past officers. Of all possible elections of the officers, how many will have at least 1 of the past office... | math | {
"style": "rule",
"ground_truth": "4242"
} | {
"index": 5309,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the end of which year did Steve have more money than Wayne for the first time?"
}
] | math | {
"style": "rule",
"ground_truth": "2004"
} | {
"index": 5310,
"solution": "Steve's and Wayne's amounts of money double and halve each year, respectively. By 2004, Steve has more money than Wayne."
} |
DeepScaleR | [
{
"role": "user",
"content": "At the first site, high-class equipment was used, while at the second site, first-class equipment was used, with the amount of high-class equipment being less than that of the first-class. Initially, 30% of the equipment from the first site was transferred to the second site. T... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"index": 5311,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the first site, higher-class equipment was used, while at the second site, first-class equipment was used, with higher-class being less than first-class. Initially, 30% of the equipment from the first site was transferred to the second site. Then, 10% of the equipment at the... | math | {
"style": "rule",
"ground_truth": "17"
} | {
"index": 5312,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the grocery store last week, small boxes of facial tissue were priced at 4 boxes for $5. This week they are on sale at 5 boxes for $4. The percent decrease in the price per box during the sale was closest to"
}
] | math | {
"style": "rule",
"ground_truth": "35\\%"
} | {
"index": 5313,
"solution": "1. **Calculate the original price per box:**\n Last week, the boxes were sold at 4 boxes for $5. Therefore, the price per box last week was:\n \\[\n \\frac{5}{4} = 1.25 \\text{ dollars per box}\n \\]\n\n2. **Calculate the new price per box:**\n This week, the boxes are on sal... |
DeepScaleR | [
{
"role": "user",
"content": "At the grocery store, I bought $4$ different items. I brought $3$ identical bags, and handed them to the cashier. How many ways are there for the cashier to put the items I bought in the $3$ identical bags, assuming he might leave some of the bags empty?"
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 5314,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the height \\(BH\\) of triangle \\(ABC\\), a certain point \\(D\\) is marked. Line \\(AD\\) intersects side \\(BC\\) at point \\(E\\), and line \\(CD\\) intersects side \\(AB\\) at point \\(F\\). Points \\(G\\) and \\(J\\) are the projections of points \\(F\\) and \\(E\\) re... | math | {
"style": "rule",
"ground_truth": "\\sqrt{2}: 1"
} | {
"index": 5315,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the intersection of perpendicular roads, a highway from Moscow to Kazan intersects with a road from Vladimir to Ryazan. Dima and Tolya are traveling at constant speeds from Moscow to Kazan and from Vladimir to Ryazan, respectively.\n\nWhen Dima crossed the intersection, Toly... | math | {
"style": "rule",
"ground_truth": "1500"
} | {
"index": 5316,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the mall's food court, Crystal wants to buy a meal consisting of one entree, one drink and one dessert. The table below lists Crystal's favorite foods in the food court. How many distinct possible meals can she buy from these options?\n\n\\begin{tabular}{ |c | c | c | }\n\\h... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 5317,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the moment when Pierrot left the \"Commercial\" bar, heading to the \"Theatrical\" bar, Jeannot was leaving the \"Theatrical\" bar on his way to the \"Commercial\" bar. They were walking at constant (but different) speeds. When the vagabonds met, Pierrot proudly noted that h... | math | {
"style": "rule",
"ground_truth": "1000"
} | {
"index": 5318,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the mountain hut, the coach said, \"If we continue at this comfortable pace of $4 \\mathrm{~km}$ per hour, we will arrive at the station 45 minutes after the departure of our train.\"\n\nThen he pointed to a group that had just passed us: \"They are using poles, and therefor... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 5319,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the namesake festival, 45 Alexanders, 122 Borises, 27 Vasily, and several Gennady attended. At the beginning of the festival, all of them lined up so that no two people with the same name stood next to each other. What is the minimum number of Gennadys that could have attend... | math | {
"style": "rule",
"ground_truth": "49"
} | {
"index": 5320,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the rally commemorating the 60th anniversary of the Chinese people's victory in the War of Resistance against Japan, two schools each send 3 representatives to speak in turns, criticizing the heinous crimes committed by the Japanese aggressors and praising the heroic deeds o... | math | {
"style": "rule",
"ground_truth": "72"
} | {
"index": 5321,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the refreshment point, four athletes drank all the stock of Coke-Loco lemonade. If only athlete Bystrov had drunk half as much, one-tenth of the lemonade would have been left. If, additionally, athlete Shustrov had also drunk half as much, one-eighth of the lemonade would ha... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"index": 5322,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the round table, $10$ people are sitting, some of them are knights, and the rest are liars (knights always say pride, and liars always lie) . It is clear thath I have at least one knight and at least one liar. \nWhat is the largest number of those sitting at the table can s... | math | {
"style": "rule",
"ground_truth": "9"
} | {
"index": 5323,
"solution": "\nTo solve this problem, we need to maximize the number of people at a round table who can truthfully say: \"Both of my neighbors are knights.\" Considering the rules:\n- Knights always tell the truth.\n- Liars always lie.\n- At least one knight and one liar are present.\n\nLet's analy... |
DeepScaleR | [
{
"role": "user",
"content": "At the signal of the trainer, two ponies simultaneously started running uniformly along the outer circumference of the circus arena in opposite directions. The first pony ran slightly faster than the second and, by the time they met, had run 5 meters more than the second pony. ... | math | {
"style": "rule",
"ground_truth": "6.25"
} | {
"index": 5324,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At the start of this month, Mathilde and Salah each had 100 coins. For Mathilde, this was $25 \\%$ more coins than she had at the start of last month. For Salah, this was $20 \\%$ fewer coins than he had at the start of last month. What was the total number of coins that they h... | math | {
"style": "rule",
"ground_truth": "205"
} | {
"index": 5325,
"solution": "Suppose that Mathilde had $m$ coins at the start of last month and Salah had $s$ coins at the start of last month. From the given information, 100 is $25 \\%$ more than $m$, so $100=1.25 m$ which means that $m=\\frac{100}{1.25}=80$. From the given information, 100 is $20 \\%$ less than... |
DeepScaleR | [
{
"role": "user",
"content": "At the start of this month, Mathilde and Salah each had 100 coins. For Mathilde, this was 25% more coins than she had at the start of last month. For Salah, this was 20% fewer coins than he had at the start of last month. What was the total number of coins that they had at the ... | math | {
"style": "rule",
"ground_truth": "205"
} | {
"index": 5326,
"solution": "Suppose that Mathilde had $m$ coins at the start of last month and Salah had $s$ coins at the start of last month. From the given information, 100 is 25% more than $m$, so $100=1.25m$ which means that $m=\\frac{100}{1.25}=80$. From the given information, 100 is 20% less than $s$, so $1... |
DeepScaleR | [
{
"role": "user",
"content": "At the theater children get in for half price. The price for $5$ adult tickets and $4$ child tickets is $24.50$. How much would $8$ adult tickets and $6$ child tickets cost?"
}
] | math | {
"style": "rule",
"ground_truth": "38.50"
} | {
"index": 5327,
"solution": "1. **Define the variables:**\n Let $x$ be the price of an adult ticket. Then, the price of a child ticket is $\\frac{x}{2}$.\n\n2. **Set up the equation based on the given information:**\n The total cost for $5$ adult tickets and $4$ child tickets is $24.50. Therefore, we can write... |
DeepScaleR | [
{
"role": "user",
"content": "At time $0$ , an ant is at $(1,0)$ and a spider is at $(-1,0)$ . The ant starts walking counterclockwise around the unit circle, and the spider starts creeping to the right along the $x$ -axis. It so happens that the ant's horizontal speed is always half the spider's. W... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{14}}{4}"
} | {
"index": 5328,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At time $t=0,$ a ball is thrown downward at 24 feet per second from a height of 160 feet above the ground. The equation $h = -16t^2 - 24t +160$ describes the height (in feet) of the ball. In how many seconds will the ball hit the ground? Express your answer as a decimal."
}
... | math | {
"style": "rule",
"ground_truth": "2.5"
} | {
"index": 5329,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At what angle to the x-axis is the tangent to the graph of the function \\( g(x) = x^2 \\ln x \\) inclined at the point \\( x_0 = 1 \\)?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{4}"
} | {
"index": 5330,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At what point does the line $3y-4x=12$ intersect the $x$-axis? Express your answer as an ordered pair."
}
] | math | {
"style": "rule",
"ground_truth": "(-3,0)"
} | {
"index": 5331,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At what point does the line containing the points $(1, 7)$ and $(3, 11)$ intersect the $y$-axis? Express your answer as an ordered pair."
}
] | math | {
"style": "rule",
"ground_truth": "(0,5)"
} | {
"index": 5332,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At what value of $a$ do the graphs of $y=ax^2+3x+1$ and $y=-x-1$ intersect at exactly one point?"
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"index": 5333,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "At what value of $b$ do the graphs of $y=bx^2+5x+3$ and $y=-2x-3$ intersect at exactly one point?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{49}{24}"
} | {
"index": 5334,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Athletes A and B have probabilities of successfully jumping over a 2-meter high bar of 0.7 and 0.6, respectively. The outcomes of their jumps are independent of each other. Find:\n\n(Ⅰ) The probability that A succeeds on the third attempt.\n\n(Ⅱ) The probability that at least o... | math | {
"style": "rule",
"ground_truth": "0.3024"
} | {
"index": 5335,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Athletes A, B, and C, along with 4 volunteers, are to be arranged in a line. If A and B are next to each other and C is not at either end, determine the number of different ways to arrange them."
}
] | math | {
"style": "rule",
"ground_truth": "960"
} | {
"index": 5336,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Attach a single digit to the left and right of the eight-digit number 20222023 so that the resulting 10-digit number is divisible by 72. (Specify all possible solutions.)"
}
] | math | {
"style": "rule",
"ground_truth": "3202220232"
} | {
"index": 5337,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Attempt to obtain one billion (1,000,000,000) by multiplying two integers, each of which contains no zeros."
}
] | math | {
"style": "rule",
"ground_truth": "512 * 1953125"
} | {
"index": 5338,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Augustin has six $1 \\times 2 \\times \\pi$ bricks. He stacks them, one on top of another, to form a tower six bricks high. Each brick can be in any orientation so long as it rests flat on top of the next brick below it (or on the floor). How many distinct heights of towers can... | math | {
"style": "rule",
"ground_truth": "28"
} | {
"index": 5339,
"solution": "If there are $k$ bricks which are placed so that they contribute either 1 or 2 height, then the height of these $k$ bricks can be any integer from $k$ to $2 k$. Furthermore, towers with different values of $k$ cannot have the same height. Thus, for each $k$ there are $k+1$ possible tow... |
DeepScaleR | [
{
"role": "user",
"content": "Aunt Anna is $42$ years old. Caitlin is $5$ years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin?"
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"index": 5340,
"solution": "1. **Determine Brianna's Age:**\n Given that Aunt Anna is $42$ years old and Brianna is half as old as Aunt Anna, we calculate Brianna's age as follows:\n \\[\n \\text{Brianna's age} = \\frac{1}{2} \\times \\text{Aunt Anna's age} = \\frac{1}{2} \\times 42 = 21 \\text{ years}\n ... |
DeepScaleR | [
{
"role": "user",
"content": "Aunt Wang needs 3 minutes to cut a paper-cut for window decoration. After cutting each one, she rests for 1 minute. She starts cutting at 9:40. After cutting 10 paper-cuts, it is \\_\\_\\_\\_ hour \\_\\_\\_\\_ minute."
}
] | math | {
"style": "rule",
"ground_truth": "10:19"
} | {
"index": 5341,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Auston is 60 inches tall. Using the conversion 1 inch = 2.54 cm, how tall is Auston in centimeters? Express your answer as a decimal to the nearest tenth."
}
] | math | {
"style": "rule",
"ground_truth": "152.4"
} | {
"index": 5342,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Automobile license plates for a state consist of four letters followed by a dash and two single digits. How many different license plate combinations are possible if exactly one letter is repeated exactly once, but digits cannot be repeated? [asy]\nsize(150);\ndraw((0,0)--(0,5)... | math | {
"style": "rule",
"ground_truth": "8,\\!424,\\!000"
} | {
"index": 5343,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Automobile license plates for a state consist of four letters followed by a dash and two single digits. How many different license plate combinations are possible if exactly two letters are repeated once each (meaning two pairs of identical letters), and digits can be repeated?... | math | {
"style": "rule",
"ground_truth": "390000"
} | {
"index": 5344,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Automobile license plates for a state consist of three letters followed by a dash and three single digits. How many different license plate combinations are possible if exactly two letters are each repeated once (yielding a total of four letters where two are the same), and the... | math | {
"style": "rule",
"ground_truth": "877,500"
} | {
"index": 5345,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Ava and Tiffany participate in a knockout tournament consisting of a total of 32 players. In each of 5 rounds, the remaining players are paired uniformly at random. In each pair, both players are equally likely to win, and the loser is knocked out of the tournament. The probabi... | math | {
"style": "rule",
"ground_truth": "116"
} | {
"index": 5346,
"solution": "Each match eliminates exactly one player, so exactly $32-1=31$ matches are played, each of which consists of a different pair of players. Among the $\\binom{32}{2}=\\frac{32 \\cdot 31}{2}=496$ pairs of players, each pair is equally likely to play each other at some point during the tou... |
DeepScaleR | [
{
"role": "user",
"content": "Ava's machine takes four-digit positive integers as input. When the four-digit integer $ABCD$ is input, the machine outputs the integer $A \times B + C \times D$. What is the output when the input is 2023?"
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"index": 5347,
"solution": "Using the given rule, the output of the machine is $2 \times 0 + 2 \times 3 = 0 + 6 = 6$."
} |
DeepScaleR | [
{
"role": "user",
"content": "Aws plays a solitaire game on a fifty-two card deck: whenever two cards of the same color are adjacent, he can remove them. Aws wins the game if he removes all the cards. If Aws starts with the cards in a random order, what is the probability for him to win?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\left( \\binom{26}{13} \\right)^2}{\\binom{52}{26}}"
} | {
"index": 5348,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Azar and Carl play a game of tic-tac-toe. Azar places an \\(X\\) in one of the boxes in a \\(3\\)-by-\\(3\\) array of boxes, then Carl places an \\(O\\) in one of the remaining boxes. After that, Azar places an \\(X\\) in one of the remaining boxes, and so on until all boxes ar... | math | {
"style": "rule",
"ground_truth": "148"
} | {
"index": 5349,
"solution": "To solve this problem, we need to count the number of ways the tic-tac-toe board can be filled such that Carl wins by placing his third $O$ in a winning position, and there are exactly 3 $X$s and 3 $O$s on the board. We will consider two cases based on the arrangement of the $O$s: eith... |
DeepScaleR | [
{
"role": "user",
"content": "Azar, Carl, Jon, and Sergey are the four players left in a singles tennis tournament. They are randomly assigned opponents in the semifinal matches, and the winners of those matches play each other in the final match to determine the winner of the tournament. When Azar plays Ca... | math | {
"style": "rule",
"ground_truth": "125"
} | {
"index": 5350,
"solution": "Let $A$ be Azar, $C$ be Carl, $J$ be Jon, and $S$ be Sergey. The $4$ circles represent the $4$ players, and the arrow is from the winner to the loser with the winning probability as the label.\n This problem can be solved by using $2$ cases.\n$\\textbf{Case 1:}$ $C$'s opponent for the ... |
DeepScaleR | [
{
"role": "user",
"content": "Azmi has four blocks, each in the shape of a rectangular prism and each with dimensions $2 \times 3 \times 6$. She carefully stacks these four blocks on a flat table to form a tower that is four blocks high. What is the number of possible heights for this tower?"
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 5351,
"solution": "The height of each block is 2, 3 or 6. Thus, the total height of the tower of four blocks is the sum of the four heights, each of which equals 2, 3 or 6. If 4 blocks have height 6, the total height equals $4 \times 6=24$. If 3 blocks have height 6, the fourth block has height 3 or 2. T... |
DeepScaleR | [
{
"role": "user",
"content": "Back in 1930, Tillie had to memorize her multiplication facts from $0 \\times 0$ to $12 \\times 12$. The multiplication table she was given had rows and columns labeled with the factors, and the products formed the body of the table. To the nearest hundredth, what fraction of t... | math | {
"style": "rule",
"ground_truth": "0.21"
} | {
"index": 5352,
"solution": "1. **Determine the total number of products in the table**: \n The multiplication table ranges from $0 \\times 0$ to $12 \\times 12$. Since each factor (both rows and columns) ranges from $0$ to $12$, there are $13$ options for each factor (including $0$). Therefore, the total number... |
DeepScaleR | [
{
"role": "user",
"content": "Bag $A$ contains two 10 yuan bills and three 1 yuan bills, and Bag $B$ contains four 5 yuan bills and three 1 yuan bills. Two bills are randomly drawn from each bag. What is the probability that the total value of the bills remaining in Bag $A$ is greater than the total value o... | math | {
"style": "rule",
"ground_truth": "9/35"
} | {
"index": 5353,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Bag A has 3 white marbles and 4 black marbles. Bag B has 6 yellow marbles and 4 blue marbles. Bag C has 2 yellow marbles and 5 blue marbles. A marble is drawn at random from Bag A. If it is white, a marble is drawn at random from Bag B, otherwise, if it is black, a marble i... | math | {
"style": "rule",
"ground_truth": "\\frac{103}{245}"
} | {
"index": 5354,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Bag A has three chips labeled 1, 3, and 5. Bag B has three chips labeled 2, 4, and 6. If one chip is drawn from each bag, how many different values are possible for the sum of the two numbers on the chips?"
}
] | math | {
"style": "rule",
"ground_truth": "5"
} | {
"index": 5355,
"solution": "1. **Identify the chips in each bag:**\n - Bag A contains odd numbers: 1, 3, 5.\n - Bag B contains even numbers: 2, 4, 6.\n\n2. **Understand the nature of sums:**\n - The sum of an odd number (from Bag A) and an even number (from Bag B) is always odd.\n\n3. **Calculate the possib... |
DeepScaleR | [
{
"role": "user",
"content": "Bangladesh National Mathematical Olympiad 2016 Higher Secondary\n\n<u>**Problem 2:**</u>\n(a) How many positive integer factors does $6000$ have?\n\n(b) How many positive integer factors of $6000$ are not perfect squares?"
}
] | math | {
"style": "rule",
"ground_truth": "34"
} | {
"index": 5356,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Bao was given $\\$1,\\!000$ for his birthday. He decided to invest the money in a bank account that earns $10\\%$ interest, compounded annually. In dollars, how much total interest will Bao have earned 3 years later?"
}
] | math | {
"style": "rule",
"ground_truth": "331"
} | {
"index": 5357,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Barbara, Edward, Abhinav, and Alex took turns writing this test. Working alone, they could finish it in $10$ , $9$ , $11$ , and $12$ days, respectively. If only one person works on the test per day, and nobody works on it unless everyone else has spent at least as many day... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 5358,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Barney Schwinn noted that his bike's odometer showed a reading of $2332$, a palindrome. After riding for $5$ hours one day and $4$ hours the next day, he observed that the odometer displayed another palindrome, $2552$. Calculate Barney's average riding speed during this period.... | math | {
"style": "rule",
"ground_truth": "\\frac{220}{9}"
} | {
"index": 5359,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Barney Schwinn notices that the odometer on his bicycle reads $1441$, a palindrome, because it reads the same forward and backward. After riding $4$ more hours that day and $6$ the next, he notices that the odometer shows another palindrome, $1661$. What was his average speed i... | math | {
"style": "rule",
"ground_truth": "22"
} | {
"index": 5360,
"solution": "1. **Identify the initial and final odometer readings**: Barney's initial odometer reading is $1441$ and after riding for some time, the final reading is $1661$.\n\n2. **Calculate the total distance traveled**: \n \\[\n \\text{Distance} = \\text{Final odometer reading} - \\text{Ini... |
DeepScaleR | [
{
"role": "user",
"content": "Baron Munchausen told a story. \"There were a whole crowd of us. We reached a crossroads. Then half of our group turned left, a third turned right, and a fifth went straight.\" \"But wait, the Duke remarked, the sum of half, a third, and a fifth isn't equal to one, so you are l... | math | {
"style": "rule",
"ground_truth": "37"
} | {
"index": 5361,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Barry has three sisters. The average age of the three sisters is 27. The average age of Barry and his three sisters is 28. What is Barry's age?"
}
] | math | {
"style": "rule",
"ground_truth": "31"
} | {
"index": 5362,
"solution": "Since the average age of the three sisters is 27, then the sum of their ages is $3 \times 27=81$. When Barry is included the average age of the four people is 28, so the sum of the ages of the four people is $4 \times 28=112$. Barry's age is the difference between the sum of the ages o... |
DeepScaleR | [
{
"role": "user",
"content": "Barry picks infinitely many points inside a unit circle, each independently and uniformly at random, $P_{1}, P_{2}, \\ldots$ Compute the expected value of $N$, where $N$ is the smallest integer such that $P_{N+1}$ is inside the convex hull formed by the points $P_{1}, P_{2}, \\... | math | {
"style": "rule",
"ground_truth": "6.54"
} | {
"index": 5363,
"solution": "Clearly, $N \\geq 3$, and let's scale the circle to have area 1. We can see that the probability to not reach $N=4$ is equal to the probability that the fourth point is inside the convex hull of the past three points. That is, the probability is just one minus the expected area of thos... |
DeepScaleR | [
{
"role": "user",
"content": "Barry wrote 6 different numbers, one on each side of 3 cards, and laid the cards on a table, as shown. The sums of the two numbers on each of the three cards are equal. The three numbers on the hidden sides are prime numbers. What is the average of the hidden prime numbers? [as... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 5364,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Base prime representation of a natural number is defined using the exponents of its prime factorization as follows. Each place in a base prime represents a prime number, and it is occupied by the corresponding exponent of that prime, starting on the right side with the smallest... | math | {
"style": "rule",
"ground_truth": "220"
} | {
"index": 5365,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Based on the data provided, what were the average daily high and low temperatures in Addington from September 15th, 2008 to September 21st, 2008, inclusive? The high temperatures in degrees Fahrenheit for these days are 49, 62, 58, 57, 46, 55, 60 and the corresponding low tempe... | math | {
"style": "rule",
"ground_truth": "42.6"
} | {
"index": 5366,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Based on the definition of the derivative, find $f^{\\prime}(0)$:\n\n$$\nf(x)=\\left\\{\\begin{array}{c}\n\\frac{2^{\\operatorname{tg} x}-2^{\\sin x}}{x^{2}}, x \\neq 0 \\\\\n0, x=0\n\\end{array}\\right.\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\ln \\sqrt{2}"
} | {
"index": 5367,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "BdMO National 2016 Higher Secondary \n\n<u>**Problem 4:**</u>\nConsider the set of integers $ \\left \\{ 1, 2, ......... , 100 \\right \\} $ . Let $ \\left \\{ x_1, x_2, ......... , x_{100} \\right \\}$ be some arbitrary arrangement of the integers $ \\left \\{ 1, 2, ...... | math | {
"style": "rule",
"ground_truth": "198"
} | {
"index": 5368,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Beatrix is going to place six rooks on a $6 \\times 6$ chessboard where both the rows and columns are labeled $1$ to $6$; the rooks are placed so that no two rooks are in the same row or the same column. The $value$ of a square is the sum of its row number and column number. Th... | math | {
"style": "rule",
"ground_truth": "371"
} | {
"index": 5369,
"solution": "So we first count the number of permutations with score $\\ge 2$. This is obviously $6!=720$. Then, the number of permutations with score $\\ge 3$ can also be computed: in the first column, there are five ways to place a rook- anywhere but the place with score $1$. In the next column, ... |
DeepScaleR | [
{
"role": "user",
"content": "Beatriz loves odd numbers. How many numbers between 0 and 1000 can she write using only odd digits?"
}
] | math | {
"style": "rule",
"ground_truth": "155"
} | {
"index": 5370,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Bees, in processing flower nectar into honey, remove a significant amount of water. Research has shown that nectar usually contains about $70\\%$ water, while the honey produced from it contains only $17\\%$ water. How many kilograms of nectar must bees process to obtain 1 kilo... | math | {
"style": "rule",
"ground_truth": "2.77"
} | {
"index": 5371,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Before Ashley started a three-hour drive, her car's odometer reading was 29792, a palindrome. (A palindrome is a number that reads the same way from left to right as it does from right to left). At her destination, the odometer reading was another palindrome. If Ashley never ex... | math | {
"style": "rule",
"ground_truth": "70 \\frac{1}{3}"
} | {
"index": 5372,
"solution": "1. **Identify the range of possible distances traveled**: Ashley's maximum speed is 75 miles per hour, and she drove for 3 hours. Therefore, the maximum distance she could have traveled is:\n \\[\n 3 \\times 75 = 225 \\text{ miles}\n \\]\n\n2. **Determine the next possible palind... |
DeepScaleR | [
{
"role": "user",
"content": "Before starting to paint, Bill had $130$ ounces of blue paint, $164$ ounces of red paint, and $188$ ounces of white paint. Bill painted four equally sized stripes on a wall, making a blue stripe, a red stripe, a white stripe, and a pink stripe. Pink is a mixture of red and whit... | math | {
"style": "rule",
"ground_truth": "114"
} | {
"index": 5373,
"solution": "Just like in solution 1, we note that all colors will be used equally, except for the pink stripe. This must bring red and white down to $130$ each, so $34$ red and $58$ white are used, making for a total of $92$ for the pink stripe. Thus, the other stripes also use $92$. The answer is... |
DeepScaleR | [
{
"role": "user",
"content": "Before the district play, the Unicorns had won $45$% of their basketball games. During district play, they won six more games and lost two, to finish the season having won half their games. How many games did the Unicorns play in all?"
}
] | math | {
"style": "rule",
"ground_truth": "48"
} | {
"index": 5374,
"solution": "1. Let $y$ be the total number of games the Unicorns played before the district play, and $x$ be the number of games they won. According to the problem, they won 45% of these games, so we have the equation:\n \\[\n \\frac{x}{y} = 0.45\n \\]\n Multiplying both sides by $y$ gives... |
DeepScaleR | [
{
"role": "user",
"content": "Before the lesson, Nestor Petrovich wrote several words on the board. When the bell rang for the lesson, he noticed a mistake in the first word. If he corrects the mistake in the first word, the words with mistakes will constitute $24\\%$, and if he erases the first word from t... | math | {
"style": "rule",
"ground_truth": "28"
} | {
"index": 5375,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Before the soccer match between the \"North\" and \"South\" teams, five predictions were made:\n\na) There will be no draw;\n\nb) \"South\" will concede goals;\n\nc) \"North\" will win;\n\nd) \"North\" will not lose;\n\ne) Exactly 3 goals will be scored in the match.\n\nAfter t... | math | {
"style": "rule",
"ground_truth": "2-1"
} | {
"index": 5376,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Before the soccer match between the teams \"North\" and \"South\", five predictions were made:\n\na) There will be no draw;\n\nb) Goals will be scored against \"South\";\n\nc) \"North\" will win;\n\nd) \"North\" will not lose;\n\ne) Exactly 3 goals will be scored in the match.\... | math | {
"style": "rule",
"ground_truth": "1:2"
} | {
"index": 5377,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Begin by adding 78.652 to 24.3981. After adding, subtract 0.025 from the result. Finally, round the answer to the nearest hundredth."
}
] | math | {
"style": "rule",
"ground_truth": "103.03"
} | {
"index": 5378,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Beginner millionaire Bill buys a bouquet of 7 roses for $20. Then, he can sell a bouquet of 5 roses for $20 per bouquet. How many bouquets does he need to buy to \"earn\" a difference of $1000?"
}
] | math | {
"style": "rule",
"ground_truth": "125"
} | {
"index": 5379,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Beginning with a $3 \\mathrm{~cm}$ by $3 \\mathrm{~cm}$ by $3 \\mathrm{~cm}$ cube, a $1 \\mathrm{~cm}$ by $1 \\mathrm{~cm}$ by $1 \\mathrm{~cm}$ cube is cut from one corner and a $2 \\mathrm{~cm}$ by $2 \\mathrm{~cm}$ by $2 \\mathrm{~cm}$ cube is cut from the opposite corner. I... | math | {
"style": "rule",
"ground_truth": "54"
} | {
"index": 5380,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Bella begins to walk from her house toward her friend Ella's house. At the same time, Ella begins to ride her bicycle toward Bella's house. They each maintain a constant speed, and Ella rides $5$ times as fast as Bella walks. The distance between their houses is $2$ miles, whic... | math | {
"style": "rule",
"ground_truth": "704"
} | {
"index": 5381,
"solution": "1. **Understanding the problem**: Bella and Ella start moving towards each other from their respective houses, which are 2 miles apart. Bella walks and Ella rides a bicycle, with Ella's speed being 5 times Bella's speed. We need to find how many steps Bella takes before they meet.\n\n2... |
DeepScaleR | [
{
"role": "user",
"content": "Below is a portion of the graph of a function, $y=E(x)$:\n\n[asy]\nimport graph; size(8cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-4.5,xmax=4.5,ymin=-0.99,ymax=6.5;\n\npen cqcqcq=rgb(0.75,0.75,0.75);\n/*grid*/ pen gs=linewid... | math | {
"style": "rule",
"ground_truth": "5"
} | {
"index": 5382,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is a portion of the graph of a function, $y=f(x)$:\n\n[asy]\nimport graph; size(8cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.25,xmax=5.25,ymin=-3.25,ymax=4.25;\n\npen cqcqcq=rgb(0.75,0.75,0.75);\n\n/*grid*/ pen gs=li... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"index": 5383,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is a portion of the graph of a function, $y=h(x)$:\n\n[asy]\nimport graph; size(8cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-4.25,xmax=4.25,ymin=-7.25,ymax=6.25;\n\npen cqcqcq=rgb(0.75,0.75,0.75);\n\n/*grid*/ pen gs=li... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"index": 5384,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is a portion of the graph of a function, $y=p(x)$:\n\n[asy]\nimport graph; size(6cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.5,xmax=3.5,ymin=-4.25,ymax=6.25;\n\npen cqcqcq=rgb(0.75,0.75,0.75);\n/*grid*/ pen gs=linewi... | math | {
"style": "rule",
"ground_truth": "4"
} | {
"index": 5385,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is a portion of the graph of a function, $y=u(x)$:\n\n[asy]\nimport graph; size(5.5cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.25,xmax=3.25,ymin=-3.25,ymax=3.25;\n\npen cqcqcq=rgb(0.75,0.75,0.75);\n\n/*grid*/ pen gs=... | math | {
"style": "rule",
"ground_truth": "0"
} | {
"index": 5386,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is a portion of the graph of a quadratic function, $y=p(x)=dx^2 + ex + f$:\n\nThe value of $p(12)$ is an integer. The graph's axis of symmetry is $x = 10.5$, and the graph passes through the point $(3, -5)$. Based on this, what is the value of $p(12)$?"
}
] | math | {
"style": "rule",
"ground_truth": "-5"
} | {
"index": 5387,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is a portion of the graph of a quadratic function, $y=q(x)=ax^2+bx+c$:\n\n[asy]\nimport graph; size(8cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-0.99,xmax=10.5,ymin=-5.5,ymax=5.5;\n\npen cqcqcq=rgb(0.75,0.75,0.75);\n/*... | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"index": 5388,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is a portion of the graph of an invertible function, $y=f(x)$:\n\n[asy]\nimport graph; size(8cm); real lsf=0.5; pen dps=linewidth(0.7)+fontsize(10); defaultpen(dps); pen ds=black; real xmin=-3.25,xmax=3.25,ymin=-6.25,ymax=7.25;\n\npen cqcqcq=rgb(0.75,0.75,0.75);\n\n/*grid... | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"index": 5389,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is an arithmetic expression where 9 Chinese characters represent the digits 1 to 9, and different characters represent different digits. What is the maximum possible value for the expression?\n\n草 $\\times$ 绿 + 花儿 $\\times$ 红 + 春光明 $\\times$ 媚"
}
] | math | {
"style": "rule",
"ground_truth": "6242"
} | {
"index": 5390,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is pictured a regular seven-pointed star. Find the measure of angle \\( a \\) in radians."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5\\pi}{7}"
} | {
"index": 5391,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is pictured a regular seven-pointed star. Find the measure of angle \\(a\\) in radians."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5\\pi}{7}"
} | {
"index": 5392,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is the graph of $y = a \\csc bx$ for some positive constants $a$ and $b.$ Find $a.$\n\n[asy]import TrigMacros;\n\nsize(500);\n\nreal g(real x)\n{\n\treturn 2*csc(x/3);\n}\n\ndraw(graph(g,-6*pi + 0.01, -3*pi - 0.01),red);\ndraw(graph(g,-3*pi + 0.01,-0.01),red);\ndraw(grap... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"index": 5393,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is the graph of $y = a \\sin (bx + c) + d$ for some positive constants $a,$ $b,$ $c,$ and $d.$ Find $a.$\n\n[asy]import TrigMacros;\n\nsize(400);\n\nreal f(real x)\n{\n\treturn 2*sin(3*x + pi) + 1;\n}\n\ndraw(graph(f,-3*pi,3*pi,n=700,join=operator ..),red);\ntrig_axes(-3... | math | {
"style": "rule",
"ground_truth": "2"
} | {
"index": 5394,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is the graph of $y = a \\sin (bx + c) + d$ for some positive constants $a,$ $b,$ $c,$ and $d.$ Find $b.$\n\n[asy]import TrigMacros;\n\nsize(400);\n\nreal f(real x)\n{\n\treturn 2*sin(3*x + pi) + 1;\n}\n\ndraw(graph(f,-3*pi,3*pi,n=700,join=operator ..),red);\ntrig_axes(-3... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"index": 5395,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is the graph of $y = a \\sin (bx + c) + d$ for some positive constants $a,$ $b,$ $c,$ and $d.$ Find $d.$\n\n[asy]import TrigMacros;\n\nsize(400);\n\nreal f(real x)\n{\n\treturn 2*sin(3*x + pi) + 1;\n}\n\ndraw(graph(f,-3*pi,3*pi,n=700,join=operator ..),red);\ntrig_axes(-3... | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 5396,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is the graph of $y = a \\sin (bx + c)$ for some constants $a$, $b$, and $c$. Assume $a>0$ and $b>0$. Find the smallest possible value of $c$ if it is given that the graph reaches its minimum at $x = 0$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3\\pi}{2}"
} | {
"index": 5397,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is the graph of $y = a \\sin bx$ for some constants $a < 0$ and $b > 0.$ Find $a.$\n\n[asy]import TrigMacros;\n\nsize(400);\n\nreal g(real x)\n{\n\treturn (-2*sin(x/3));\n}\n\ndraw(graph(g,-3*pi,3*pi,n=700,join=operator ..),red);\ntrig_axes(-3*pi,3*pi,-3,3,pi/2,1);\nlaye... | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"index": 5398,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Below is the graph of $y = a \\tan bx$ for some positive constants $a$ and $b.$ Find $ab.$\n\n[asy]import TrigMacros;\n\nsize(250);\n\nreal g(real x)\n{\n\treturn 2*tan(3/2*x);\n}\n\ndraw(graph(g,-pi + 0.01,-pi/3 - 0.01),red);\ndraw(graph(g,-pi/3 + 0.01,pi/3 - 0.01),red);\ndra... | math | {
"style": "rule",
"ground_truth": "3"
} | {
"index": 5399,
"solution": ""
} |
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