data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "A square with side length 8 is cut in half, creating two congruent rectangles. What are the dimensions of one of these rectangles?"
}
] | math | {
"style": "rule",
"ground_truth": "4 \\times 8"
} | {
"index": 3700,
"solution": "1. **Identify the original dimensions of the square**: The square has a side length of 8 units. Therefore, each side of the square is 8 units long.\n\n2. **Understand the effect of cutting the square in half**: When the square is cut in half, one dimension is halved while the other rem... |
DeepScaleR | [
{
"role": "user",
"content": "A square with side length \\(10 \\text{ cm}\\) is drawn on a piece of paper. How many points on the paper are exactly \\(10 \\text{ cm}\\) away from two of the vertices of this square?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 3701,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A square with sides 6 inches is shown. If $P$ is a point such that the segment $\\overline{PA}$, $\\overline{PB}$, $\\overline{PC}$ are equal in length, and segment $\\overline{PC}$ is perpendicular to segment $\\overline{FD}$, what is the area, in square inches, of triangle $A... | math | {
"style": "rule",
"ground_truth": "\\dfrac{27}{4}"
} | {
"index": 3702,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A square with sides 8 inches is shown. If $Q$ is a point such that the segments $\\overline{QA}$, $\\overline{QB}$, $\\overline{QC}$ are equal in length, and segment $\\overline{QC}$ is perpendicular to segment $\\overline{HD}$, find the area, in square inches, of triangle $AQB... | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 3703,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A square with sides of 10 inches is shown. If $P$ is a point such that the segments $\\overline{PA}$, $\\overline{PB}$, and $\\overline{PC}$ are equal in length, and segment $\\overline{PC}$ is perpendicular to segment $\\overline{GD}$, what is the area, in square inches, of tr... | math | {
"style": "rule",
"ground_truth": "\\frac{75}{4}"
} | {
"index": 3704,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A square with sides of length $1$ is divided into two congruent trapezoids and a pentagon, which have equal areas, by joining the center of the square with points on three of the sides, as shown. Find $x$, the length of the longer parallel side of each trapezoid."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{6}"
} | {
"index": 3705,
"solution": "\nLet's denote the square as $ABCD$ with side length $1$. Assume the center of the square is $O$ and the points on the sides where $O$ connects are $P$, $Q$, and $R$ on sides $AB$, $BC$, and $CD$ respectively. The trapezoids are formed by $APRO$ and $CQRO$, and the pentagon is $BQROP$.... |
DeepScaleR | [
{
"role": "user",
"content": "A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floor?"
}
] | math | {
"style": "rule",
"ground_truth": "361"
} | {
"index": 3706,
"solution": "1. **Understanding the problem**: We are given a square floor covered with congruent square tiles, and the total number of tiles on the two diagonals is 37. We need to find the total number of tiles covering the floor.\n\n2. **Analyzing the diagonals**: The diagonals of a square inters... |
DeepScaleR | [
{
"role": "user",
"content": "A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is 88 and the floor forms a perfect square with an even side length, find the total number of tiles that cover the floor."
}
] | math | {
"style": "rule",
"ground_truth": "1936"
} | {
"index": 3707,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A squirrel travels at a constant 4 miles per hour. How long does it take for this squirrel to travel 1 mile? Express your answer in minutes."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 3708,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A stack of $2000$ cards is labelled with the integers from $1$ to $2000,$ with different integers on different cards. The cards in the stack are not in numerical order. The top card is removed from the stack and placed on the table, and the next card is moved to the bottom of t... | math | {
"style": "rule",
"ground_truth": "927"
} | {
"index": 3709,
"solution": "To simplify matters, we want a power of $2$. Hence, we will add $48$ 'fake' cards which we must discard in our actual count. Using similar logic as Solution 1, we find that 1999 has position $1024$ in a $2048$ card stack, where the fake cards towards the front.\n Let the fake cards hav... |
DeepScaleR | [
{
"role": "user",
"content": "A stack of logs has 12 logs on the bottom row, and one less in each successive row, ending with three logs at the top. How many logs are in the stack?"
}
] | math | {
"style": "rule",
"ground_truth": "75"
} | {
"index": 3710,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A stack of logs has 15 logs on the bottom row, and each successive row has two fewer logs, ending with five special logs at the top. How many total logs are in the stack, and how many are the special logs?"
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 3711,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A stacking of circles in the plane consists of a base, or some number of unit circles centered on the $x$-axis in a row without overlap or gaps, and circles above the $x$-axis that must be tangent to two circles below them (so that if the ends of the base were secured and gravi... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 3712,
"solution": "$C(4)=14$."
} |
DeepScaleR | [
{
"role": "user",
"content": "A stalker throws a small nut from the Earth's surface at an angle of $\\alpha=30^{\\circ}$ to the horizontal with an initial speed $v_{0}=10 \\, \\mathrm{m}/\\mathrm{s}$. The normal acceleration due to gravity is $g=10 \\, \\mathrm{m}/\\mathrm{s}^{2}$. At the highest point of i... | math | {
"style": "rule",
"ground_truth": "250"
} | {
"index": 3713,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A stalker, to detect a gravitational anomaly (an area where the acceleration due to gravity changes sharply in magnitude), throws a small nut from the surface of the Earth at an angle \\(\\alpha = 30^\\circ\\) to the horizontal with a speed \\(v_0 = 20 \\, \\text{m/s}\\). The n... | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 3714,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard $n$-sided die has $n$ sides labeled 1 to $n$. Luis, Luke, and Sean play a game in which they roll a fair standard 4-sided die, a fair standard 6-sided die, and a fair standard 8-sided die, respectively. They lose the game if Luis's roll is less than Luke's roll, and ... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"index": 3715,
"solution": "We perform casework on Luke's roll. If Luke rolls $n$, with $2 \\leq n \\leq 5$, then the probability Luis rolls less than Luke is $\\frac{n-1}{4}$, and the probability Sean rolls more than Luke is $\\frac{8-n}{8}$. If Luke rolls 6 then Luis will definitely roll less than Luke, and Sea... |
DeepScaleR | [
{
"role": "user",
"content": "A standard 52-card deck contains cards of 4 suits and 13 numbers, with exactly one card for each pairing of suit and number. If Maya draws two cards with replacement from this deck, what is the probability that the two cards have the same suit or have the same number, but not b... | math | {
"style": "rule",
"ground_truth": "15/52"
} | {
"index": 3716,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\\spadesuit$, $\\heartsuit$, $\\diamondsuit$, and $\\clubsuit$), such that there is exactly one card for any given rank and suit. Two of the suits ($\\spadesuit$ and $\\... | math | {
"style": "rule",
"ground_truth": "\\dfrac14"
} | {
"index": 3717,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\\spadesuit$, $\\heartsuit$, $\\diamondsuit$, and $\\clubsuit$), such that there is exactly one card for any given rank and suit. Two of the suits ($\\spadesuit$ and $\\... | math | {
"style": "rule",
"ground_truth": "\\dfrac{1}{13}"
} | {
"index": 3718,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\\spadesuit$, $\\heartsuit$, $\\diamondsuit$, and $\\clubsuit$), such that there is exactly one card for any given rank and suit. Two of the suits ($\\spadesuit$ and $\\... | math | {
"style": "rule",
"ground_truth": "\\dfrac{13}{51}"
} | {
"index": 3719,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\\spadesuit$, $\\heartsuit$, $\\diamondsuit$, and $\\clubsuit$), such that there is exactly one card for any given rank and suit. Two of the suits ($\\spadesuit$ and $\\... | math | {
"style": "rule",
"ground_truth": "\\dfrac{1}{52}"
} | {
"index": 3720,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\\spadesuit$, $\\heartsuit$, $\\diamondsuit$, and $\\clubsuit$), such that there is exactly one card for any given rank and suit. Two of the suits ($\\spadesuit$ and $\\... | math | {
"style": "rule",
"ground_truth": "\\dfrac{11}{850}"
} | {
"index": 3721,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard deck of 52 cards is arranged randomly. What is the probability that the top three cards alternate in color, starting with a red card, then a black card, followed by another red card?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{13}{102}"
} | {
"index": 3722,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard deck of 52 cards is divided into 4 suits, with each suit containing 13 cards. Two of these suits are red, and the other two are black. The deck is shuffled, placing the cards in random order. What is the probability that the first three cards drawn from the deck are ... | math | {
"style": "rule",
"ground_truth": "\\frac{40}{85}"
} | {
"index": 3723,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard deck of 52 cards is randomly arranged. What is the probability that the top three cards are $\\spadesuit$, $\\heartsuit$, and $\\spadesuit$ in that sequence?"
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{78}{5100}"
} | {
"index": 3724,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard deck of 54 playing cards (with four cards of each of thirteen ranks, as well as two Jokers) is shuffled randomly. Cards are drawn one at a time until the first queen is reached. What is the probability that the next card is also a queen?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{27}"
} | {
"index": 3725,
"solution": "Since the four queens are equivalent, we can compute the probability that a specific queen, say the queen of hearts, is right after the first queen. Remove the queen of hearts; then for every ordering of the 53 other cards, there are 54 locations for the queen of hearts, and exactly on... |
DeepScaleR | [
{
"role": "user",
"content": "A standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. Two of the suits ($\\heartsuit$ and $\\diamondsuit$, called 'hearts' and 'diamonds') are red, the other two ($\\spadesuit$ and $\\clubsuit$, called 'spades' and 'clubs') are black. The car... | math | {
"style": "rule",
"ground_truth": "2652"
} | {
"index": 3726,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. Two of the suits ($\\heartsuit$ and $\\diamondsuit$, called `hearts' and `diamonds') are red, the other two ($\\spadesuit$ and $\\clubsuit$, called `spades' and `clubs') are black. The car... | math | {
"style": "rule",
"ground_truth": "\\frac{25}{102}"
} | {
"index": 3727,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. Two of the suits ($\\heartsuit$ and $\\diamondsuit$) are red, and the other two ($\\spadesuit$ and $\\clubsuit$) are black. The cards in the deck are shuffled. What is the probability that t... | math | {
"style": "rule",
"ground_truth": "\\frac{169}{2652}"
} | {
"index": 3728,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard die is rolled consecutively two times. Calculate the probability that the face-up numbers are adjacent natural numbers."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{18}"
} | {
"index": 3729,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard die is rolled eight times. What is the probability that the product of all eight rolls is divisible by 4?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{247}{256}"
} | {
"index": 3730,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard die is rolled eight times. What is the probability that the product of all eight rolls is odd and consists only of prime numbers? Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6561}"
} | {
"index": 3731,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard die is rolled eight times. What is the probability that the product of all eight rolls is odd and that each number rolled is a prime number? Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6561}"
} | {
"index": 3732,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard die is rolled six times. What is the probability that the product of all six rolls is odd? Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{64}"
} | {
"index": 3733,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard domino game consists of 28 tiles. Each tile is made up of two integers ranging from 0 to 6, inclusive. All possible combinations $(a, b)$, where $a \\leq b$, are listed exactly once. Note that tile $(4,2)$ is listed as tile $(2,4)$, because $2 \\leq 4$. Excluding the... | math | {
"style": "rule",
"ground_truth": "\\frac{13}{2}"
} | {
"index": 3734,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard six-sided die is rolled 3 times. If the sum of the numbers rolled on the first two rolls equals the number rolled on the third roll, what is the probability that at least one of the numbers rolled is a 2?"
}
] | math | {
"style": "rule",
"ground_truth": "$\\frac{8}{15}$"
} | {
"index": 3735,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard six-sided die is rolled, and $P$ is the product of the five numbers that are visible. What is the largest number that is certain to divide $P$?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 3736,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A standard six-sided fair die is rolled four times. The probability that the product of all four numbers rolled is a perfect square is $\\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$."
}
] | math | {
"style": "rule",
"ground_truth": "187"
} | {
"index": 3737,
"solution": "Note that rolling a 1/4 will not affect whether or not the product is a perfect square. This means that in order for the product to be a perfect square, all non 1/4 numbers rolled must come in pairs, with the only exception being the triplet 2,3, 6. Now we can do casework:\n If there a... |
DeepScaleR | [
{
"role": "user",
"content": "A starship enters an extraordinary meteor shower. Some of the meteors travel along a straight line at the same speed, equally spaced. Another group of meteors travels similarly along another straight line, parallel to the first, with the same speed but in the opposite direction... | math | {
"style": "rule",
"ground_truth": "9.1"
} | {
"index": 3738,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A state requires that all boat licenses consist of the letter A or M followed by any five digits. What is the number of groups of letters and numbers available for boat licenses?"
}
] | math | {
"style": "rule",
"ground_truth": "200000"
} | {
"index": 3739,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A stationery store sells a certain type of pen bag for $18$ yuan each. Xiao Hua went to buy this pen bag. When checking out, the clerk said, \"If you buy one more, you can get a 10% discount, which is $36 cheaper than now.\" Xiao Hua said, \"Then I'll buy one more, thank you.\"... | math | {
"style": "rule",
"ground_truth": "486"
} | {
"index": 3740,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A steak initially at a temperature of 5°C is put into an oven. After 15 minutes, its temperature reaches 45°C. After another 15 minutes, its temperature is 77°C. The oven maintains a constant temperature. The steak changes temperature at a rate proportional to the difference be... | math | {
"style": "rule",
"ground_truth": "205"
} | {
"index": 3741,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A steamboat, 2 hours after departing from dock $A$, stops for 1 hour and then continues its journey at a speed that is 0.8 times its initial speed. As a result, it arrives at dock $B$ 3.5 hours late. If the stop had occurred 180 km further, and all other conditions remained the... | math | {
"style": "rule",
"ground_truth": "270"
} | {
"index": 3742,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A stick 5 cm long, a stick 9 cm long, and a third stick $n$ cm long form a triangle. What is the sum of all possible whole number values of $n$?"
}
] | math | {
"style": "rule",
"ground_truth": "81"
} | {
"index": 3743,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A stock investment increased by $15\\%$ in the first year. At the start of the next year, by what percent must the stock now decrease to return to its original price at the beginning of the first year?"
}
] | math | {
"style": "rule",
"ground_truth": "13.04\\%"
} | {
"index": 3744,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A stock investment increased by 30% in 2006. Starting at this new value, what percentage decrease is needed in 2007 to return the stock to its original price at the beginning of 2006?"
}
] | math | {
"style": "rule",
"ground_truth": "23.077\\%"
} | {
"index": 3745,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A stock investment went up $25\\%$ in 2006. Starting at this increased value, what percent would it have to go down in 2007 to be back to its original price at the beginning of 2006?"
}
] | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 3746,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A stone is dropped into a well and the report of the stone striking the bottom is heard $7.7$ seconds after it is dropped. Assume that the stone falls $16t^2$ feet in t seconds and that the velocity of sound is $1120$ feet per second. The depth of the well is:"
}
] | math | {
"style": "rule",
"ground_truth": "784"
} | {
"index": 3747,
"solution": "1. **Define Variables:**\n Let $d$ be the depth of the well in feet, $t_1$ be the time in seconds it takes for the stone to fall to the bottom of the well, and $t_2$ be the time in seconds it takes for the sound to travel back up to the top of the well. We know that the total time fo... |
DeepScaleR | [
{
"role": "user",
"content": "A store arranges a decorative tower of balls where the top level has 2 balls and each lower level has 3 more balls than the level above. The display uses 225 balls. What is the number of levels in the tower?"
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 3748,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store decides to discount a certain type of clothing due to the change of season. If each piece of clothing is sold at 50% of the marked price, there will be a loss of 20 yuan per piece. However, if sold at 80% of the marked price, there will be a profit of 40 yuan per piece.... | math | {
"style": "rule",
"ground_truth": "120"
} | {
"index": 3749,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store has equal amounts of candies priced at 2 rubles per kilogram and candies priced at 3 rubles per kilogram. At what price should the mixture of these candies be sold?"
}
] | math | {
"style": "rule",
"ground_truth": "2.4"
} | {
"index": 3750,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store has three types of boxes containing marbles in large, medium, and small sizes, respectively holding 13, 11, and 7 marbles. If someone wants to buy 20 marbles, it can be done without opening the boxes (1 large box plus 1 small box). However, if someone wants to buy 23 ma... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 3751,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store increased the original price of a shirt by a certain percent and then lowered the new price by the same amount. Given that the resulting price was $84\\%$ of the original price, by what percent was the price increased and decreased?"
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 3752,
"solution": "Let the original price of the shirt be denoted as $P$. We are given that the final price is $84\\%$ of the original price, which can be expressed mathematically as:\n\\[ 0.84P \\]\n\nLet the percentage by which the price was increased and then decreased be $x\\%$. This means the price ... |
DeepScaleR | [
{
"role": "user",
"content": "A store increased the price of a certain Super VCD by 40% and then advertised a \"10% discount and a free 50 yuan taxi fare\" promotion. As a result, each Super VCD still made a profit of 340 yuan. What was the cost price of each Super VCD?"
}
] | math | {
"style": "rule",
"ground_truth": "1500"
} | {
"index": 3753,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store is having a sale for a change of season, offering discounts on a certain type of clothing. If each item is sold at 40% of the marked price, there is a loss of 30 yuan per item, while selling it at 70% of the marked price yields a profit of 60 yuan per item.\nFind:\n(1) ... | math | {
"style": "rule",
"ground_truth": "50\\%"
} | {
"index": 3754,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store normally sells windows at $100 each. This week the store is offering one free window for each purchase of four. Dave needs seven windows and Doug needs eight windows. How many dollars will they save if they purchase the windows together rather than separately?"
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 3755,
"solution": "1. **Understanding the Offer**: The store offers one free window for every four purchased. This means for every five windows considered (four purchased + one free), the cost is for four windows only.\n\n2. **Calculating Individual Savings**:\n - **Dave's Purchase**: Dave needs 7 wind... |
DeepScaleR | [
{
"role": "user",
"content": "A store normally sells windows at $100 each. This week the store is offering one free window for each purchase of four. Dave needs seven windows and Doug needs eight windows. How much will they save if they purchase the windows together rather than separately?"
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 3756,
"solution": "1. **Understanding the discount offer**: The store offers one free window for every four purchased. This effectively means a discount of $100$ dollars for every five windows bought, as the fifth window is free.\n\n2. **Calculating individual purchases**:\n - **Dave's purchase**: Dave... |
DeepScaleR | [
{
"role": "user",
"content": "A store offers an initial discount of 25% on all its merchandise. Subsequently, an additional discount of 10% is applied to the already reduced prices. The store advertises that the final price of the goods is 35% less than the original price. What is the actual percentage diff... | math | {
"style": "rule",
"ground_truth": "2.5\\%"
} | {
"index": 3757,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store owner bought $1500$ pencils at $\\$ 0.10$ each. If he sells them for $\\$ 0.25$ each, how many of them must he sell to make a profit of exactly $\\$ 100.00$?"
}
] | math | {
"style": "rule",
"ground_truth": "1000"
} | {
"index": 3758,
"solution": "1. **Calculate the total cost of the pencils**: The store owner bought $1500$ pencils at $0.10$ each. Therefore, the total cost is:\n \\[\n 1500 \\times 0.10 = 150\n \\]\n So, the total cost is $150$ dollars.\n\n2. **Determine the profit required**: The store owner wants to mak... |
DeepScaleR | [
{
"role": "user",
"content": "A store owner bought 2000 markers at $0.20 each. To make a minimum profit of $200, if he sells the markers for $0.50 each, calculate the number of markers he must sell at least to achieve or exceed this profit."
}
] | math | {
"style": "rule",
"ground_truth": "1200"
} | {
"index": 3759,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store owner purchases merchandise at a discount of 30% off the original list price. To ensure a profit, the owner wants to mark up the goods such that after offering a 15% discount on the new marked price, the final selling price still yields a 30% profit compared to the cost... | math | {
"style": "rule",
"ground_truth": "107\\%"
} | {
"index": 3760,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store prices an item in dollars and cents so that when 4% sales tax is added, no rounding is necessary because the result is exactly $n$ dollars where $n$ is a positive integer. The smallest value of $n$ is"
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 3761,
"solution": "1. **Define the variables**: Let the price of the item in cents be $x$. Since the sales tax is 4%, the total cost including tax is $x + 0.04x = 1.04x$ cents.\n\n2. **Convert the total cost to dollars**: Since $1$ dollar = $100$ cents, the total cost in dollars is $\\frac{1.04x}{100} = ... |
DeepScaleR | [
{
"role": "user",
"content": "A store prices an item so that when 5% sales tax is added to the price in cents, the total cost rounds naturally to the nearest multiple of 5 dollars. What is the smallest possible integer dollar amount $n$ to which the total cost could round?\nA) $50$ \nB) $55$ \nC) $60$ \... | math | {
"style": "rule",
"ground_truth": "55"
} | {
"index": 3762,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store purchased a batch of New Year cards at a price of 21 cents each and sold them for a total of 14.57 yuan. If each card is sold at the same price and the selling price does not exceed twice the purchase price, how many cents did the store earn in total?"
}
] | math | {
"style": "rule",
"ground_truth": "470"
} | {
"index": 3763,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store received a cistern of milk. The seller has a balance scale without weights (you can place cans on the pans of the scale) and three identical cans, two of which are empty and the third contains 1 liter of milk. How can you measure exactly 85 liters of milk into one can u... | math | {
"style": "rule",
"ground_truth": "85"
} | {
"index": 3764,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store received a large container of milk. The salesperson has a balance scale that lacks weights (milk bottles can be placed on the scale), and there are 3 identical milk bottles, two of which are empty, and one has 1 liter of milk. How can exactly 85 liters of milk be measur... | math | {
"style": "rule",
"ground_truth": "85"
} | {
"index": 3765,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store received apples of the first grade worth 228 rubles and apples of the second grade worth 180 rubles. During unloading, the apples got mixed up. Calculations showed that if all the apples are now sold at a price 90 kopeks lower than the price per kilogram of first grade ... | math | {
"style": "rule",
"ground_truth": "85"
} | {
"index": 3766,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store sells a batch of football souvenir books, with a cost price of $40$ yuan per book and a selling price of $44$ yuan per book. The store can sell 300 books per day. The store decides to increase the selling price, and after investigation, it is found that for every $1$ yu... | math | {
"style": "rule",
"ground_truth": "2640"
} | {
"index": 3767,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store sells a type of notebook. The retail price for each notebook is 0.30 yuan, a dozen (12 notebooks) is priced at 3.00 yuan, and for purchases of more than 10 dozen, each dozen can be paid for at 2.70 yuan. \n(1) There are 57 students in the ninth grade class 1, and each ... | math | {
"style": "rule",
"ground_truth": "51.30"
} | {
"index": 3768,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store sells chalk in three types of packages: regular, unusual, and excellent. Initially, the quantitative ratio of the types was 2:3:6. After some packages of regular and unusual chalk—totaling no more than 100 packages—were delivered to the store, and $40\\%$ of the excelle... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 3769,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store sells jellybeans at a fixed price per gram. The price for 250 g of jellybeans is $\\$ 7.50$. What mass of jellybeans sells for $\\$ 1.80$?"
}
] | math | {
"style": "rule",
"ground_truth": "60 \\mathrm{~g}"
} | {
"index": 3770,
"solution": "The store sells 250 g of jellybeans for $\\$ 7.50$, which is 750 cents. Therefore, 1 g of jellybeans costs $750 \\div 250=3$ cents. This means that $\\$ 1.80$, which is 180 cents, will buy $180 \\div 3=60 \\mathrm{~g}$ of jellybeans."
} |
DeepScaleR | [
{
"role": "user",
"content": "A store sells two suits at the same time, both priced at 168 yuan. One suit makes a 20% profit, while the other incurs a 20% loss. Calculate the net profit or loss of the store."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 3771,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A store sold an air conditioner for 2000 yuan and a color TV for 2000 yuan. The air conditioner made a 30% profit, while the color TV incurred a 20% loss. Could you help the store owner calculate whether the store made a profit or a loss on this transaction, and by how much?"
... | math | {
"style": "rule",
"ground_truth": "38.5"
} | {
"index": 3772,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A storm in Sydney, Australia, caused $\\$$30 million in damage. That estimate was in Australian dollars. At that time, 1.5 Australian dollars were worth 1 American dollar. Determine the number of American dollars of damage the storm caused."
}
] | math | {
"style": "rule",
"ground_truth": "20,\\!000,\\!000"
} | {
"index": 3773,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A straight concrete sidewalk is to be $3$ feet wide, $60$ feet long, and $3$ inches thick. How many cubic yards of concrete must a contractor order for the sidewalk if concrete must be ordered in a whole number of cubic yards?"
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"index": 3774,
"solution": "To find the volume of the concrete needed for the sidewalk, we first convert all dimensions to yards (since 1 yard = 3 feet and 1 yard = 36 inches).\n\n1. **Convert dimensions to yards:**\n - Width: $3$ feet = $\\frac{3}{3} = 1$ yard.\n - Length: $60$ feet = $\\frac{60}{3} = 20$ ya... |
DeepScaleR | [
{
"role": "user",
"content": "A straight line $l$ passes through a vertex and a focus of an ellipse. If the distance from the center of the ellipse to $l$ is one quarter of its minor axis length, calculate the eccentricity of the ellipse."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{1}{2}"
} | {
"index": 3775,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A straight line joins the points $(-1,1)$ and $(3,9)$. Its $x$-intercept is:"
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{3}{2}"
} | {
"index": 3776,
"solution": "1. **Identify the coordinates of the given points and calculate the slope ($m$) of the line.**\n The points given are $(-1,1)$ and $(3,9)$. The slope formula is:\n \\[\n m = \\frac{\\Delta y}{\\Delta x} = \\frac{y_2 - y_1}{x_2 - x_1} = \\frac{9 - 1}{3 - (-1)} = \\frac{8}{4} = 2.\... |
DeepScaleR | [
{
"role": "user",
"content": "A straight line passing through the point $(0,4)$ is perpendicular to the line $x-3y-7=0$. Its equation is:"
}
] | math | {
"style": "rule",
"ground_truth": "y+3x-4=0"
} | {
"index": 3777,
"solution": "1. **Identify the slope of the given line**: The equation of the given line is $x - 3y - 7 = 0$. We can rewrite this equation in slope-intercept form, $y = mx + c$, where $m$ is the slope. First, solve for $y$:\n \\[\n x - 3y - 7 = 0 \\implies 3y = x - 7 \\implies y = \\frac{1}{3}x... |
DeepScaleR | [
{
"role": "user",
"content": "A straight one-mile stretch of highway, 40 feet wide, is closed. Robert rides his bike on a path composed of semicircles as shown. If he rides at 5 miles per hour, how many hours will it take to cover the one-mile stretch?\n[asy]\nsize(10cm); pathpen=black; pointpen=black; D(ar... | math | {
"style": "rule",
"ground_truth": "\\frac{\\pi}{10}"
} | {
"index": 3778,
"solution": "\n#### Step-by-step Analysis:\n\n1. **Understanding the Path**: Robert rides his bike on a path composed of semicircles along a one-mile stretch of highway that is 40 feet wide. We need to determine the radius of these semicircles. Since the highway is 40 feet wide and assuming Robert ... |
DeepScaleR | [
{
"role": "user",
"content": "A straight one-way city street has 8 consecutive traffic lights. Every light remains green for 1.5 minutes, yellow for 3 seconds, and red for 1.5 minutes. The lights are synchronized so that each light turns red 10 seconds after the preceding one turns red. Calculate the longes... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 3779,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A straight one-way city street has 8 consecutive traffic lights. Every light remains green for 1.5 minutes, yellow for 3 seconds, and red for 1.5 minutes. The lights are synchronized so that each light turns red 10 seconds after the preceding one turns red. What is the longest ... | math | {
"style": "rule",
"ground_truth": "20"
} | {
"index": 3780,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A straight river that is $264$ meters wide flows from west to east at a rate of $14$ meters per minute. Melanie and Sherry sit on the south bank of the river with Melanie a distance of $D$ meters downstream from Sherry. Relative to the water, Melanie swims at $80$ meters per mi... | math | {
"style": "rule",
"ground_truth": "550"
} | {
"index": 3781,
"solution": "Claim\n Median $AM$ and altitude $AH$ are drawn in triangle $ABC$. $AB = c, AC = b < c, BC = a$ are known. Let's denote $MH = x$.\n Prove that \\begin{align*}2ax = c^{2} – b^{2}\\end{align*}\nProof \\[BH + CH = a,\\] \\begin{align*} BH^{2} – CH^{2} = c^{2} – b^{2}\\implies BH - CH &= \... |
DeepScaleR | [
{
"role": "user",
"content": "A street has 20 houses on each side, for a total of 40 houses. The addresses on the south side of the street form an arithmetic sequence, as do the addresses on the north side of the street. On the south side, the addresses are 4, 10, 16, etc., and on the north side they are 3,... | math | {
"style": "rule",
"ground_truth": "84"
} | {
"index": 3782,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A street has parallel curbs 40 feet apart. A crosswalk bounded by two parallel stripes crosses the street at an angle. The length of the curb between the stripes is 15 feet and each stripe is 50 feet long. Find the distance, in feet, between the stripes."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 3783,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A strictly increasing sequence of positive integers $a_1$, $a_2$, $a_3$, $\\cdots$ has the property that for every positive integer $k$, the subsequence $a_{2k-1}$, $a_{2k}$, $a_{2k+1}$ is geometric and the subsequence $a_{2k}$, $a_{2k+1}$, $a_{2k+2}$ is arithmetic. Suppose tha... | math | {
"style": "rule",
"ground_truth": "504"
} | {
"index": 3784,
"solution": "We first create a similar sequence where $a_1=1$ and $a_2=2$. Continuing the sequence,\n\\[1, 2,4,6,9,12,16,20,25,30,36,42,49,\\cdots\\]\n Here we can see a pattern; every second term (starting from the first) is a square, and every second term (starting from the third) is the end of a... |
DeepScaleR | [
{
"role": "user",
"content": "A string consisting of letters A, C, G, and U is untranslatable if and only if it has no AUG as a consecutive substring. For example, ACUGG is untranslatable. Let \\(a_{n}\\) denote the number of untranslatable strings of length \\(n\\). It is given that there exists a unique t... | math | {
"style": "rule",
"ground_truth": "(4,0,-1)"
} | {
"index": 3785,
"solution": "If a sequence is untranslatable, the first \\(n-1\\) letters must form an untranslatable sequence as well. Therefore, we can count \\(a_{n}\\) by - Append any letter to an untranslatable sequence of length \\(n-1\\), so \\(4 a_{n-1}\\) ways. - Then, subtract with the case when the sequ... |
DeepScaleR | [
{
"role": "user",
"content": "A string has 150 beads of red, blue, and green colors. It is known that among any six consecutive beads, there is at least one green bead, and among any eleven consecutive beads, there is at least one blue bead. What is the maximum number of red beads that can be on the string?... | math | {
"style": "rule",
"ground_truth": "112"
} | {
"index": 3786,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A string has been cut into 4 pieces, all of different lengths. The length of each piece is 2 times the length of the next smaller piece. What fraction of the original string is the longest piece?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{8}{15}"
} | {
"index": 3787,
"solution": "Let \\(L\\) be the length of the string. If \\(x\\) is the length of the shortest piece, then since each of the other pieces is twice the length of the next smaller piece, then the lengths of the remaining pieces are \\(2x, 4x\\), and \\(8x\\). Since these four pieces make up the full ... |
DeepScaleR | [
{
"role": "user",
"content": "A string of 33 pearls has its middle pearl as the largest and most valuable. The values of the remaining pearls decrease by $3000 \\mathrm{Ft}$ per pearl towards one end and by $4500 \\mathrm{Ft}$ per pearl towards the other end. How much is the middle pearl worth if the total ... | math | {
"style": "rule",
"ground_truth": "90000"
} | {
"index": 3788,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A string of digits is defined to be similar to another string of digits if it can be obtained by reversing some contiguous substring of the original string. For example, the strings 101 and 110 are similar, but the strings 3443 and 4334 are not. (Note that a string is always si... | math | {
"style": "rule",
"ground_truth": "1126"
} | {
"index": 3789,
"solution": "We first count the number of substrings that one could pick to reverse to yield a new substring. If we insert two dividers into the sequence of 50 digits, each arrangement of 2 dividers among the 52 total objects specifies a substring that is contained between the two dividers, for a t... |
DeepScaleR | [
{
"role": "user",
"content": "A strip of size $1 \\times 10$ is divided into unit squares. The numbers $1, 2, \\ldots, 10$ are written in these squares. First, the number 1 is written in one of the squares, then the number 2 is written in one of the neighboring squares, then the number 3 is written in one o... | math | {
"style": "rule",
"ground_truth": "512"
} | {
"index": 3790,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student accidentally added five to both the numerator and denominator of a fraction, changing the fraction's value to $\\frac12$. If the original numerator was a 2, what was the original denominator?"
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"index": 3791,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student at Harvard named Kevin was counting his stones by 11. He messed up $n$ times and instead counted 9s and wound up at 2007. How many values of $n$ could make this limerick true?"
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"index": 3792,
"solution": "The mathematical content is that $9 n+11 k=2007$, for some nonnegative integers $n$ and $k$. As $2007=9 \\cdot 223, k$ must be divisible by 9. Using modulo 11, we see that $n$ is 3 more than a multiple of 11. Thus, the possibilities are $n=223,212,201, \\ldots, 3$, which are 21 in numb... |
DeepScaleR | [
{
"role": "user",
"content": "A student correctly added the two two-digit numbers on the left of the board and got the answer 137. What answer will she obtain if she adds the two four-digit numbers on the right of the board?"
}
] | math | {
"style": "rule",
"ground_truth": "13837"
} | {
"index": 3793,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student council must select a two-person welcoming committee and a three-person planning committee from among its members. There are exactly $10$ ways to select a two-person team for the welcoming committee. It is possible for students to serve on both committees. In how many... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 3794,
"solution": "1. **Determine the number of students on the council**: \n Let the number of students on the council be $x$. The number of ways to select a two-person welcoming committee is given by the combination formula $\\binom{x}{2}$, which represents the number of ways to choose 2 students fro... |
DeepScaleR | [
{
"role": "user",
"content": "A student has 2 identical photo albums and 3 identical stamp albums. The student wants to give away 4 albums, one to each of four friends. How many different ways can the student give away the albums?"
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 3795,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student has five different physics questions numbered 1, 2, 3, 4, and 5, and four different chemistry questions numbered 6, 7, 8, and 9. The student randomly selects two questions, each with an equal probability of being chosen. Let the event `(x, y)` represent \"the two ques... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{12}"
} | {
"index": 3796,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student is given a budget of $10,000 to produce a rectangular banner for a school function. The length and width (in meters) of the banner must be integers. If each meter in length costs $330 while each meter in width costs $450, what is the maximum area (in square meters) of... | math | {
"style": "rule",
"ground_truth": "165"
} | {
"index": 3797,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student is using the given data in the problem statement to find an approximate solution (accurate to 0.1) for the equation $\\lg x = 2 - x$. He sets $f(x) = \\lg x + x - 2$, finds that $f(1) < 0$ and $f(2) > 0$, and uses the \"bisection method\" to obtain 4 values of $x$, ca... | math | {
"style": "rule",
"ground_truth": "1.75"
} | {
"index": 3798,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A student must choose a program of four courses from a list of courses consisting of English, Algebra, Geometry, History, Art, and Latin. This program must contain English and at least one mathematics course. In how many ways can this program be chosen?"
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"index": 3799,
"solution": ""
} |
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