data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "A two-digit number, when multiplied by 109, yields a four-digit number. It is divisible by 23, and the quotient is a one-digit number. The maximum value of this two-digit number is $\\qquad$."
}
] | math | {
"style": "rule",
"ground_truth": "69"
} | {
"index": 4100,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A two-digit number, when three times the sum of its units and tens digits is subtracted by -2, still results in the original number. Express this two-digit number algebraically."
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"index": 4101,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A two-digit positive integer $x$ has the property that when 109 is divided by $x$, the remainder is 4. What is the sum of all such two-digit positive integers $x$?"
}
] | math | {
"style": "rule",
"ground_truth": "71"
} | {
"index": 4102,
"solution": "Suppose that the quotient of the division of 109 by $x$ is $q$. Since the remainder is 4, this is equivalent to $109=q x+4$ or $q x=105$. Put another way, $x$ must be a positive integer divisor of 105. Since $105=5 \times 21=5 \times 3 \times 7$, its positive integer divisors are $1,3,... |
DeepScaleR | [
{
"role": "user",
"content": "A two-digit positive integer is said to be $cuddly$ if it is equal to the sum of its nonzero tens digit and the square of its units digit. How many two-digit positive integers are cuddly?"
}
] | math | {
"style": "rule",
"ground_truth": "1"
} | {
"index": 4103,
"solution": "Let's analyze the problem step by step:\n\n1. **Define the Problem:**\n A two-digit integer is represented as $10a + b$, where $a$ is the tens digit and $b$ is the units digit. The integer is called $\\emph{cuddly}$ if it satisfies the equation:\n \\[\n 10a + b = a + b^2\n \\]\... |
DeepScaleR | [
{
"role": "user",
"content": "A two-gallon container had all of its dimensions tripled. How many gallons does the new container hold?"
}
] | math | {
"style": "rule",
"ground_truth": "54"
} | {
"index": 4104,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A two-inch cube ($2\\times2\\times2$) of silver weighs 3 pounds and is worth $\\$200$. How much is a three-inch cube of silver worth? Round your answer to the nearest dollar."
}
] | math | {
"style": "rule",
"ground_truth": "\\$675"
} | {
"index": 4105,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A two-meter gas pipe has rusted in two places. Determine the probability that all three resulting parts can be used as connections to gas stoves, if according to regulations, the stove should not be located at a distance closer than 50 cm from the main gas pipeline."
}
] | math | {
"style": "rule",
"ground_truth": "1/16"
} | {
"index": 4106,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A two-meter gas pipe has rusted in two places. Determine the probability that all three resulting pieces can be used as connections to gas stoves, given that according to regulations, a stove should not be located closer than 50 cm to the main gas pipe."
}
] | math | {
"style": "rule",
"ground_truth": "1/16"
} | {
"index": 4107,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A two-row triangle is created with a total of 15 pieces: nine unit rods and six connectors, as shown. What is the total number of pieces that would be used to create an eight-row triangle?\n\n[asy]\ndraw((0,0)--(4,0)--(2,2sqrt(3))--(0,0)--cycle,linewidth(1));\ndraw((2,0)--(3,sq... | math | {
"style": "rule",
"ground_truth": "153"
} | {
"index": 4108,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A typesetter scattered part of a set - a set of a five-digit number that is a perfect square, written with the digits $1, 2, 5, 5,$ and $6$. Find all such five-digit numbers."
}
] | math | {
"style": "rule",
"ground_truth": "15625"
} | {
"index": 4109,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A typical triangle is defined as one in which each angle is at least \\(30^{\\circ}\\).\n\nA triangle is identified using the following procedure. The perimeter of a circle is divided into 180 equal arcs, and 3 distinct points are randomly chosen from these division points. (An... | math | {
"style": "rule",
"ground_truth": "0.25"
} | {
"index": 4110,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A unicorn is tethered by a $20$-foot silver rope to the base of a magician's cylindrical tower whose radius is $8$ feet. The rope is attached to the tower at ground level and to the unicorn at a height of $4$ feet. The unicorn has pulled the rope taut, the end of the rope is $4... | math | {
"style": "rule",
"ground_truth": "813"
} | {
"index": 4111,
"solution": "Note that by Power of a Point, the point the unicorn is at has power $4 \\cdot 20 = 80$ which implies that the tangent from that point to the tower is of length $\\sqrt{80}=4\\sqrt{5},$ however this is length of the rope projected into 2-D. If we let $\\theta$ be the angle between the ... |
DeepScaleR | [
{
"role": "user",
"content": "A uniform cubic die with faces numbered $1, 2, 3, 4, 5, 6$ is rolled three times independently, resulting in outcomes $a_1, a_2, a_3$. Find the probability of the event \"$|a_1 - a_2| + |a_2 - a_3| + |a_3 - a_1| = 6$\"."
}
] | math | {
"style": "rule",
"ground_truth": "1/4"
} | {
"index": 4112,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A uniform solid semi-circular disk of radius $R$ and negligible thickness rests on its diameter as shown. It is then tipped over by some angle $\\gamma$ with respect to the table. At what minimum angle $\\gamma$ will the disk lose balance and tumble over? Express your ans... | math | {
"style": "rule",
"ground_truth": "23"
} | {
"index": 4113,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A uniform tetrahedron has its four faces numbered with 1, 2, 3, and 4. It is randomly thrown twice, and the numbers on the bottom face of the tetrahedron are $x_1$ and $x_2$, respectively. Let $t = (x_{1}-3)^{2}+(x_{2}-3)^{2}$. \n(1) Calculate the probabilities of $t$ reaching... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{16}"
} | {
"index": 4114,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A unit cube has vertices $P_1,P_2,P_3,P_4,P_1',P_2',P_3',$ and $P_4'$. Vertices $P_2$, $P_3$, and $P_4$ are adjacent to $P_1$, and for $1\\le i\\le 4,$ vertices $P_i$ and $P_i'$ are opposite to each other. A regular octahedron has one vertex in each of the segments $\\overline{... | math | {
"style": "rule",
"ground_truth": "\\frac{3 \\sqrt{2}}{4}"
} | {
"index": 4115,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A unit cube is cut twice to form three triangular prisms, two of which are congruent, as shown in Figure 1. The cube is then cut in the same manner along the dashed lines shown in Figure 2. This creates nine pieces. What is the volume of the piece that contains vertex $W$?\n\n[... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{12}"
} | {
"index": 4116,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A unit has a total of 620 staff members. To investigate the time workers spend commuting, it was decided to survey 62 workers using a systematic sampling method. The entire staff was divided into 62 segments with equal intervals, and a simple random sampling method was used to ... | math | {
"style": "rule",
"ground_truth": "394"
} | {
"index": 4117,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A unit purchased a vacant lot for 21.6 million yuan, planning to build a building of at least 10 floors, with each floor being 2000 square meters. It is calculated that if the building is built to $x$ ($x \\geqslant 10$) floors, then the average construction cost per square met... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 4118,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A unit square $A B C D$ and a circle $\\Gamma$ have the following property: if $P$ is a point in the plane not contained in the interior of $\\Gamma$, then $\\min (\\angle A P B, \\angle B P C, \\angle C P D, \\angle D P A) \\leq 60^{\\circ}$. The minimum possible area of $\\Ga... | math | {
"style": "rule",
"ground_truth": "106"
} | {
"index": 4119,
"solution": "Note that the condition for $\\Gamma$ in the problem is equivalent to the following condition: if $\\min (\\angle A P B, \\angle B P C, \\angle C P D, \\angle D P A)>60^{\\circ}$, then $P$ is contained in the interior of $\\Gamma$. Let $X_{1}, X_{2}, X_{3}$, and $X_{4}$ be the four poi... |
DeepScaleR | [
{
"role": "user",
"content": "A university has 120 foreign language teachers. Among them, 50 teach English, 45 teach Japanese, and 40 teach French. There are 15 teachers who teach both English and Japanese, 10 who teach both English and French, and 8 who teach both Japanese and French. Additionally, 4 teach... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 4120,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A valid license plate in Xanadu consists of two letters followed by three digits. How many valid license plates are possible?"
}
] | math | {
"style": "rule",
"ground_truth": "676,\\!000"
} | {
"index": 4121,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A valuable right-angled triangular metal plate $A B O$ is placed in a plane rectangular coordinate system (as shown in the diagram), with $A B = B O = 1$ (meter) and $A B \\perp O B$. Due to damage in the shaded part of the triangular plate, a line $M N$ passing through the poi... | math | {
"style": "rule",
"ground_truth": "-\\frac{1}{2}"
} | {
"index": 4122,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A value of $x$ satisfying the equation $x^2 + b^2 = (a - x)^2$ is:"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{a^2 - b^2}{2a}"
} | {
"index": 4123,
"solution": "1. Start with the given equation:\n \\[ x^2 + b^2 = (a - x)^2 \\]\n\n2. Expand the right-hand side:\n \\[ (a - x)^2 = a^2 - 2ax + x^2 \\]\n\n3. Substitute back into the original equation:\n \\[ x^2 + b^2 = a^2 - 2ax + x^2 \\]\n\n4. Simplify by canceling out \\(x^2\\) from both si... |
DeepScaleR | [
{
"role": "user",
"content": "A venture capital firm is considering investing in the development of a new energy product, with estimated investment returns ranging from 100,000 yuan to 10,000,000 yuan. The firm is planning to establish a reward scheme for the research team: the reward amount $y$ (in units o... | math | {
"style": "rule",
"ground_truth": "328"
} | {
"index": 4124,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A vertex-induced subgraph is a subset of the vertices of a graph together with any edges whose endpoints are both in this subset. An undirected graph contains 10 nodes and $m$ edges, with no loops or multiple edges. What is the minimum possible value of $m$ such that this graph... | math | {
"style": "rule",
"ground_truth": "31"
} | {
"index": 4125,
"solution": "Suppose that we want to find the vertex-induced subgraph of maximum size where each vertex has degree at least 5. To do so, we start with the entire graph and repeatedly remove any vertex with degree less than 5. If there are vertices left after this process terminates, then the subgra... |
DeepScaleR | [
{
"role": "user",
"content": "A very bizarre weighted coin comes up heads with probability $\\frac12$, tails with probability $\\frac13$, and rests on its edge with probability $\\frac16$. If it comes up heads, I win 1 dollar. If it comes up tails, I win 3 dollars. But if it lands on its edge, I lose 5 d... | math | {
"style": "rule",
"ground_truth": "\\$\\dfrac23 \\approx \\$0.67"
} | {
"index": 4126,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A very large number $x$ is equal to $2^23^34^45^56^67^78^89^9$. What is the smallest positive integer that, when multiplied with $x$, produces a product that is a perfect square?"
}
] | math | {
"style": "rule",
"ground_truth": "105"
} | {
"index": 4127,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A vessel with a capacity of 100 liters is filled with a brine solution containing 10 kg of dissolved salt. Every minute, 3 liters of water flows into it, and the same amount of the resulting mixture is pumped into another vessel of the same capacity, initially filled with water... | math | {
"style": "rule",
"ground_truth": "333.33"
} | {
"index": 4128,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A vessel with a capacity of 6 liters contains 4 liters of a 70% sulfuric acid solution. Another vessel of the same capacity contains 3 liters of a 90% sulfuric acid solution. Some amount of the solution is transferred from the second vessel to the first one so that the first ve... | math | {
"style": "rule",
"ground_truth": "76"
} | {
"index": 4129,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A volleyball net is in the shape of a rectangle with dimensions of $50 \\times 600$ cells.\n\nWhat is the maximum number of strings that can be cut so that the net does not fall apart into pieces?"
}
] | math | {
"style": "rule",
"ground_truth": "30000"
} | {
"index": 4130,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A volunteer organizes a spring sports event and wants to form a vibrant and well-trained volunteer team. They plan to randomly select 3 people from 4 male volunteers and 3 female volunteers to serve as the team leader. The probability of having at least one female volunteer as ... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{17}"
} | {
"index": 4131,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A waiter at the restaurant U Šejdíře always adds the current date to the bill: he increases the total amount spent by as many crowns as the day of the month it is.\n\nIn September, a group of three friends dined at the restaurant twice. The first time, each person paid separate... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 4132,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A watch loses $2\\frac{1}{2}$ minutes per day. It is set right at $1$ P.M. on March 15. Let $n$ be the positive correction, in minutes, to be added to the time shown by the watch at a given time. When the watch shows $9$ A.M. on March 21, $n$ equals:"
}
] | math | {
"style": "rule",
"ground_truth": "14\\frac{14}{23}"
} | {
"index": 4133,
"solution": "1. **Calculate the total time passed on the watch**: \n The watch is set at 1 P.M. on March 15 and shows 9 A.M. on March 21. To find the total time passed according to the watch:\n - From 1 P.M. on March 15 to 1 P.M. on March 21 is 6 days.\n - From 1 P.M. to 9 A.M. the next day i... |
DeepScaleR | [
{
"role": "user",
"content": "A water tower in the shape of a cylinder has radius 10 m and height 30 m. A spiral staircase, with constant slope, circles once around the outside of the water tower. A vertical ladder of height 5 m then extends to the top of the tower. What is the total distance along the stai... | math | {
"style": "rule",
"ground_truth": "72.6 \\mathrm{~m}"
} | {
"index": 4134,
"solution": "To calculate the total distance, we add the length of the vertical ladder (5 m) to the length of the spiral staircase. The spiral staircase wraps once around the tower. Since the tower has radius 10 m, then its circumference is $2 \\times \\pi \\times 10=20 \\pi \\mathrm{m}$. We can th... |
DeepScaleR | [
{
"role": "user",
"content": "A wealthy king has his blacksmith fashion him a large cup, whose inside is a cone of height 9 inches and base diameter 6 inches. At one of his many feasts, he orders the mug to be filled to the brim with cranberry juice. For each positive integer $n$, the king stirs his drink v... | math | {
"style": "rule",
"ground_truth": "\\frac{216 \\pi^{3}-2187 \\sqrt{3}}{8 \\pi^{2}}"
} | {
"index": 4135,
"solution": "First, we find the total amount of juice consumed. We can simply subtract the amount of juice remaining at infinity from the initial amount of juice in the cup, which of course is simply the volume of the cup; we'll denote this value by $V$. Since volume in the cup varies as the cube o... |
DeepScaleR | [
{
"role": "user",
"content": "A weather forecast predicts that for each day from Monday to Friday this week, there is a $40\\%$ chance of sun, a $25\\%$ chance of getting 4 inches of rain, and a $35\\%$ chance of getting 10 inches of rain. What is the expected value of the total number of inches of rain whi... | math | {
"style": "rule",
"ground_truth": "22.5"
} | {
"index": 4136,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A weight of 200 grams rests on a table. It was flipped and placed on the table on its other side, the area of which is 15 sq. cm smaller. As a result, the pressure on the table increased by 1200 Pa. Find the area of the side on which the weight originally rested. Give your answ... | math | {
"style": "rule",
"ground_truth": "24.85"
} | {
"index": 4137,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A weightless pulley has a rope with masses of 3 kg and 6 kg. Neglecting friction, find the force exerted by the pulley on its axis. Consider the acceleration due to gravity to be $10 \\, \\mathrm{m/s}^2$. Give the answer in newtons, rounding it to the nearest whole number if ne... | math | {
"style": "rule",
"ground_truth": "80"
} | {
"index": 4138,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A wheel is rolled without slipping through $15$ laps on a circular race course with radius $7$ . The wheel is perfectly circular and has radius $5$ . After the three laps, how many revolutions around its axis has the wheel been turned through?"
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"index": 4139,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A wheel with radius $1\\text{ m}$ is rolled in a straight line through one complete revolution on a flat horizontal surface. How many meters did the center of the wheel travel horizontally from its starting location?"
}
] | math | {
"style": "rule",
"ground_truth": "2 \\pi"
} | {
"index": 4140,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A white cylindrical silo has a diameter of 30 feet and a height of 80 feet. A red stripe with a horizontal width of 3 feet is painted on the silo, as shown, making two complete revolutions around it. What is the area of the stripe in square feet?\n\n[asy]\nsize(250);defaultpe... | math | {
"style": "rule",
"ground_truth": "240"
} | {
"index": 4141,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A whole block of modeling clay is a right rectangular prism six inches by two inches by one inch. How many whole blocks need to be unwrapped to mold a cylindrical sculpture seven inches high and four inches in diameter?"
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"index": 4142,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A whole number is said to be ''9-heavy'' if the remainder when the number is divided by 9 is greater than 5. What is the least three-digit 9-heavy whole number?"
}
] | math | {
"style": "rule",
"ground_truth": "105"
} | {
"index": 4143,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A whole number was increased by 2, and its square decreased by 2016. What was the number initially (before the increase)?"
}
] | math | {
"style": "rule",
"ground_truth": "-505"
} | {
"index": 4144,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A whole number, $M$, is chosen so that $\\frac{M}{4}$ is strictly between 8 and 9. What is the value of $M$?"
}
] | math | {
"style": "rule",
"ground_truth": "33"
} | {
"index": 4145,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A whole number, $N$, is chosen so that $\\frac{N}{3}$ is strictly between 7.5 and 8. What is the value of $N$ ?"
}
] | math | {
"style": "rule",
"ground_truth": "23"
} | {
"index": 4146,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A wholesaler bought 500 kilograms of a certain type of fruit at a price of 40 yuan per kilogram. According to market forecasts, the selling price $y$ (yuan per kilogram) of this fruit is a function of the storage time $x$ (days), given by $y=60+2x$. However, an average of 10 ki... | math | {
"style": "rule",
"ground_truth": "11600"
} | {
"index": 4147,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A wholesaler gives different discounts based on the size of the customer's order. The steps to calculate the amount payable by the customer are as follows: \nS1 Input the order amount x (unit: pieces); input the unit price A (unit: yuan); \nS2 If x < 250, then the discount ra... | math | {
"style": "rule",
"ground_truth": "980"
} | {
"index": 4148,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A wholesaler purchased $50$ packs of shirts of size $L$ from a clothing manufacturer. Due to the negligence of the packaging workers, some packs were mixed with shirts of size $M$. The number of $M$ shirts mixed in (pieces) and the corresponding number of packs (packs) are show... | math | {
"style": "rule",
"ground_truth": "\\frac{3}{25}"
} | {
"index": 4149,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A wire has a length of 6 meters and has 5 nodes that divide the wire into 6 equal parts. If a node is randomly selected to cut the wire, what is the probability that both resulting pieces will have lengths not less than 2 meters?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"index": 4150,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A wire is cut into two pieces, one of length $a$ and the other of length $b$. The piece of length $a$ is bent to form an equilateral triangle, and the piece of length $b$ is bent to form a regular hexagon. The triangle and the hexagon have equal area. What is $\\frac{a}{b}$?"
... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt6}2"
} | {
"index": 4151,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A wire is cut into two pieces: one of length $a$ bent to form a square, and another of length $b$ bent to form a regular octagon. The square and the octagon have equal areas. What is the ratio $\\frac{a}{b}$?"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2(1+\\sqrt{2})}}{2}"
} | {
"index": 4152,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A wire of length $80$cm is randomly cut into three segments. The probability that each segment is no less than $20$cm is $\\_\\_\\_\\_\\_\\_\\_.$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{16}"
} | {
"index": 4153,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A wishing well is located at the point $(11,11)$ in the $xy$ -plane. Rachelle randomly selects an integer $y$ from the set $\\left\\{ 0, 1, \\dots, 10 \\right\\}$ . Then she randomly selects, with replacement, two integers $a,b$ from the set $\\left\\{ 1,2,\\dots,10 \... | math | {
"style": "rule",
"ground_truth": "111"
} | {
"index": 4154,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A wizard is crafting a magical elixir. For this, he requires one of four magical herbs and one of six enchanted gems. However, one of the gems cannot be used with three of the herbs. Additionally, another gem can only be used if it is paired with one specific herb. How many val... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 4155,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A woman buys a property for $15,000, aiming for a $6\\%$ return on her investment annually. She sets aside $15\\%$ of the rent each month for maintenance, and pays $360 annually in taxes. What must be the monthly rent to meet her financial goals?\nA) $110.00$\nB) $123.53$\nC) $... | math | {
"style": "rule",
"ground_truth": "123.53"
} | {
"index": 4156,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A woman buys a property for $150,000 with a goal to achieve a $7\\%$ annual return on her investment. She sets aside $15\\%$ of each month's rent for maintenance costs, and pays property taxes at $0.75\\%$ of the property's value each year. Calculate the monthly rent she needs ... | math | {
"style": "rule",
"ground_truth": "1139.71"
} | {
"index": 4157,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A woman invests in a property for $12,000 with the aim of receiving a $6\\%$ return on her investment after covering all expenses including taxes and insurance. She pays $360 annually in taxes and $240 annually for insurance. She also keeps aside $10\\%$ of each month's rent fo... | math | {
"style": "rule",
"ground_truth": "122.22"
} | {
"index": 4158,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A woman labels the squares of a very large chessboard $1$ through $64$. On each square $k$, the woman puts $2^k$ grains of rice. How many more grains of rice are placed on the $10^{th}$ square than on the first $8$ squares combined?"
}
] | math | {
"style": "rule",
"ground_truth": "514"
} | {
"index": 4159,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A woman wants freshly baked cookies delivered exactly at 18:00 for an event. Delivery trucks, upon finishing baking, travel with varying speeds due to potential traffic conditions:\n- If there is moderate traffic, the trucks travel at an average speed of 60 km/h and would arriv... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 4160,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A wooden block is 4 inches long, 4 inches wide, and 1 inch high. The block is painted red on all six sides and then cut into sixteen 1 inch cubes. How many of the cubes each have a total number of red faces that is an even number?\n\n[asy]\n\nsize(4cm,4cm);\n\npair A,B,C,D,E,F,... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"index": 4161,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A wooden block is 5 inches long, 5 inches wide, and 1 inch high. The block is painted red on all six sides and then cut into twenty-five 1-inch cubes. How many of the resulting cubes each have a total number of red faces that is an odd number?"
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 4162,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A wooden cube $n$ units on a side is painted red on all six faces and then cut into $n^3$ unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is $n$?"
}
] | math | {
"style": "rule",
"ground_truth": "4"
} | {
"index": 4163,
"solution": "1. **Understanding the problem**: We start with a cube of side length $n$, which is painted on all six faces. This cube is then cut into $n^3$ smaller unit cubes. Each unit cube has 6 faces. We need to find $n$ such that exactly one-fourth of the total number of faces of all the unit c... |
DeepScaleR | [
{
"role": "user",
"content": "A wooden cube has edges of length $3$ meters. Square holes, of side one meter, centered in each face are cut through to the opposite face. The edges of the holes are parallel to the edges of the cube. The entire surface area including the inside, in square meters, is"
}
] | math | {
"style": "rule",
"ground_truth": "72"
} | {
"index": 4164,
"solution": "1. **Calculate the original surface area of the cube**: \n The cube has 6 faces, and each face is a square with side length 3 meters. The area of one face is therefore $3^2 = 9$ square meters. Thus, the total surface area of the cube before any modifications is:\n \\[\n 6 \\times... |
DeepScaleR | [
{
"role": "user",
"content": "A wooden cube with edge length $n$ units (where $n$ is an integer $>2$) is painted black all over. By slices parallel to its faces, the cube is cut into $n^3$ smaller cubes each of unit length. If the number of smaller cubes with just one face painted black is equal to the numb... | math | {
"style": "rule",
"ground_truth": "8"
} | {
"index": 4165,
"solution": "1. **Understanding the problem**: We have a cube of side length $n$ units, painted black on all sides, and then cut into $n^3$ smaller unit cubes. We need to find $n$ such that the number of smaller cubes with exactly one face painted is equal to the number of smaller cubes with no fac... |
DeepScaleR | [
{
"role": "user",
"content": "A wooden cube with edges of length $3$ meters has square holes, of side one meter, centered in each face, cut through to the opposite face. Find the entire surface area, including the inside, of this cube in square meters."
}
] | math | {
"style": "rule",
"ground_truth": "72"
} | {
"index": 4166,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A wooden cube, whose edges are one centimeter long, rests on a horizontal surface. Illuminated by a point source of light that is $x$ centimeters directly above an upper vertex, the cube casts a shadow on the horizontal surface. The area of the shadow, which does not include th... | math | {
"style": "rule",
"ground_truth": "166"
} | {
"index": 4167,
"solution": "[asy] import three; size(250);defaultpen(0.7+fontsize(9)); real unit = 0.5; real r = 2.8; triple O=(0,0,0), P=(0,0,unit+unit/(r-1)); dot(P); draw(O--P); draw(O--(unit,0,0)--(unit,0,unit)--(0,0,unit)); draw(O--(0,unit,0)--(0,unit,unit)--(0,0,unit)); draw((unit,0,0)--(unit,unit,0)--(unit... |
DeepScaleR | [
{
"role": "user",
"content": "A wooden model of a square pyramid has a base edge of 12 cm and an altitude of 8 cm. A cut is made parallel to the base of the pyramid that separates it into two pieces: a smaller pyramid and a frustum. Each base edge of the smaller pyramid is 6 cm and its altitude is 4 cm. How... | math | {
"style": "rule",
"ground_truth": "336"
} | {
"index": 4168,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A word is an ordered, non-empty sequence of letters, such as $word$ or $wrod$ . How many distinct $3$ -letter words can be made from a subset of the letters $c, o, m, b, o$ , where each letter in the list is used no more than the number of times it appears?"
}
] | math | {
"style": "rule",
"ground_truth": "33"
} | {
"index": 4169,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A worker first receives a 25% cut in wages, then undergoes a 10% increase on the reduced wage. Determine the percent raise on his latest wage that the worker needs to regain his original pay."
}
] | math | {
"style": "rule",
"ground_truth": "21.21\\%"
} | {
"index": 4170,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A workshop has 11 workers, of which 5 are fitters, 4 are turners, and the remaining 2 master workers can act as both fitters and turners. If we need to select 4 fitters and 4 turners to repair a lathe from these 11 workers, there are __ different methods for selection."
}
] | math | {
"style": "rule",
"ground_truth": "185"
} | {
"index": 4171,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A workshop has fewer than $60$ employees. When these employees are grouped in teams of $8$, $5$ employees remain without a team. When arranged in teams of $6$, $3$ are left without a team. How many employees are there in the workshop?"
}
] | math | {
"style": "rule",
"ground_truth": "45"
} | {
"index": 4172,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A workshop produces a type of instrument with a fixed cost of $7500. Each additional unit of the instrument requires an additional investment of $100. The total revenue function is given by: $H(x) = \\begin{cases} 400x - x^2, (0 \\leq x \\leq 200) \\\\ 40000, (x > 200) \\end{ca... | math | {
"style": "rule",
"ground_truth": "15000"
} | {
"index": 4173,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A workshop produces items of types $A$ and $B$. One item of type $A$ requires 10 kg of steel and 23 kg of non-ferrous metals, while an item of type $B$ requires 70 kg of steel and 40 kg of non-ferrous metals. The profit from selling an item of type $A$ is 80 thousand rubles, an... | math | {
"style": "rule",
"ground_truth": "2180"
} | {
"index": 4174,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A workshop produces products of types $A$ and $B$. Producing one unit of product $A$ requires 10 kg of steel and 23 kg of non-ferrous metals, while producing one unit of product $B$ requires 70 kg of steel and 40 kg of non-ferrous metals. The profit from selling one unit of pro... | math | {
"style": "rule",
"ground_truth": "2180"
} | {
"index": 4175,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A workshop produces transformers of types $A$ and $B$. One transformer of type $A$ uses 5 kg of transformer iron and 3 kg of wire, while one transformer of type $B$ uses 3 kg of iron and 2 kg of wire. The profit from selling one transformer of type $A$ is 12 thousand rubles, an... | math | {
"style": "rule",
"ground_truth": "1502"
} | {
"index": 4176,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A writer composed a series of essays totaling 60,000 words over a period of 150 hours. However, during the first 50 hours, she was exceptionally productive and wrote half of the total words. Calculate the average words per hour for the entire 150 hours and separately for the fi... | math | {
"style": "rule",
"ground_truth": "600"
} | {
"index": 4177,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A yogurt shop sells four flavors of yogurt and has six different toppings. How many combinations of one flavor and two different toppings are available?"
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 4178,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A younger brother leaves home and walks to the park at a speed of 4 kilometers per hour. Two hours later, the older brother leaves home and rides a bicycle at a speed of 20 kilometers per hour to catch up with the younger brother. How long will it take for the older brother to ... | math | {
"style": "rule",
"ground_truth": "0.5"
} | {
"index": 4179,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A youth radio station, to attract listeners' attention, gives away gifts and grand prizes among them. Gifts are given away hourly over sixteen hours (one gift per hour), and grand prizes are given away during four evening hours (one grand prize per hour). The probability that l... | math | {
"style": "rule",
"ground_truth": "0.862"
} | {
"index": 4180,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A zealous geologist is sponsoring a contest in which entrants have to guess the age of a shiny rock. He offers these clues: the age of the rock is formed from the six digits 2, 2, 2, 3, 7, and 9, and the rock's age begins with an odd digit.\n\nHow many possibilities are there f... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 4181,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A zoo has a menagerie containing four pairs of different animals, one male and one female for each. The zookeeper wishes to feed the animals in a specific pattern: each time he feeds a single animal, the next one he feeds must be a different gender. If he starts by feeding the ... | math | {
"style": "rule",
"ground_truth": "144"
} | {
"index": 4182,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A zoo has six pairs of different animals (one male and one female for each species). The zookeeper wishes to begin feeding the male lion and must alternate between genders each time. Additionally, after feeding any lion, the next animal cannot be a tiger. How many ways can he f... | math | {
"style": "rule",
"ground_truth": "14400"
} | {
"index": 4183,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A zoo houses five different pairs of animals, each pair consisting of one male and one female. To maintain a feeding order by gender alternation, if the initial animal fed is a male lion, how many distinct sequences can the zookeeper follow to feed all the animals?"
}
] | math | {
"style": "rule",
"ground_truth": "2880"
} | {
"index": 4184,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A zookeeper distributes a pile of peaches among several monkeys. If each monkey gets 6 peaches, there are 57 peaches left. If each monkey gets 9 peaches, 5 monkeys get none, and one monkey gets only 3 peaches. How many peaches are there in total?"
}
] | math | {
"style": "rule",
"ground_truth": "273"
} | {
"index": 4185,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A'Niu is riding a horse to cross a river. There are four horses named A, B, C, and D. It takes 2 minutes for horse A to cross the river, 3 minutes for horse B, 7 minutes for horse C, and 6 minutes for horse D. Only two horses can be driven across the river at a time. The questi... | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 4186,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A) For a sample of size $n$ taken from a normal population with a known standard deviation $\\sigma$, the sample mean $\\bar{x}$ is found. At a significance level $\\alpha$, it is required to find the power function of the test of the null hypothesis $H_{0}: a=a_{0}$ regarding ... | math | {
"style": "rule",
"ground_truth": "0.8925"
} | {
"index": 4187,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A, B, C, D, and E are five students who obtained the top 5 positions (no ties) in a math competition. When taking a photo, they stood in a line and each of them made the following statement:\n\nA said: The two students next to me have rankings lower than mine;\nB said: The two ... | math | {
"style": "rule",
"ground_truth": "23514"
} | {
"index": 4188,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A, B, C, and D obtained the top 4 positions in the school (no ties). They made the following statements:\n- A: \"I am neither first nor second.\"\n- B: \"I am neither second nor third.\"\n- C: \"My position is adjacent to B.\"\n- D: \"My position is adjacent to C.\"\n\nGiven th... | math | {
"style": "rule",
"ground_truth": "4123"
} | {
"index": 4189,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A, B, C, and D obtained the top four positions (without ties) in the school, and they made the following statements:\nA: \"I am neither first nor second.\"\nB: \"My position is adjacent to C's position.\"\nC: \"I am neither second nor third.\"\nD: \"My position is adjacent to B... | math | {
"style": "rule",
"ground_truth": "4213"
} | {
"index": 4190,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A, B, and C are guessing a two-digit number.\n\nA says: The number has an even number of factors, and it is greater than 50.\nB says: The number is odd, and it is greater than 60.\nC says: The number is even, and it is greater than 70.\n\nIf each of them is only half correct, w... | math | {
"style": "rule",
"ground_truth": "64"
} | {
"index": 4191,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A, B, and C are three people passing a ball to each other. The first pass is made by A, who has an equal chance of passing the ball to either of the other two people. After three passes, the probability that the ball is still with A is _______."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"index": 4192,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "A, B, and C start from the same point on a circular track with a circumference of 360 meters: A starts first and runs in the counterclockwise direction; before A completes a lap, B and C start simultaneously and run in the clockwise direction; when A and B meet for the first ti... | math | {
"style": "rule",
"ground_truth": "90"
} | {
"index": 4193,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "ABC is a triangle. D is the midpoint of AB, E is a point on the side BC such that BE = 2 EC and ∠ADC = ∠BAE. Find ∠BAC."
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 4194,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "ABCD is a rectangle, D is the center of the circle, and B is on the circle. If AD=4 and CD=3, then the area of the shaded region is between"
}
] | math | {
"style": "rule",
"ground_truth": "7 and 8"
} | {
"index": 4195,
"solution": "1. **Identify the given information**: We are given a rectangle ABCD with D as the center of a circle and B on the circle. The lengths AD and CD are given as 4 and 3 respectively.\n\n2. **Calculate the diagonal AC using the Pythagorean Theorem**: Since ABCD is a rectangle, the diagonal... |
DeepScaleR | [
{
"role": "user",
"content": "ABCD is a square with side of unit length. Points E and F are taken respectively on sides AB and AD so that AE = AF and the quadrilateral CDFE has maximum area. In square units this maximum area is:"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{8}"
} | {
"index": 4196,
"solution": "1. **Define the problem setup**: Let $ABCD$ be a square with side length 1. Points $E$ and $F$ are on sides $AB$ and $AD$ respectively such that $AE = AF = x$. We need to maximize the area of quadrilateral $CDFE$.\n\n2. **Express the area of $CDFE$**: Consider dropping a perpendicular ... |
DeepScaleR | [
{
"role": "user",
"content": "ABCD is a square. BDEF is a rhombus with A, E, and F collinear. Find ∠ADE."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 4197,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "ABCD is a trapezium inscribed in a circle centered at O. It is given that AB is parallel to CD, angle COD is three times angle AOB, and the ratio of AB to CD is 2:5. Calculate the ratio of the area of triangle BOC to the area of triangle AOB."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{2}"
} | {
"index": 4198,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "ABCD is an isosceles trapezoid with \\(AB = CD\\). \\(\\angle A\\) is acute, \\(AB\\) is the diameter of a circle, \\(M\\) is the center of the circle, and \\(P\\) is the point of tangency of the circle with the side \\(CD\\). Denote the radius of the circle as \\(x\\). Then \\... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 4199,
"solution": ""
} |
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