data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "Given that $θ \\in (0,π)$, and $\\sin ( \\frac {π}{4}-θ)= \\frac { \\sqrt {2}}{10}$, find $\\tan 2θ$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac {24}{7}"
} | {
"index": 15100,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that $θ$ is a real number, if the complex number $z=\\sin 2θ-1+i( \\sqrt {2}\\cos θ-1)$ is a purely imaginary number, then the imaginary part of $z$ is _______."
}
] | math | {
"style": "rule",
"ground_truth": "-2"
} | {
"index": 15101,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that $θ$ is an angle in the second quadrant and $\\tan(\\begin{matrix}θ+ \\frac{π}{4}\\end{matrix}) = \\frac{1}{2}$, find the value of $\\sin(θ) + \\cos(θ)$."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{\\sqrt{10}}{5}"
} | {
"index": 15102,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that $θ$ is an angle in the second quadrant, and $\\sin θ$ and $\\cos θ$ are the two roots of the equation $2x^2 + (\\sqrt{3} - 1)x + m = 0$ (where $m \\in \\mathbb{R}$), find the value of $\\sin θ - \\cos θ$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1 + \\sqrt{3}}{2}"
} | {
"index": 15103,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that $θ$ is an angle in the second quadrant, if $\\tan \\left(θ+ \\frac {π}{4}\\right)= \\frac {1}{2}$, calculate the value of $\\sin θ-\\cos θ$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac {2 \\sqrt {10}}{5}"
} | {
"index": 15104,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that $θ$ is an angle in the third quadrant and $\\sin (θ- \\frac {π}{4})= \\frac {3}{5}$, find $\\tan (θ+ \\frac {π}{4})=$____."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac {4}{3}"
} | {
"index": 15105,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that $θ∈[0,π]$, find the probability that $\\sin (θ+ \\frac {π}{3}) < \\frac {1}{2}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 15106,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that (1+ex)<sup>2019</sup>=a<sub>0</sub>+a<sub>1</sub>x+a<sub>2</sub>x<sup>2</sup>+……+a<sub>2019</sub>x<sup>2019</sup>, find the value of:\n- $$\\frac {a_{1}}{e}$$+ $$\\frac {a_{2}}{e^{2}}$$\\- $$\\frac {a_{3}}{e^{3}}$$+ $$\\frac {a_{4}}{e^{4}}$$\\-……- $$\\frac {a_{2019}}... | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 15107,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that -1, a, b, -4 form an arithmetic sequence, and -1, c, d, e, -4 form a geometric sequence, calculate the value of $$\\frac{b-a}{d}$$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 15108,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that -9, a_{1}, a_{2}, -1 are four real numbers forming an arithmetic sequence, and -9, b_{1}, b_{2}, b_{3}, -1 are five real numbers forming a geometric sequence, find the value of b_{2}(a_{2}-a_{1})."
}
] | math | {
"style": "rule",
"ground_truth": "-8"
} | {
"index": 15109,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 0.5 liters is approximately 1.05 pints, how many pints are in one liter? Express your answer as a decimal to the nearest tenth."
}
] | math | {
"style": "rule",
"ground_truth": "2.1"
} | {
"index": 15110,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 10 is the arithmetic mean of the set $\\{6, 13, 18, 4, x\\}$, what is the value of $x$?"
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"index": 15111,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 10 spots for the finals of the 2009 National High School Mathematics Competition are to be distributed to four different schools in a certain district, with the requirement that one school gets 1 spot, another gets 2 spots, a third gets 3 spots, and the last one gets... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 15112,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 2 students exercised 0 days, 4 students exercised 1 day, 5 students exercised 2 days, 3 students exercised 4 days, 7 students exercised 5 days, and 2 students exercised 6 days, calculate the average number of days exercised last week by the students in Ms. Brown's cl... | math | {
"style": "rule",
"ground_truth": "3.17"
} | {
"index": 15113,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 2 students exercised for 0 days, 4 students exercised for 1 day, 2 students exercised for 2 days, 5 students exercised for 3 days, 4 students exercised for 4 days, 7 students exercised for 5 days, 3 students exercised for 6 days, and 2 students exercised for 7 days, ... | math | {
"style": "rule",
"ground_truth": "3.66"
} | {
"index": 15114,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 2 teachers and 4 students are to be divided into 2 groups, each consisting of 1 teacher and 2 students, calculate the total number of different arrangements for the social practice activities in two different locations, A and B."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 15115,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 20% of the birds are geese, 40% are swans, 10% are herons, and 20% are ducks, and the remaining are pigeons, calculate the percentage of the birds that are not herons and are ducks."
}
] | math | {
"style": "rule",
"ground_truth": "22.22\\%"
} | {
"index": 15116,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 216 sprinters enter a 100-meter dash competition, and the track has 6 lanes, determine the minimum number of races needed to find the champion sprinter."
}
] | math | {
"style": "rule",
"ground_truth": "43"
} | {
"index": 15117,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 28×15=420, directly write out the results of the following multiplications:\n2.8×1.5=\\_\\_\\_\\_\\_\\_、0.28×1.5=\\_\\_\\_\\_\\_\\_、0.028×0.15=\\_\\_\\_\\_\\_\\_."
}
] | math | {
"style": "rule",
"ground_truth": "0.0042"
} | {
"index": 15118,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 3 females and 2 males participate in a performance sequence, and the 2 males cannot appear consecutively, and female A cannot be the first to appear, determine the total number of different performance sequences."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 15119,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 3 people are to be selected from 5 girls and 2 boys, if girl A is selected, determine the probability that at least one boy is selected."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{5}"
} | {
"index": 15120,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 30 balls are put into four boxes A, B, C, and D, such that the sum of the number of balls in A and B is greater than the sum of the number of balls in C and D, find the total number of possible ways."
}
] | math | {
"style": "rule",
"ground_truth": "2600"
} | {
"index": 15121,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 5 students are to be distributed into two groups, A and B, with at least one person in each group, and student A cannot be in group A, calculate the number of different distribution schemes."
}
] | math | {
"style": "rule",
"ground_truth": "15"
} | {
"index": 15122,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 5 students each specialize in one subject (Chinese, Mathematics, Physics, Chemistry, History) and there are 5 test papers (one for each subject: Chinese, Mathematics, Physics, Chemistry, History), a teacher randomly distributes one test paper to each student. Calcula... | math | {
"style": "rule",
"ground_truth": "89/120"
} | {
"index": 15123,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 50 students are selected from 2013 students using a two-step process, first eliminating 13 students through simple random sampling and then selecting 50 from the remaining 2000 using systematic sampling, determine the probability of each person being selected."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{50}{2013}"
} | {
"index": 15124,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 6 rational numbers are placed sequentially on a given circle, now select any 3 adjacent numbers $a$, $b$, $c$ in a clockwise direction, satisfying $a = |b - c|$. It is also known that the total sum of all the placed numbers is 1. What are the values of these 6 number... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4}"
} | {
"index": 15125,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 60% of all students in Ms. Hanson's class answered \"Yes\" to the question \"Do you love science\" at the beginning of the school year, 40% answered \"No\", 80% answered \"Yes\" and 20% answered \"No\" at the end of the school year, calculate the difference between t... | math | {
"style": "rule",
"ground_truth": "40\\%"
} | {
"index": 15126,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 600 athletes are numbered from 001 to 600 and divided into three color groups (red: 001 to 311, white: 312 to 496, and yellow: 497 to 600), calculate the probability of randomly drawing an athlete wearing white clothing."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{8}{25}"
} | {
"index": 15127,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 7,999,999,999 has at most two prime factors, find its largest prime factor."
}
] | math | {
"style": "rule",
"ground_truth": "4,002,001"
} | {
"index": 15128,
"solution": "7,999,999,999=8 \\cdot 10^{9}-1=2000^{3}-1=(2000-1)\\left(2000^{2}+2000+1\\right)$, so \\left(2000^{2}+2000+1\\right)=4,002,001$ is its largest prime factor."
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 70% of the light bulbs are produced by Factory A with a pass rate of 95%, and 30% are produced by Factory B with a pass rate of 80%, calculate the probability of buying a qualified light bulb produced by Factory A from the market."
}
] | math | {
"style": "rule",
"ground_truth": "0.665"
} | {
"index": 15129,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 8 balls are randomly and independently painted either red or blue with equal probability, find the probability that exactly 4 balls are red and exactly 4 balls are blue, and all red balls come before any blue balls in the order they were painted."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{256}"
} | {
"index": 15130,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 8 first-year high school students are divided evenly between two companies, A and B, with the condition that two students with excellent English grades cannot be assigned to the same company and three students with computer skills cannot be assigned to the same compa... | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 15131,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that 800 students were surveyed, and their pasta and pizza preferences were lasagna (150 students), manicotti (120 students), ravioli (180 students), spaghetti (200 students), and pizza (150 students), calculate the ratio of the number of students who preferred spaghetti ... | math | {
"style": "rule",
"ground_truth": "\\frac{4}{3}"
} | {
"index": 15132,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that A and B are any two points on the line l, and O is a point outside of l. If there is a point C on l that satisfies the equation $\\overrightarrow {OC}= \\overrightarrow {OA}cosθ+ \\overrightarrow {OB}cos^{2}θ$, find the value of $sin^{2}θ+sin^{4}θ+sin^{6}θ$."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt {5}-1"
} | {
"index": 15133,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that A and B can only take on the first three roles, and the other three volunteers (C, D, and E) can take on all four roles, calculate the total number of different selection schemes for four people from five volunteers."
}
] | math | {
"style": "rule",
"ground_truth": "72"
} | {
"index": 15134,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that A is a moving point on the ray $x+y=0$ (where $x \\leq 0$), and B is a moving point on the positive half of the x-axis, if line AB is tangent to the circle $x^2+y^2=1$, the minimum value of $|AB|$ is _______ ."
}
] | math | {
"style": "rule",
"ground_truth": "2 + 2\\sqrt{2}"
} | {
"index": 15135,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Adam has a triangular field ABC with AB = 5, BC = 8, and CA = 11, and he intends to separate the field into two parts by building a straight fence from A to a point D on side BC such that AD bisects ∠BAC, find the area of the part of the field ABD."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5 \\sqrt{21}}{4}"
} | {
"index": 15136,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Alice is 1.6 meters tall, can reach 50 centimeters above her head, and the ceiling is 3 meters tall, find the minimum height of the stool in centimeters needed for her to reach a ceiling fan switch located 15 centimeters below the ceiling."
}
] | math | {
"style": "rule",
"ground_truth": "63"
} | {
"index": 15137,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Alice's car averages 30 miles per gallon of gasoline, and Bob's car averages 20 miles per gallon of gasoline, and Alice drives 120 miles and Bob drives 180 miles, calculate the combined rate of miles per gallon of gasoline for both cars."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{300}{13}"
} | {
"index": 15138,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Anne, Cindy, and Ben repeatedly take turns tossing a die in the order Anne, Cindy, Ben, find the probability that Cindy will be the first one to toss a five."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{30}{91}"
} | {
"index": 15139,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Asha's study times were 40, 60, 50, 70, 30, 55, 45 minutes each day of the week and Sasha's study times were 50, 70, 40, 100, 10, 55, 0 minutes each day, find the average number of additional minutes per day Sasha studied compared to Asha."
}
] | math | {
"style": "rule",
"ground_truth": "-3.57"
} | {
"index": 15140,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Ben constructs a $4$-step staircase using $26$ toothpicks, determine the number of additional toothpicks needed to extend the staircase to a $6$-step staircase,"
}
] | math | {
"style": "rule",
"ground_truth": "22"
} | {
"index": 15141,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Ben spent some amount of money and David spent $0.5 less for each dollar Ben spent, and Ben paid $16.00 more than David, determine the total amount they spent together in the bagel store."
}
] | math | {
"style": "rule",
"ground_truth": "48.00"
} | {
"index": 15142,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Bill's age in two years will be three times his current age, and the digits of both Jack's and Bill's ages are reversed, find the current age difference between Jack and Bill."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 15143,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Bob was instructed to subtract 5 from a certain number and then divide the result by 7, but instead subtracted 7 and then divided by 5, yielding an answer of 47, determine what his answer would have been had he worked the problem correctly."
}
] | math | {
"style": "rule",
"ground_truth": "33"
} | {
"index": 15144,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Carl has 24 fence posts and places one on each of the four corners, with 3 yards between neighboring posts, where the number of posts on the longer side is three times the number of posts on the shorter side, determine the area, in square yards, of Carl's lawn."
}
... | math | {
"style": "rule",
"ground_truth": "243"
} | {
"index": 15145,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Charlie estimates 80,000 fans in Chicago, Daisy estimates 70,000 fans in Denver, and Ed estimates 65,000 fans in Edmonton, and given the actual attendance in Chicago is within $12\\%$ of Charlie's estimate, Daisy's estimate is within $15\\%$ of the actual attendance ... | math | {
"style": "rule",
"ground_truth": "29000"
} | {
"index": 15146,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Chelsea is ahead by 60 points halfway through a 120-shot archery contest, with each shot scoring 10, 8, 5, 3, or 0 points and Chelsea scoring at least 5 points on every shot, determine the smallest number of bullseyes (10 points) Chelsea needs to shoot in her next n ... | math | {
"style": "rule",
"ground_truth": "49"
} | {
"index": 15147,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Chelsea is leading by 60 points halfway through a 120-shot archery competition, each shot can score 10, 7, 3, or 0 points, and Chelsea always scores at least 3 points. If Chelsea's next \\(n\\) shots are all for 10 points, she will secure her victory regardless of he... | math | {
"style": "rule",
"ground_truth": "52"
} | {
"index": 15148,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Chloe's telephone numbers have the form $555-ab-cdef$, where $a$, $b$, $c$, $d$, $e$, and $f$ are distinct digits, in descending order, and are chosen between $1$ and $8$, calculate the total number of possible telephone numbers that Chloe can have."
}
] | math | {
"style": "rule",
"ground_truth": "28"
} | {
"index": 15149,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Connie adds $3$ to a number and gets $45$ as her answer, but she should have subtracted $3$ from the number to get the correct answer, determine the correct number."
}
] | math | {
"style": "rule",
"ground_truth": "39"
} | {
"index": 15150,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Crystal runs due north for 2 miles, then northwest for 1 mile, and southwest for 1 mile, find the distance of the last portion of her run that returns her directly to her starting point."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{6}"
} | {
"index": 15151,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that D is a point on the hypotenuse BC of right triangle ABC, and $AC= \\sqrt {3}DC$, $BD=2DC$. If $AD=2 \\sqrt {3}$, then $DC=\\_\\_\\_\\_\\_\\_$."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt {6}"
} | {
"index": 15152,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that EF = 40 units, FG = 30 units, and one diagonal EH = 50 units, calculate the perimeter of parallelogram EFGH."
}
] | math | {
"style": "rule",
"ground_truth": "140"
} | {
"index": 15153,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Erin the ant starts at a given corner of a hypercube (4-dimensional cube) and crawls along exactly 15 edges in such a way that she visits every corner exactly once and then finds that she is unable to return along an edge to her starting point, determine the number o... | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 15154,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that F is the right focus of the ellipse $\\frac{x^{2}}{a^{2}}+ \\frac{y^{2}}{b^{2}}=1(a>b>0)$, and A is one endpoint of the ellipse's minor axis. If F is the trisection point of the chord of the ellipse that passes through AF, calculate the eccentricity of the ellipse."
... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{3}"
} | {
"index": 15155,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that F<sub>1</sub>(-c, 0) and F<sub>2</sub>(c, 0) are the left and right foci of the ellipse G: $$\\frac{x^2}{a^2}+ \\frac{y^2}{4}=1 \\quad (a>0),$$ point M is a point on the ellipse, and MF<sub>2</sub> is perpendicular to F<sub>1</sub>F<sub>2</sub>, with |MF<sub>1</sub>|... | math | {
"style": "rule",
"ground_truth": "\\frac{9}{2}"
} | {
"index": 15156,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Fox wants to ensure he has 20 coins left after crossing the bridge four times, and paying a $50$-coin toll each time, determine the number of coins that Fox had at the beginning."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 15157,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Gill leaves Lille at 09:00, the train travels the first 27 km at 96 km/h and then stops at Lens for 3 minutes before traveling the final 29 km to Lillers at 96 km/h, calculate the arrival time at Lillers."
}
] | math | {
"style": "rule",
"ground_truth": "09:38"
} | {
"index": 15158,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Isabella's fort has dimensions $15$ feet in length, $12$ feet in width, and $6$ feet in height, with one-foot thick floor and walls, determine the number of one-foot cubical blocks required to construct this fort."
}
] | math | {
"style": "rule",
"ground_truth": "430"
} | {
"index": 15159,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Jackie has $40$ thin rods, one of each integer length from $1 \\text{ cm}$ through $40 \\text{ cm}$, with rods of lengths $5 \\text{ cm}$, $12 \\text{ cm}$, and $20 \\text{ cm}$ already placed on a table, find the number of the remaining rods that she can choose as t... | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 15160,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Jeff, Maria, and Lee paid $90, $150, and $210 respectively, find j - m where Jeff gave Lee $j dollars and Maria gave Lee $m dollars to settle the debts such that everyone paid equally."
}
] | math | {
"style": "rule",
"ground_truth": "60"
} | {
"index": 15161,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Jennifer plans to build a fence around her garden in the shape of a rectangle, with $24$ fence posts, and evenly distributing the remaining along the edges, with $6$ yards between each post, and with the longer side of the garden, including corners, having three time... | math | {
"style": "rule",
"ground_truth": "855"
} | {
"index": 15162,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Jessica uses 150 grams of lemon juice and 100 grams of sugar, and there are 30 calories in 100 grams of lemon juice and 386 calories in 100 grams of sugar, and water contains no calories, compute the total number of calories in 300 grams of her lemonade."
}
] | math | {
"style": "rule",
"ground_truth": "152.1"
} | {
"index": 15163,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Jessie moves from 0 to 24 in six steps, and travels four steps to reach point x, then one more step to reach point z, and finally one last step to point y, calculate the value of y."
}
] | math | {
"style": "rule",
"ground_truth": "24"
} | {
"index": 15164,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Jo and Blair take turns counting from 1, with Jo adding 2 to the last number said and Blair subtracting 1 from the last number said, determine the 53rd number said."
}
] | math | {
"style": "rule",
"ground_truth": "79"
} | {
"index": 15165,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Jo climbs a flight of 8 stairs, and Jo can take the stairs 1, 2, 3, or 4 at a time, or a combination of these steps that does not exceed 4 with a friend, determine the number of ways Jo and the friend can climb the stairs together, including instances where either Jo... | math | {
"style": "rule",
"ground_truth": "108"
} | {
"index": 15166,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Josie jogs parallel to a canal along which a boat is moving at a constant speed in the same direction and counts 130 steps to reach the front of the boat from behind it, and 70 steps from the front to the back, find the length of the boat in terms of Josie's steps."
... | math | {
"style": "rule",
"ground_truth": "91"
} | {
"index": 15167,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Joy has 40 thin rods, one each of every integer length from 1 cm through 40 cm, with rods of lengths 4 cm, 9 cm, and 18 cm already placed on a table, determine how many of the remaining rods can be chosen as the fourth rod to form a quadrilateral with positive area."... | math | {
"style": "rule",
"ground_truth": "22"
} | {
"index": 15168,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Kira needs to store 25 files onto disks, each with 2.0 MB of space, where 5 files take up 0.6 MB each, 10 files take up 1.0 MB each, and the rest take up 0.3 MB each, determine the minimum number of disks needed to store all 25 files."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 15169,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Lauren has 4 sisters and 7 brothers, and her brother Lucas has S sisters and B brothers. Find the product of S and B."
}
] | math | {
"style": "rule",
"ground_truth": "35"
} | {
"index": 15170,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Let \\\\(S_{n}\\\\) and \\\\(T_{n}\\\\) be the sums of the first \\\\(n\\\\) terms of the arithmetic sequences \\\\(\\{a_{n}\\}\\\\) and \\\\(\\{b_{n}\\}\\\\), respectively, and \\\\( \\frac {S_{n}}{T_{n}}= \\frac {n}{2n+1} (n∈N^{*})\\\\), determine the value of \\\\... | math | {
"style": "rule",
"ground_truth": "\\frac{11}{23}"
} | {
"index": 15171,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Li Ming mistakenly read the units digit of \\(a\\) as 1 instead of 7 and got a product of 255, and Wang Ning mistakenly read the tens digit of \\(a\\) as 6 instead of 5 and got a product of 335, calculate the correct product of \\(a \\cdot b\\)."
}
] | math | {
"style": "rule",
"ground_truth": "285"
} | {
"index": 15172,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Liliane has $30\\%$ more cookies than Jasmine and Oliver has $10\\%$ less cookies than Jasmine, and the total number of cookies in the group is $120$, calculate the percentage by which Liliane has more cookies than Oliver."
}
] | math | {
"style": "rule",
"ground_truth": "44.44\\%"
} | {
"index": 15173,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Liz had no money initially, and her friends gave her one-sixth, one-fifth, and one-fourth of their respective amounts, find the fractional part of the group's total money that Liz has."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{5}"
} | {
"index": 15174,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Lucas makes a batch of lemonade using 200 grams of lemon juice, 100 grams of sugar, and 300 grams of water. If there are 25 calories in 100 grams of lemon juice and 386 calories in 100 grams of sugar, and water has no calories, determine the total number of calories ... | math | {
"style": "rule",
"ground_truth": "145"
} | {
"index": 15175,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Lucas's odometer showed 27372 miles, which is a palindrome, and 3 hours later it showed another palindrome, calculate Lucas's average speed, in miles per hour, during this 3-hour period."
}
] | math | {
"style": "rule",
"ground_truth": "33.33"
} | {
"index": 15176,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Luis wants to arrange his sticker collection in rows with exactly 4 stickers in each row, and he has 29 stickers initially, find the minimum number of additional stickers Luis must purchase so that the total number of stickers can be exactly split into 5 equal groups... | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 15177,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that M and N are the intersection points of circle A: $x^2 + y^2 - 2x = 0$ and circle B: $x^2 + y^2 + 2x - 4y = 0$, find the area of triangle BMN."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{2}"
} | {
"index": 15178,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that M is a point on the parabola $y^2 = 2px$ ($p > 0$), F is the focus of the parabola $C$, and $|MF| = p$. K is the intersection point of the directrix of the parabola $C$ and the x-axis. Calculate the measure of angle $\\angle MKF$."
}
] | math | {
"style": "rule",
"ground_truth": "45"
} | {
"index": 15179,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Marie has 2500 coins consisting of pennies (1-cent coins), nickels (5-cent coins), and dimes (10-cent coins) with at least one of each type of coin, calculate the difference in cents between the greatest possible and least amounts of money that Marie can have."
}
] | math | {
"style": "rule",
"ground_truth": "22473"
} | {
"index": 15180,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Mary is 30% older than Sally, and Sally is 50% younger than Danielle, and the sum of their ages is 45 years, determine Mary's age on her next birthday."
}
] | math | {
"style": "rule",
"ground_truth": "14"
} | {
"index": 15181,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Mary reversed the digits of a two-digit multiplier $b$, while multiplying correctly with a positive integer $a$, and her erroneous product was $180$, determine the correct product of $a$ and $b$."
}
] | math | {
"style": "rule",
"ground_truth": "180"
} | {
"index": 15182,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Mike walks to his college, averaging 70 steps per minute with each step being 80 cm long, and it takes him 20 minutes to get there, determine how long it takes Tom to reach the college, given that he averages 120 steps per minute, but his steps are only 50 cm long."
... | math | {
"style": "rule",
"ground_truth": "18.67"
} | {
"index": 15183,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Mr. A initially owns a home worth $\\$15,000$, he sells it to Mr. B at a $20\\%$ profit, then Mr. B sells it back to Mr. A at a $15\\%$ loss, then Mr. A sells it again to Mr. B at a $10\\%$ profit, and finally Mr. B sells it back to Mr. A at a $5\\%$ loss, calculate ... | math | {
"style": "rule",
"ground_truth": "3541.50"
} | {
"index": 15184,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Ms. Demeanor's class consists of 50 students, more than half of her students bought crayons from the school bookstore, each buying the same number of crayons, with each crayon costing more than the number of crayons bought by each student, and the total cost for all ... | math | {
"style": "rule",
"ground_truth": "37"
} | {
"index": 15185,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Nayla has an index card measuring $5 \\times 7$ inches, and she shortens the length of one side by $2$ inches, resulting in a card with an area of $21$ square inches, determine the area of the card if instead, she shortens the length of the other side by the same amo... | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 15186,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that P and Q are points on the graphs of the functions $2x-y+6=0$ and $y=2\\ln x+2$ respectively, find the minimum value of the line segment |PQ|."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{6\\sqrt{5}}{5}"
} | {
"index": 15187,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that P is a point on the hyperbola $\\frac{x^2}{4} - \\frac{y^2}{3} = 1$, and $F_1$, $F_2$ are the two foci of the hyperbola. If $\\angle F_1PF_2 = 60^\\circ$, calculate the area of $\\triangle PF_1F_2$."
}
] | math | {
"style": "rule",
"ground_truth": "3\\sqrt{3}"
} | {
"index": 15188,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Ron has eight sticks with integer lengths, and he is unable to form a triangle using any three of these sticks as side lengths, determine the shortest possible length of the longest of the eight sticks."
}
] | math | {
"style": "rule",
"ground_truth": "21"
} | {
"index": 15189,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Ron incorrectly calculated the product of two positive integers $a$ and $b$ by reversing the digits of the three-digit number $a$, and that His wrong product totaled $468$, determine the correct value of the product of $a$ and $b$."
}
] | math | {
"style": "rule",
"ground_truth": "1116"
} | {
"index": 15190,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Ron mistakenly reversed the digits of the two-digit number $a$, and the product of $a$ and $b$ was mistakenly calculated as $221$, determine the correct product of $a$ and $b$."
}
] | math | {
"style": "rule",
"ground_truth": "527"
} | {
"index": 15191,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Sia and Kira count sequentially, where Sia skips every fifth number, find the 45th number said in this modified counting game."
}
] | math | {
"style": "rule",
"ground_truth": "54"
} | {
"index": 15192,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Sofia has a $5 \\times 7$ index card, if she shortens the length of one side by $2$ inches and the card has an area of $21$ square inches, find the area of the card in square inches if instead she shortens the length of the other side by $1$ inch."
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 15193,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Square $ABCD$ has side length $5$, point $M$ is chosen on side $AB$ so that $\\angle AMD = \\angle CMD$, calculate the degree measure of $\\angle AMD$."
}
] | math | {
"style": "rule",
"ground_truth": "45"
} | {
"index": 15194,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Star lists the whole numbers $1$ through $30$ once and Emilio copies those numbers replacing each occurrence of the digit $3$ by the digit $2$, find the difference between Star's and Emilio's total sums."
}
] | math | {
"style": "rule",
"ground_truth": "13"
} | {
"index": 15195,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Steve's empty swimming pool holds 30,000 gallons of water when full and will be filled by 5 hoses, each supplying 2.5 gallons of water per minute, calculate the time required to fill the pool."
}
] | math | {
"style": "rule",
"ground_truth": "40"
} | {
"index": 15196,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Three people, A, B, and C, are applying to universities A, B, and C, respectively, where each person can only apply to one university, calculate the conditional probability $P\\left(A|B\\right)$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"index": 15197,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Tian Ji's top horse is faster than the King of Qi's middle horse, and Tian Ji's middle horse is faster than the King of Qi's bottom horse, but Tian Ji's top horse is slower than the King of Qi's top horse, and Tian Ji's bottom horse is slower than the King of Qi's bo... | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"index": 15198,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Given that Xiao Ming ran a lap on a 360-meter circular track at a speed of 5 meters per second in the first half of the time and 4 meters per second in the second half of the time, determine the time taken to run in the second half of the distance."
}
] | math | {
"style": "rule",
"ground_truth": "44"
} | {
"index": 15199,
"solution": ""
} |
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