data_source large_stringclasses 1
value | prompt listlengths 1 1 | reward_model dict | extra_info dict |
|---|---|---|---|
math | [
{
"content": "What is the greatest common factor of 180, 240, and 300? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "60",
"style": "rule"
} | {
"index": "35200",
"split": "train"
} |
math | [
{
"content": "Given a regular pyramid V-ABCD with a base edge length of 4 and a lateral edge length of $\\sqrt{13}$, its surface area is ______. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "40",
"style": "rule"
} | {
"index": "35201",
"split": "train"
} |
math | [
{
"content": "Points $A$, $B$, $C$, and $D$ are located on $\\overline{AB}$ such that $AB = 3AD = 6BC$. If a point is selected at random on $\\overline{AB}$, what is the probability that it is between $C$ and $D$? Express your answer as a common fraction.\n\n[asy]\n\ndraw((0,0)--(12,.0000000001));\ndot((0,0)); ... | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"index": "35202",
"split": "train"
} |
math | [
{
"content": "Select 5 people from 3 orthopedic doctors, 4 neurosurgeons, and 5 internists to form an earthquake relief medical team. The number of ways to select such that there is at least one doctor from each specialty is (answer in digits). Please output the final answer within \\boxed{}.",
"role": "use... | {
"ground_truth": "590",
"style": "rule"
} | {
"index": "35203",
"split": "train"
} |
math | [
{
"content": "In a circular arrangement of 101 natural numbers, it is known that among any 5 consecutive numbers, there are at least two even numbers. What is the minimum number of even numbers that can be among the listed numbers? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "41",
"style": "rule"
} | {
"index": "35204",
"split": "train"
} |
math | [
{
"content": "Solve for $x$: $$5^{x + 4} = 125^x.$$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "x = 2",
"style": "rule"
} | {
"index": "35205",
"split": "train"
} |
math | [
{
"content": "We define the polynomial $$ P (x) = 2014x^{2013} + 2013x^{2012} +... + 4x^3 + 3x^2 + 2x. $$ Find the largest prime divisor of $P (2)$ . Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "61",
"style": "rule"
} | {
"index": "35206",
"split": "train"
} |
math | [
{
"content": "The third quartile of the data $13$, $11$, $12$, $15$, $16$, $18$, $21$, $17$ is ______. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "17.5",
"style": "rule"
} | {
"index": "35207",
"split": "train"
} |
math | [
{
"content": "In right triangle $ABC$ with $\\angle B = 90^\\circ$, we have $$2\\sin A = 3\\cos A.$$What is $\\sin A$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{3\\sqrt{13}}{13}",
"style": "rule"
} | {
"index": "35208",
"split": "train"
} |
math | [
{
"content": "How many positive integers less than 10,000 have at most three different digits? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "4119",
"style": "rule"
} | {
"index": "35209",
"split": "train"
} |
math | [
{
"content": "A box contains $3$ shiny pennies and $4$ dull pennies. One by one, pennies are drawn at random from the box and not replaced. If the probability is $a/b$ that it will take more than four draws until the third shiny penny appears and $a/b$ is in lowest terms, then $a+b=$ Please output the final ans... | {
"ground_truth": "66",
"style": "rule"
} | {
"index": "35210",
"split": "train"
} |
math | [
{
"content": "For a nonnegative integer $n$ and a strictly increasing sequence of real numbers $t_0,t_1,\\dots,t_n$, let $f(t)$ be the corresponding real-valued function defined for $t \\geq t_0$ by the following properties: \\begin{enumerate} \\item[(a)] $f(t)$ is continuous for $t \\geq t_0$, and is twice dif... | {
"ground_truth": "29",
"style": "rule"
} | {
"index": "35211",
"split": "train"
} |
math | [
{
"content": "Which of the following integers is equal to a perfect square: $2^{3}$, $3^{5}$, $4^{7}$, $5^{9}$, $6^{11}$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "4^{7}",
"style": "rule"
} | {
"index": "35212",
"split": "train"
} |
math | [
{
"content": "Given that \\\\(AB\\\\) is a chord passing through the focus of the parabola \\\\(y^{2} = 4\\sqrt{3}x\\\\), and the midpoint \\\\(M\\\\) of \\\\(AB\\\\) has an x-coordinate of \\\\(2\\\\), calculate the length of \\\\(AB\\\\. Please output the final answer within \\boxed{}.",
"role": "user"
... | {
"ground_truth": "4 + 2\\sqrt{3}",
"style": "rule"
} | {
"index": "35213",
"split": "train"
} |
math | [
{
"content": "Let $a$, $b$, and $c$ be positive integers with $a\\ge$ $b\\ge$ $c$ such that\n$a^2-b^2-c^2+ab=2011$ and\n$a^2+3b^2+3c^2-3ab-2ac-2bc=-1997$.\nWhat is $a$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "253",
"style": "rule"
} | {
"index": "35214",
"split": "train"
} |
math | [
{
"content": "Given that $\\sqrt {3}\\sin x+\\cos x= \\frac {2}{3}$, find the value of $\\tan (x+ \\frac {7\\pi}{6})$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{\\sqrt{2}}{4}",
"style": "rule"
} | {
"index": "35215",
"split": "train"
} |
math | [
{
"content": "Let $S$ be the set of all rational numbers $r$, $0<r<1$, that have a repeating decimal expansion in the form $0.abcabcabc\\ldots=0.\\overline{abc}$, where the digits $a$, $b$, and $c$ are not necessarily distinct. To write the elements of $S$ as fractions in lowest terms, how many different numera... | {
"ground_truth": "660",
"style": "rule"
} | {
"index": "35216",
"split": "train"
} |
math | [
{
"content": "Given the sequence $\\{a\\_n\\}$ that satisfies $a\\_n-(-1)^{n}a\\_{n-1}=n$ $(n\\geqslant 2)$, and $S\\_n$ is the sum of the first $n$ terms of the sequence, find the value of $S\\_{40}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "440",
"style": "rule"
} | {
"index": "35217",
"split": "train"
} |
math | [
{
"content": "Solve the following equations:\n\na) $\\log _{1 / 5} \\frac{2+x}{10}=\\log _{1 / 5} \\frac{2}{x+1}$;\n\nb) $\\log _{3}\\left(x^{2}-4 x+3\\right)=\\log _{3}(3 x+21)$;\n\nc) $\\log _{1 / 10} \\frac{2 x^{2}-54}{x+3}=\\log _{1 / 10}(x-4)$;\n\nd) $\\log _{(5+x) / 3} 3=\\log _{-1 /(x+1)} 3$. Please outp... | {
"ground_truth": "-4",
"style": "rule"
} | {
"index": "35218",
"split": "train"
} |
math | [
{
"content": "When programming a computer to print the first 10,000 natural numbers greater than 0: $1,2,3, \\cdots, 10000$, the printer unfortunately has a malfunction. Each time it prints the digits 7 or 9, it prints $x$ instead. How many numbers are printed incorrectly? Please output the final answer within ... | {
"ground_truth": "5904",
"style": "rule"
} | {
"index": "35219",
"split": "train"
} |
math | [
{
"content": "If $2^{x-3}=4^2$, find $x$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "7",
"style": "rule"
} | {
"index": "35220",
"split": "train"
} |
math | [
{
"content": "How many zeros are in the expansion of $999,\\!999,\\!999,\\!998^2$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "11",
"style": "rule"
} | {
"index": "35221",
"split": "train"
} |
math | [
{
"content": "Let \\( S = \\{1, 2, \\ldots, 280\\} \\). Find the smallest natural number \\( n \\) such that every \\( n \\)-element subset of \\( S \\) contains 5 pairwise coprime numbers. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "217",
"style": "rule"
} | {
"index": "35222",
"split": "train"
} |
math | [
{
"content": "Six identical rectangles are arranged to form a larger rectangle \\( ABCD \\). The area of \\( ABCD \\) is 6000 square units. What is the length \\( z \\), rounded off to the nearest integer? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "32",
"style": "rule"
} | {
"index": "35223",
"split": "train"
} |
math | [
{
"content": "Find the smallest \\( n \\) such that whenever the elements of the set \\(\\{1, 2, \\ldots, n\\}\\) are colored red or blue, there always exist \\( x, y, z, w \\) (not necessarily distinct) of the same color such that \\( x + y + z = w \\). Please output the final answer within \\boxed{}.",
"r... | {
"ground_truth": "11",
"style": "rule"
} | {
"index": "35224",
"split": "train"
} |
math | [
{
"content": "Calculate the volume of the tetrahedron with vertices at points \\( A_{1}, A_{2}, A_{3}, A_{4} \\). Additionally, find its height dropped from vertex \\( A_{4} \\) onto the face \\( A_{1} A_{2} A_{3} \\).\n\nVertices:\n- \\( A_{1}(-1, 2, 4) \\)\n- \\( A_{2}(-1, -2, -4) \\)\n- \\( A_{3}(3, 0, -1) \... | {
"ground_truth": "24",
"style": "rule"
} | {
"index": "35225",
"split": "train"
} |
math | [
{
"content": "How many times should two dice be rolled so that the probability of getting two sixes at least once is greater than $1/2$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "25",
"style": "rule"
} | {
"index": "35226",
"split": "train"
} |
math | [
{
"content": "A teacher received letters on Monday to Friday with counts of $10$, $6$, $8$, $5$, $6$ respectively. Calculate the standard deviation of this data set. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\dfrac {4 \\sqrt {5}}{5}",
"style": "rule"
} | {
"index": "35227",
"split": "train"
} |
math | [
{
"content": "Find the smallest positive integer that cannot be expressed in the form $\\frac{2^{a}-2^{b}}{2^{c}-2^{d}}$, where $a$, $b$, $c$, and $d$ are all positive integers. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "11",
"style": "rule"
} | {
"index": "35228",
"split": "train"
} |
math | [
{
"content": "Alpha and Beta both took part in a two-day problem-solving competition. At the end of the second day, each had attempted questions worth a total of 500 points. Alpha scored 160 points out of 300 points attempted on the first day, and scored 140 points out of 200 points attempted on the second day.... | {
"ground_truth": "849",
"style": "rule"
} | {
"index": "35229",
"split": "train"
} |
math | [
{
"content": "Let $x_1,$ $x_2,$ $\\dots,$ $x_n$ be nonnegative real numbers such that $x_1 + x_2 + \\dots + x_n = 1$ and\n\\[x_1^2 + x_2^2 + \\dots + x_n^2 \\le \\frac{1}{100}.\\]Find the smallest possible value of $n.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "100",
"style": "rule"
} | {
"index": "35230",
"split": "train"
} |
math | [
{
"content": "Let $f(x) = 4x - 9$ and $g(f(x)) = 3x^2 + 4x - 2.$ Find $g(-10).$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{-45}{16}",
"style": "rule"
} | {
"index": "35231",
"split": "train"
} |
math | [
{
"content": "Given $a$ and $b$ are positive numbers such that $a^b = b^a$ and $b = 4a$, solve for the value of $a$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt[3]{4}",
"style": "rule"
} | {
"index": "35232",
"split": "train"
} |
math | [
{
"content": "How many tetrahedrons can be formed using the vertices of a regular triangular prism? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "12",
"style": "rule"
} | {
"index": "35233",
"split": "train"
} |
math | [
{
"content": "Suppose $656_7=3ab_{10}$, where $a$ and $b$ represent base-10 digits. Find $\\frac{a\\cdot b}{15}$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1",
"style": "rule"
} | {
"index": "35234",
"split": "train"
} |
math | [
{
"content": "Let $ABC$ be a triangle with incenter $I$, centroid $G$, and $|AC|>|AB|$. If $IG\\parallel BC$, $|BC|=2$, and $\\text{Area}(ABC)=3\\sqrt{5}/8$, calculate $|AB|$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{9}{8}",
"style": "rule"
} | {
"index": "35235",
"split": "train"
} |
math | [
{
"content": "If \\( \\sqrt{\\frac{3}{x} + 3} = \\frac{5}{3} \\), solve for \\( x \\). Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-\\frac{27}{2}",
"style": "rule"
} | {
"index": "35236",
"split": "train"
} |
math | [
{
"content": "What value of $k$ will make $x^2 - 16x + k$ the square of a binomial? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "64",
"style": "rule"
} | {
"index": "35237",
"split": "train"
} |
math | [
{
"content": "Karen has seven envelopes and seven letters of congratulations to various HMMT coaches. If she places the letters in the envelopes at random with each possible configuration having an equal probability, what is the probability that exactly six of the letters are in the correct envelopes? Please ou... | {
"ground_truth": "0",
"style": "rule"
} | {
"index": "35238",
"split": "train"
} |
math | [
{
"content": "Find the quotient when $x^5 + 7$ is divided by $x + 1.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "x^4 - x^3 + x^2 - x + 1",
"style": "rule"
} | {
"index": "35239",
"split": "train"
} |
math | [
{
"content": "In the figure shown, segment $AB$ is parallel to segment $YZ$. If $AZ = 42$ units, $BQ = 12$ units, and $QY = 24$ units, what is the length of segment $QZ$? [asy]\nimport olympiad; import geometry; size(150); defaultpen(linewidth(0.8));\npair Y = (0,0), Z = (16,0), A = (0,8), B = (6,8);\ndraw(A--B... | {
"ground_truth": "28",
"style": "rule"
} | {
"index": "35240",
"split": "train"
} |
math | [
{
"content": "Compute the sum of the geometric series $-1 -3-9-27 -81-243-729$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-1093",
"style": "rule"
} | {
"index": "35241",
"split": "train"
} |
math | [
{
"content": "\\[\n1.047. \\left(\\frac{\\sqrt{561^{2} - 459^{2}}}{4 \\frac{2}{7} \\cdot 0.15 + 4 \\frac{2}{7} : \\frac{20}{3}} + 4 \\sqrt{10}\\right) : \\frac{1}{3} \\sqrt{40}\n\\] Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "125",
"style": "rule"
} | {
"index": "35242",
"split": "train"
} |
math | [
{
"content": "$A B C D E$ is a cyclic convex pentagon, and $A C=B D=C E . A C$ and $B D$ intersect at $X$, and $B D$ and $C E$ intersect at $Y$. If $A X=6, X Y=4$, and $Y E=7$, then the area of pentagon $A B C D E$ can be written as $\\frac{a \\sqrt{b}}{c}$, where $a, b, c$ are integers, $c$ is positive, $b$ is... | {
"ground_truth": "2852",
"style": "rule"
} | {
"index": "35243",
"split": "train"
} |
math | [
{
"content": "Three people, A, B, and C, start from point $A$ to point $B$. A starts at 8:00, B starts at 8:20, and C starts at 8:30. They all travel at the same speed. Ten minutes after C starts, the distance from A to point $B$ is exactly half the distance from B to point $B$. At this time, C is 2015 meters a... | {
"ground_truth": "2418",
"style": "rule"
} | {
"index": "35244",
"split": "train"
} |
math | [
{
"content": "The difference \\(\\sqrt{|40 \\sqrt{2}-57|}-\\sqrt{40 \\sqrt{2}+57}\\) is an integer. Find this number. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-10",
"style": "rule"
} | {
"index": "35245",
"split": "train"
} |
math | [
{
"content": "Given a six-digit phone number, how many different seven-digit phone numbers exist such that, by crossing out one digit, you obtain the given six-digit number? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "70",
"style": "rule"
} | {
"index": "35246",
"split": "train"
} |
math | [
{
"content": "Right triangle $ACD$ with right angle at $C$ is constructed outwards on the hypotenuse $\\overline{AC}$ of isosceles right triangle $ABC$ with leg length $1$, as shown, so that the two triangles have equal perimeters. What is $\\sin(2\\angle BAD)$? Please output the final answer within \\boxed{}."... | {
"ground_truth": "\\frac{7}{9}",
"style": "rule"
} | {
"index": "35247",
"split": "train"
} |
math | [
{
"content": "Sixteen 6-inch wide square posts are evenly spaced with 4 feet between them to enclose a square field. What is the outer perimeter, in feet, of the fence? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "56",
"style": "rule"
} | {
"index": "35248",
"split": "train"
} |
math | [
{
"content": "What is the sum of three consecutive even integers if the sum of the first and third integers is $128$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "192",
"style": "rule"
} | {
"index": "35249",
"split": "train"
} |
math | [
{
"content": "For each positive integer $n$, let $f(n)$ be the sum of the digits in the base-four representation of $n$ and let $g(n)$ be the sum of the digits in the base-eight representation of $f(n)$. For example, $f(2020) = f(133210_{\\text{4}}) = 10 = 12_{\\text{8}}$, and $g(2020) = \\text{the digit sum of... | {
"ground_truth": "151",
"style": "rule"
} | {
"index": "35250",
"split": "train"
} |
math | [
{
"content": "Find the absolute value of the difference of single-digit integers \\( C \\) and \\( D \\) such that in base \\( 5 \\):\n$$ \\begin{array}{c@{}c@{\\;}c@{}c@{}c@{}c}\n& & & D & D & C_5 \\\\\n& & & \\mathbf{3} & \\mathbf{2} & D_5 \\\\\n& & + & C & \\mathbf{2} & \\mathbf{4_5} \\\\\n\\cline{2-6}\n& & ... | {
"ground_truth": "1_5",
"style": "rule"
} | {
"index": "35251",
"split": "train"
} |
math | [
{
"content": "Let $ABC$ be a triangle with $|AB|=18$ , $|AC|=24$ , and $m(\\widehat{BAC}) = 150^\\circ$ . Let $D$ , $E$ , $F$ be points on sides $[AB]$ , $[AC]$ , $[BC]$ , respectively, such that $|BD|=6$ , $|CE|=8$ , and $|CF|=2|BF|$ . Let $H_1$ , $H_2$ , $H_3$ be the reflections of the orth... | {
"ground_truth": "96",
"style": "rule"
} | {
"index": "35252",
"split": "train"
} |
math | [
{
"content": "How many multiples of 5 are there between 5 and 205? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "41",
"style": "rule"
} | {
"index": "35253",
"split": "train"
} |
math | [
{
"content": "Grisha wrote 100 numbers on the board. Then he increased each number by 1 and noticed that the product of all 100 numbers did not change. He increased each number by 1 again, and again the product of all the numbers did not change, and so on. Grisha repeated this procedure $k$ times, and each of t... | {
"ground_truth": "99",
"style": "rule"
} | {
"index": "35254",
"split": "train"
} |
math | [
{
"content": "0.8 + 0.02 Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "0.82",
"style": "rule"
} | {
"index": "35255",
"split": "train"
} |
math | [
{
"content": "A rectangle has one side of length 5 and the other side less than 4. When the rectangle is folded so that two opposite corners coincide, the length of the crease is \\(\\sqrt{6}\\). Calculate the length of the other side. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\sqrt{5}",
"style": "rule"
} | {
"index": "35256",
"split": "train"
} |
math | [
{
"content": "In $\\triangle ABC$, points $E$ and $F$ are on $AB$ and $BC$, respectively, such that $AE = BF$ and $BE = CF$. If $\\angle BAC = 70^{\\circ}$, what is the measure of $\\angle ABC$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "40^{\\circ}",
"style": "rule"
} | {
"index": "35257",
"split": "train"
} |
math | [
{
"content": "A rectangle in the coordinate plane has vertices at $(0, 0), (1000, 0), (1000, 1000),$ and $(0, 1000)$. Compute the radius $d$ to the nearest tenth such that the probability the point is within $d$ units from any lattice point is $\\tfrac{1}{4}$. Please output the final answer within \\boxed{}.",
... | {
"ground_truth": "0.3",
"style": "rule"
} | {
"index": "35258",
"split": "train"
} |
math | [
{
"content": "Find the remainder when $x^3 - 3x + 5$ is divided by $x + 2.$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3",
"style": "rule"
} | {
"index": "35259",
"split": "train"
} |
math | [
{
"content": "Let \\( f(x) = \\frac{x + a}{x^2 + \\frac{1}{2}} \\), where \\( x \\) is a real number and the maximum value of \\( f(x) \\) is \\( \\frac{1}{2} \\) and the minimum value of \\( f(x) \\) is \\( -1 \\). If \\( t = f(0) \\), find the value of \\( t \\). Please output the final answer within \\boxed{... | {
"ground_truth": "-\\frac{1}{2}",
"style": "rule"
} | {
"index": "35260",
"split": "train"
} |
math | [
{
"content": "Cynthia and Lynnelle are collaborating on a problem set. Over a $24$ -hour period, Cynthia and Lynnelle each independently pick a random, contiguous $6$ -hour interval to work on the problem set. Compute the probability that Cynthia and Lynnelle work on the problem set during completely disjoint... | {
"ground_truth": "4/9",
"style": "rule"
} | {
"index": "35261",
"split": "train"
} |
math | [
{
"content": "There are 6 married couples at a party. At the start of the party, every person shakes hands once with every other person except his or her spouse. How many handshakes are there? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "60",
"style": "rule"
} | {
"index": "35262",
"split": "train"
} |
math | [
{
"content": "Consider the sequence of six real numbers 60, 10, 100, 150, 30, and $x$ . The average (arithmetic mean) of this sequence is equal to the median of the sequence. What is the sum of all the possible values of $x$ ? (The median of a sequence of six real numbers is the average of the two middle n... | {
"ground_truth": "135",
"style": "rule"
} | {
"index": "35263",
"split": "train"
} |
math | [
{
"content": "Three natural numbers are written on the board: two ten-digit numbers \\( a \\) and \\( b \\), and their sum \\( a + b \\). What is the maximum number of odd digits that could be written on the board? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "30",
"style": "rule"
} | {
"index": "35264",
"split": "train"
} |
math | [
{
"content": "Consider the function $g(x)$ satisfying \n\\[ g(xy) = 2g(x)g(y) \\]\nfor all real numbers $x$ and $y$ and $g(0) = 2.$ Find $g(10)$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{1}{2}",
"style": "rule"
} | {
"index": "35265",
"split": "train"
} |
math | [
{
"content": "Given the function $f(x) = x^3 - 6x + 5, x \\in \\mathbb{R}$.\n\n(1) Find the equation of the tangent line to the function $f(x)$ at $x = 1$;\n\n(2) Find the extreme values of $f(x)$ in the interval $[-2, 2]$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "5 - 4\\sqrt{2}",
"style": "rule"
} | {
"index": "35266",
"split": "train"
} |
math | [
{
"content": "Multiply $2$ by $54$. For each proper divisor of $1,000,000$, take its logarithm base $10$. Sum these logarithms to get $S$, and find the integer closest to $S$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "141",
"style": "rule"
} | {
"index": "35267",
"split": "train"
} |
math | [
{
"content": "A quadrilateral $ABCD$ has a right angle at $\\angle ABC$ and satisfies $AB = 12$ , $BC = 9$ , $CD = 20$ , and $DA = 25$ . Determine $BD^2$ .\n. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "769",
"style": "rule"
} | {
"index": "35268",
"split": "train"
} |
math | [
{
"content": "Find the sum of the digits in the answer to\n$\\underbrace{9999\\cdots 99}_{94\\text{ nines}} \\times \\underbrace{4444\\cdots 44}_{94\\text{ fours}}$\nwhere a string of $94$ nines is multiplied by a string of $94$ fours. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "846",
"style": "rule"
} | {
"index": "35269",
"split": "train"
} |
math | [
{
"content": "Convert the binary number $110101_{(2)}$ to decimal. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "53",
"style": "rule"
} | {
"index": "35270",
"split": "train"
} |
math | [
{
"content": "Define the sequence \\(\\{a_n\\}\\) where \\(a_n = n^3 + 4\\) for \\(n \\in \\mathbf{N}_+\\). Let \\(d_n = \\gcd(a_n, a_{n+1})\\), which is the greatest common divisor of \\(a_n\\) and \\(a_{n+1}\\). Find the maximum value of \\(d_n\\). Please output the final answer within \\boxed{}.",
"role"... | {
"ground_truth": "433",
"style": "rule"
} | {
"index": "35271",
"split": "train"
} |
math | [
{
"content": "Three students, A, B, and C, are playing badminton with the following rules:<br/>The player who loses two games in a row will be eliminated. Before the game, two players are randomly selected to play against each other, while the third player has a bye. The winner of each game will play against th... | {
"ground_truth": "\\frac{7}{16}",
"style": "rule"
} | {
"index": "35272",
"split": "train"
} |
math | [
{
"content": "Ana's monthly salary was $2000$ in May. In June she received a 20% raise. In July she received a 20% pay cut. After the two changes in June and July, Ana's monthly salary was Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1920",
"style": "rule"
} | {
"index": "35273",
"split": "train"
} |
math | [
{
"content": "The total in-store price for a blender is $\\textdollar 129.95$. A television commercial advertises the same blender for four easy payments of $\\textdollar 29.99$ and a one-time shipping and handling charge of $\\textdollar 14.95$. Calculate the number of cents saved by purchasing the blender thr... | {
"ground_truth": "496",
"style": "rule"
} | {
"index": "35274",
"split": "train"
} |
math | [
{
"content": "Let $ y_0$ be chosen randomly from $ \\{0, 50\\}$ , let $ y_1$ be chosen randomly from $ \\{40, 60, 80\\}$ , let $ y_2$ be chosen randomly from $ \\{10, 40, 70, 80\\}$ , and let $ y_3$ be chosen randomly from $ \\{10, 30, 40, 70, 90\\}$ . (In each choice, the possible outcomes are equa... | {
"ground_truth": "107",
"style": "rule"
} | {
"index": "35275",
"split": "train"
} |
math | [
{
"content": "Given $$|\\vec{a}|=3, |\\vec{b}|=2$$. If $$\\vec{a} \\cdot \\vec{b} = -3$$, then the angle between $$\\vec{a}$$ and $$\\vec{b}$$ is \\_\\_\\_\\_\\_\\_. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{2}{3}\\pi",
"style": "rule"
} | {
"index": "35276",
"split": "train"
} |
math | [
{
"content": "A facility has 7 consecutive parking spaces, and there are 3 different models of cars to be parked. If it is required that among the remaining 4 parking spaces, exactly 3 are consecutive, then the number of different parking methods is \\_\\_\\_\\_\\_\\_. Please output the final answer within \\bo... | {
"ground_truth": "72",
"style": "rule"
} | {
"index": "35277",
"split": "train"
} |
math | [
{
"content": "On the extension of side $AD$ of rhombus $ABCD$, point $K$ is taken beyond point $D$. The lines $AC$ and $BK$ intersect at point $Q$. It is known that $AK=14$ and that points $A$, $B$, and $Q$ lie on a circle with a radius of 6, the center of which belongs to segment $AA$. Find $BK$. Please output... | {
"ground_truth": "20",
"style": "rule"
} | {
"index": "35278",
"split": "train"
} |
math | [
{
"content": "Let $L(m)$ be the $x$ coordinate of the left end point of the intersection of the graphs of $y=x^2-6$ and $y=m$, where $-6<m<6$. Let $r=[L(-m)-L(m)]/m$. Then, as $m$ is made arbitrarily close to zero, the value of $r$ is: Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{1}{\\sqrt{6}}",
"style": "rule"
} | {
"index": "35279",
"split": "train"
} |
math | [
{
"content": "In triangle $ABC$, $AB=13$, $BC=14$, and $CA=15$. Distinct points $D$, $E$, and $F$ lie on segments $\\overline{BC}$, $\\overline{CA}$, and $\\overline{DE}$, respectively, such that $\\overline{AD}\\perp\\overline{BC}$, $\\overline{DE}\\perp\\overline{AC}$, and $\\overline{AF}\\perp\\overline{BF}$... | {
"ground_truth": "21",
"style": "rule"
} | {
"index": "35280",
"split": "train"
} |
math | [
{
"content": "The cost of 60 copies of the first volume and 75 copies of the second volume is 2700 rubles. In reality, the total payment for all these books was only 2370 rubles because a discount was applied: 15% off the first volume and 10% off the second volume. Find the original price of these books. Please... | {
"ground_truth": "20",
"style": "rule"
} | {
"index": "35281",
"split": "train"
} |
math | [
{
"content": "How many distinct five-digit positive integers are there such that the product of their digits equals 16? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "15",
"style": "rule"
} | {
"index": "35282",
"split": "train"
} |
math | [
{
"content": "Let the hyperbola $C:\\frac{x^2}{a^2}-y^2=1\\;(a>0)$ intersect the line $l:x+y=1$ at two distinct points $A$ and $B$. \n$(1)$ Find the range of real numbers for $a$. \n$(2)$ If the intersection point of the line $l$ and the $y$-axis is $P$, and $\\overrightarrow{PA}=\\frac{5}{12}\\overrightarrow... | {
"ground_truth": "a = \\frac{17}{13}",
"style": "rule"
} | {
"index": "35283",
"split": "train"
} |
math | [
{
"content": "Let $P$ be an interior point of triangle $ABC$ . Let $a,b,c$ be the sidelengths of triangle $ABC$ and let $p$ be it's semiperimeter. Find the maximum possible value of $$ \\min\\left(\\frac{PA}{p-a},\\frac{PB}{p-b},\\frac{PC}{p-c}\\right) $$ taking into consideration all possible choic... | {
"ground_truth": "\\frac{2}{\\sqrt{3}}",
"style": "rule"
} | {
"index": "35284",
"split": "train"
} |
math | [
{
"content": "Jackie and Phil have two fair coins and a third coin that comes up heads with probability $\\frac47$. Jackie flips the three coins, and then Phil flips the three coins. Let $\\frac {m}{n}$ be the probability that Jackie gets the same number of heads as Phil, where $m$ and $n$ are relatively prime ... | {
"ground_truth": "515",
"style": "rule"
} | {
"index": "35285",
"split": "train"
} |
math | [
{
"content": "In a square $ABCD$ with side length $4$, find the probability that $\\angle AMB$ is an acute angle. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "1-\\dfrac{\\pi}{8}",
"style": "rule"
} | {
"index": "35286",
"split": "train"
} |
math | [
{
"content": "A point $(x,y)$ is randomly picked from inside the rectangle with vertices $(0,0)$, $(3,0)$, $(3,2)$, and $(0,2)$. What is the probability that $x < y$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\dfrac{1}{3}",
"style": "rule"
} | {
"index": "35287",
"split": "train"
} |
math | [
{
"content": "Seven cards numbered $1$ through $7$ are to be lined up in a row. Find the number of arrangements of these seven cards where one of the cards can be removed, leaving the remaining six cards in either ascending or descending order. Please output the final answer within \\boxed{}.",
"role": "use... | {
"ground_truth": "74",
"style": "rule"
} | {
"index": "35288",
"split": "train"
} |
math | [
{
"content": "To the eight-digit number 20222023, append one digit to the left and one digit to the right so that the resulting ten-digit number is divisible by 72. Determine all possible solutions. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "3202220232",
"style": "rule"
} | {
"index": "35289",
"split": "train"
} |
math | [
{
"content": "What is the probability, expressed as a decimal, of drawing one marble which is either green or white from a bag containing 4 green, 3 white, and 8 black marbles? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "0.4667",
"style": "rule"
} | {
"index": "35290",
"split": "train"
} |
math | [
{
"content": "The value of $ 21!$ is $ 51{,}090{,}942{,}171{,}abc{,}440{,}000$ , where $ a$ , $ b$ , and $ c$ are digits. What is the value of $ 100a \\plus{} 10b \\plus{} c$ ? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "709",
"style": "rule"
} | {
"index": "35291",
"split": "train"
} |
math | [
{
"content": "In a certain school, there are $3$ times as many boys as girls and $9$ times as many girls as teachers. Using the letters $b, g, t$ to represent the number of boys, girls, and teachers, respectively, then the total number of boys, girls, and teachers can be represented by the expression Please out... | {
"ground_truth": "\\frac{37b}{27}",
"style": "rule"
} | {
"index": "35292",
"split": "train"
} |
math | [
{
"content": "If $x=3$, $y=2x$, and $z=3y$, what is the value of $z$? Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "18",
"style": "rule"
} | {
"index": "35293",
"split": "train"
} |
math | [
{
"content": "Given two geometric sequences $\\{a_n\\}$ and $\\{b_n\\}$, satisfying $a_1=a$ ($a>0$), $b_1-a_1=1$, $b_2-a_2=2$, and $b_3-a_3=3$. \n(1) If $a=1$, find the general formula for the sequence $\\{a_n\\}$. \n(2) If the sequence $\\{a_n\\}$ is unique, find the value of $a$. Please output the final ans... | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"index": "35294",
"split": "train"
} |
math | [
{
"content": "Given that angle $A$ is an internal angle of a triangle and $\\cos A= \\frac{3}{5}$, find $\\tan A=$ \\_\\_\\_\\_\\_\\_ and $\\tan (A+ \\frac{\\pi}{4})=$ \\_\\_\\_\\_\\_\\_. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "-7",
"style": "rule"
} | {
"index": "35295",
"split": "train"
} |
math | [
{
"content": "Let $f(n)$ be the largest prime factor of $n^{2}+1$. Compute the least positive integer $n$ such that $f(f(n))=n$. Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "89",
"style": "rule"
} | {
"index": "35296",
"split": "train"
} |
math | [
{
"content": "Given two parallel lines \\\\(l_{1}\\\\) and \\\\(l_{2}\\\\) passing through points \\\\(P_{1}(1,0)\\\\) and \\\\(P_{2}(0,5)\\\\) respectively, and the distance between \\\\(l_{1}\\\\) and \\\\(l_{2}\\\\) is \\\\(5\\\\), then the slope of line \\\\(l_{1}\\\\) is \\_\\_\\_\\_\\_\\_. Please output t... | {
"ground_truth": "\\dfrac {5}{12}",
"style": "rule"
} | {
"index": "35297",
"split": "train"
} |
math | [
{
"content": "Calculate the definite integral:\n$$\n\\int_{0}^{\\pi / 4} \\frac{5 \\operatorname{tg} x+2}{2 \\sin 2 x+5} d x\n$$ Please output the final answer within \\boxed{}.",
"role": "user"
}
] | {
"ground_truth": "\\frac{1}{2} \\ln \\left(\\frac{14}{5}\\right)",
"style": "rule"
} | {
"index": "35298",
"split": "train"
} |
math | [
{
"content": "An ordered pair $(a, c)$ of integers, each of which has an absolute value less than or equal to 6, is chosen at random. What is the probability that the equation $ax^2 - 3ax + c = 0$ will not have distinct real roots both greater than 2?\nA) $\\frac{157}{169}$ B) $\\frac{167}{169}$ C) $\\frac{14... | {
"ground_truth": "\\frac{167}{169}",
"style": "rule"
} | {
"index": "35299",
"split": "train"
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.