data_source stringclasses 2 values | messages listlengths 2 2 | ability stringclasses 1 value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"content": "Question: In a pentagon ABCDE, there is a vertical line of symmetry. Vertex E is moved to \\(E(5,0)\\), while \\(A(0,0)\\), \\(B(0,5)\\), and \\(D(5,5)\\). What is the \\(y\\)-coordinate of vertex C such that the area of pentagon ABCDE becomes 65 square units?\n\nPlease output the final answer, en... | math | {
"ground_truth": "21",
"style": "rule"
} | {
"index": 19528,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Find the largest integer $k$ such that for all integers $x$ and $y$, if $xy + 1$ is divisible by $k$, then $x + y$ is also divisible by $k$.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I nee... | math | {
"ground_truth": "24",
"style": "rule"
} | {
"index": 28504,
"split": "train"
} |
deepscaler | [
{
"content": "Question: There are 46 ones written on the board. Each minute, Carlson erases any two numbers and writes their sum on the board, then eats a number of candies equal to the product of the two erased numbers. What is the maximum number of candies he could eat in 46 minutes?\n\nPlease output the fina... | math | {
"ground_truth": "1035",
"style": "rule"
} | {
"index": 10655,
"split": "train"
} |
simplelr_math_35 | [
{
"content": "Question: Find the smallest positive angle $\\theta,$ in degrees, for which\n\\[\\cos \\theta = \\sin 60^\\circ + \\cos 42^\\circ - \\sin 12^\\circ - \\cos 6^\\circ.\\]\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<thin... | math | {
"ground_truth": "66^\\circ",
"style": "rule"
} | {
"index": 3910,
"split": "train"
} |
simplelr_math_35 | [
{
"content": "Question: Suppose the function $f$ has all real numbers in its domain and range and is invertible. Some values of $f$ are given by the following table: $$\\begin{array}{c || c | c | c | c | c}\nx & 1 & 2 & 3 & 4 & 5 \\\\\n\\hline\nf(x) & 2 & 3 & 5 & 7 & 8\n\\end{array}$$What is the value of $f(f(3... | math | {
"ground_truth": "14",
"style": "rule"
} | {
"index": 1356,
"split": "train"
} |
deepscaler | [
{
"content": "Question: For a natural number $N$, if at least five out of the nine natural numbers $1-9$ can divide $N$, then $N$ is called a \"five-divisible number\". What is the smallest \"five-divisible number\" greater than 2000?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.... | math | {
"ground_truth": "2004",
"style": "rule"
} | {
"index": 13917,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Around a circle, an isosceles trapezoid \\(ABCD\\) is described. The side \\(AB\\) touches the circle at point \\(M\\), and the base \\(AD\\) touches the circle at point \\(N\\). The segments \\(MN\\) and \\(AC\\) intersect at point \\(P\\), such that \\(NP: PM=2\\). Find the ratio \\(AD... | math | {
"ground_truth": "3:1",
"style": "rule"
} | {
"index": 29079,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Let's call a number palindromic if it reads the same left to right as it does right to left. For example, the number 12321 is palindromic.\n\na) Write down any five-digit palindromic number that is divisible by 5.\n\nb) How many five-digit palindromic numbers are there that are divisible... | math | {
"ground_truth": "100",
"style": "rule"
} | {
"index": 22277,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Arrange the numbers 1 to 9 in a row from left to right such that every three consecutive numbers form a three-digit number that is a multiple of 3. How many arrangements are there?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{... | math | {
"ground_truth": "1296",
"style": "rule"
} | {
"index": 9503,
"split": "train"
} |
deepscaler | [
{
"content": "Question: The polynomial $x^8 - 1$ is factored as\n\\[x^8 - 1 = p_1(x) p_2(x) \\dotsm p_k(x),\\]where each factor $p_i(x)$ is a non-constant polynomial with real coefficients. Find the largest possible value of $k.$\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 36464,
"split": "train"
} |
deepscaler | [
{
"content": "Question: The real numbers $a$, $b$, and $c$ satisfy the equation $({a}^{2}+\\frac{{b}^{2}}{4}+\\frac{{c}^{2}}{9}=1)$. Find the maximum value of $a+b+c$.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I ... | math | {
"ground_truth": "\\sqrt{14}",
"style": "rule"
} | {
"index": 19803,
"split": "train"
} |
simplelr_math_35 | [
{
"content": "Question: What is the measure of the acute angle formed by the hands of a clock at 4:20 a.m.? Express your answer as number of degrees.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to figure ou... | math | {
"ground_truth": "10^\\circ",
"style": "rule"
} | {
"index": 7159,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Five times $A$'s money added to $B$'s money is more than $51.00$. Three times $A$'s money minus $B$'s money is $21.00$.\nIf $a$ represents $A$'s money in dollars and $b$ represents $B$'s money in dollars, then:\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.... | math | {
"ground_truth": "$a>9, b>6$",
"style": "rule"
} | {
"index": 2684,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Given a recipe that prepares $8$ servings of fruit punch requires $3$ oranges, $2$ liters of juice, and $1$ liter of soda, and Kim has $10$ oranges, $12$ liters of juice, and $5$ liters of soda, determine the greatest number of servings of fruit punch that she can prepare by maintaining ... | math | {
"ground_truth": "26",
"style": "rule"
} | {
"index": 23285,
"split": "train"
} |
deepscaler | [
{
"content": "Question: What is the 10th term of an arithmetic sequence of 20 terms with the first term being 7 and the last term being 67?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the 10th term o... | math | {
"ground_truth": "\\frac{673}{19}",
"style": "rule"
} | {
"index": 18567,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Given vectors $\\overrightarrow{a}$ and $\\overrightarrow{b}$ satisfy $|\\overrightarrow{a}|=1$, $|\\overrightarrow{b}|= \\sqrt {2}$, and $\\overrightarrow{a}\\perp (\\overrightarrow{a}- \\overrightarrow{b})$, then the angle between vector $\\overrightarrow{a}$ and vector $\\overrightarr... | math | {
"ground_truth": "\\dfrac {\\pi}{4}",
"style": "rule"
} | {
"index": 14060,
"split": "train"
} |
deepscaler | [
{
"content": "Question: How many ways are there to put 4 balls in 3 boxes if the balls are distinguishable and the boxes are distinguishable?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to figure out how man... | math | {
"ground_truth": "81",
"style": "rule"
} | {
"index": 35024,
"split": "train"
} |
deepscaler | [
{
"content": "Question: A palindrome between $10000$ and $100000$ is chosen at random. What is the probability that it is divisible by $11$?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the probabilit... | math | {
"ground_truth": "\\frac{41}{450}",
"style": "rule"
} | {
"index": 28951,
"split": "train"
} |
deepscaler | [
{
"content": "Question: A circular spinner used in a game has a radius of 15 cm. The probability of winning on one spin of this spinner is $\\frac{1}{3}$ for the WIN sector and $\\frac{1}{4}$ for the BONUS sector. What is the area, in square centimeters, of both the WIN sector and the BONUS sector? Express your... | math | {
"ground_truth": "56.25\\pi",
"style": "rule"
} | {
"index": 28565,
"split": "train"
} |
simplelr_math_35 | [
{
"content": "Question: Solve for $x>0$ in the following arithmetic sequence: $1^2, x^2, 3^2, \\ldots$.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to solve for x > 0 in this arithmetic sequence: 1², x², 3²,... | math | {
"ground_truth": "\\sqrt{5}",
"style": "rule"
} | {
"index": 2621,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Bill can buy jags, jigs and jogs for $\\$1$, $\\$2$ and $\\$7$ each, respectively. What is the largest number of jogs he can purchase if he must buy at least one of each item and will spend exactly $\\$50$?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
... | math | {
"ground_truth": "6",
"style": "rule"
} | {
"index": 34708,
"split": "train"
} |
deepscaler | [
{
"content": "Question: In writing the integers from 20 through 99 inclusive, how many times is the digit 7 written?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to figure out how many times the digit 7 is wr... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"index": 16836,
"split": "train"
} |
deepscaler | [
{
"content": "Question: If $g(x) = 2x^2+2x-1$, what is the value of $g(g(2))$?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, let me try to figure out how to solve this problem. The question is asking for the value of g(... | math | {
"ground_truth": "263",
"style": "rule"
} | {
"index": 33890,
"split": "train"
} |
deepscaler | [
{
"content": "Question: For positive integers $n$, let $h(n)$ return the smallest positive integer $k$ such that $\\frac{1}{k}$ has exactly $n$ digits after the decimal point, and $k$ is divisible by 3. How many positive integer divisors does $h(2010)$ have?\n\nPlease output the final answer, enclosed within \\... | math | {
"ground_truth": "4022",
"style": "rule"
} | {
"index": 10278,
"split": "train"
} |
simplelr_math_35 | [
{
"content": "Question: In parallelogram $ABCD$, the measure of angle $ABC$ is 3 times the measure of angle $BCD$. How many degrees are in the measure of angle $ADC$?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I h... | math | {
"ground_truth": "135^\\circ",
"style": "rule"
} | {
"index": 3542,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Recall that the sum of the angles of a triangle is 180 degrees. In triangle $ABC$, angle $A$ is a right angle. Let $BM$ be the median of the triangle and $D$ be the midpoint of $BM$. It turns out that $\\angle ABD = \\angle ACD$. What are the measures of these angles?\n\nPlease output th... | math | {
"ground_truth": "30",
"style": "rule"
} | {
"index": 13154,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Let $D$ be the circle with equation $x^2 - 8x + y^2 + 10y = -14$. A translation of the coordinate system moves the center of $D$ to $(1, -2)$. Determine $a+b+r$ after the translation, where $(a,b)$ is the center and $r$ is the radius of the translated circle.\n\nPlease output the final a... | math | {
"ground_truth": "-1 + \\sqrt{27}",
"style": "rule"
} | {
"index": 32076,
"split": "train"
} |
deepscaler | [
{
"content": "Question: In $\\triangle ABC$, the ratio $AC:CB$ is $2:3$. The bisector of the exterior angle at $C$ intersects $BA$ extended at $P$ ($A$ is between $P$ and $B$). Determine the ratio $PA:AB$.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
... | math | {
"ground_truth": "2:1",
"style": "rule"
} | {
"index": 30774,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Find the number of ordered quadruples $(a, b, c, d)$ where each of $a, b, c,$ and $d$ are (not necessarily distinct) elements of $\\{1, 2, 3, 4, 5, 6, 7\\}$ and $3abc + 4abd + 5bcd$ is even. For example, $(2, 2, 5, 1)$ and $(3, 1, 4, 6)$ satisfy the conditions.\n\nPlease ou... | math | {
"ground_truth": "2017",
"style": "rule"
} | {
"index": 30281,
"split": "train"
} |
simplelr_math_35 | [
{
"content": "Question: What is the value of $25_{10}+36_{10}$ in base 3?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to figure out what 25 plus 36 is in base 10 first, and then convert that sum into base 3.... | math | {
"ground_truth": "2021_3",
"style": "rule"
} | {
"index": 1864,
"split": "train"
} |
deepscaler | [
{
"content": "Question: The diagonals of a rhombus are 6 inches and 8 inches. What is the perimeter, in inches, of the rhombus below? [asy]\nimport geometry; size(150); defaultpen(linewidth(0.8));\npair A = (0,0),B = (8,6),C = (16,0),D = (8,-6), E = (8,0);\ndraw(A--B--C--D--cycle);\ndraw(A--C,StickIntervalMarke... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"index": 38497,
"split": "train"
} |
simplelr_math_35 | [
{
"content": "Question: Find the smallest positive integer $x$ (measured in degrees) such that\n\\[\\tan (x - 160^{\\circ}) = \\frac{\\cos50^{\\circ}}{1 - \\sin50^{\\circ}}.\\]\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOk... | math | {
"ground_truth": "50^\\circ",
"style": "rule"
} | {
"index": 988,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Determine the volume of the released gas:\n\n\\[ \\omega\\left(\\mathrm{SO}_{2}\\right) = n\\left(\\mathrm{SO}_{2}\\right) \\cdot V_{m} = 0.1122 \\cdot 22.4 = 2.52 \\text{ liters} \\]\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
... | math | {
"ground_truth": "2.52",
"style": "rule"
} | {
"index": 29690,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Marvin had a birthday on Tuesday, May 27 in the leap year $2008$. In what year will his birthday next fall on a Saturday?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so Marvin had his birthday ... | math | {
"ground_truth": "2017",
"style": "rule"
} | {
"index": 1043,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Calculate the volume of the solid formed by rotating around the $O Y$ axis the curvilinear trapezoid which is bounded by the hyperbola $x y=2$ and the lines $y_{1}=1, y_{2}=4$, and $y_{3}=0$.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "use... | math | {
"ground_truth": "3\\pi",
"style": "rule"
} | {
"index": 7645,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Let $\\alpha \\in (\\pi, 2\\pi)$, if $\\tan\\left(\\alpha + \\frac{\\pi}{6}\\right) = 2$, then the value of $\\cos\\left(\\frac{\\pi}{6} - 2\\alpha\\right)$ is \\_\\_\\_\\_\\_.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
... | math | {
"ground_truth": "\\frac{4}{5}",
"style": "rule"
} | {
"index": 11065,
"split": "train"
} |
deepscaler | [
{
"content": "Question: A $6 \\times 9$ rectangle can be rolled to form two different cylinders. Calculate the ratio of the larger volume to the smaller volume. Express your answer as a common fraction.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
... | math | {
"ground_truth": "\\frac{3}{2}",
"style": "rule"
} | {
"index": 20166,
"split": "train"
} |
deepscaler | [
{
"content": "Question: The last 5 digits of $99 \\times 10101 \\times 111 \\times 1001001$ are _____.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the last 5 digits of the product 99 × 10101 × 111 × ... | math | {
"ground_truth": "88889",
"style": "rule"
} | {
"index": 14018,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Eliminate every second number in a clockwise direction from numbers $1, 2, 3, \\cdots, 2001$ that have been placed on a circle, starting with the number 2, until only one number remains. What is the last remaining number?\n\nPlease output the final answer, enclosed within \\boxed{} in La... | math | {
"ground_truth": "1955",
"style": "rule"
} | {
"index": 17176,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Consider a $3 \\times 3$ array where each row and each column is an arithmetic sequence with three terms. The first term of the first row is $3$, and the last term of the first row is $15$. Similarly, the first term of the last row is $9$, and the last term of the last row is $33$. Deter... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"index": 19711,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Chuck the llama is tied to the corner of a $2\\text{ m}$ by $3\\text{ m}$ shed on a $3\\text{ m}$ leash. How much area (in square meters) does Chuck have in which to play if he can go only around the outside of the shed? [asy]\ndraw((0,0)--(15,0)--(15,10)--(0,10)--cycle,black+linewidth(1... | math | {
"ground_truth": "7\\pi",
"style": "rule"
} | {
"index": 36258,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Five toppings for a pizza are available at Polina's Pizza. How many combinations of two different toppings are possible?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to figure out how ... | math | {
"ground_truth": "10",
"style": "rule"
} | {
"index": 38570,
"split": "train"
} |
deepscaler | [
{
"content": "Question: $A_{2n}^{n+3} + A_{4}^{n+1} = \\boxed{\\text{\\_\\_\\_\\_\\_\\_\\_\\_}}$.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I have this problem here: A_{2n}^{n+3} + A_{4}^{n+1} = ______. Hmm, I ne... | math | {
"ground_truth": "744",
"style": "rule"
} | {
"index": 20422,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Given the function $f(x) = x^3 + ax^2 + bx + a^2$ has an extremum of 10 at $x = 1$, find the value of $f(2)$.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the value of f(2) for... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"index": 32293,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Compute \\[\\lfloor 1 \\rfloor + \\lfloor 1.6 \\rfloor + \\lfloor 2.2 \\rfloor + \\lfloor 2.8 \\rfloor + \\dots + \\lfloor 99.4 \\rfloor + \\lfloor 100 \\rfloor,\\]where the arguments of the floor functions are in arithmetic progression.\n\nPlease output the final answer, enclosed within... | math | {
"ground_truth": "8317",
"style": "rule"
} | {
"index": 36360,
"split": "train"
} |
deepscaler | [
{
"content": "Question: A point $(x,y)$ is randomly picked from inside the rectangle with vertices $(0,0)$, $(6,0)$, $(6,2)$, and $(0,2)$. What is the probability that $x + y < 3$?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>... | math | {
"ground_truth": "\\frac{1}{4}",
"style": "rule"
} | {
"index": 30926,
"split": "train"
} |
deepscaler | [
{
"content": "Question: How many different three-letter sets of initials are possible using the letters $A$ through $J$, where no letter is repeated in any set?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to... | math | {
"ground_truth": "720",
"style": "rule"
} | {
"index": 8497,
"split": "train"
} |
deepscaler | [
{
"content": "Question: A right triangle \\(ABC\\) has a perimeter of 54, with the leg \\(AC\\) being greater than 10. A circle with a radius of 6, whose center lies on leg \\(BC\\), is tangent to lines \\(AB\\) and \\(AC\\). Find the area of triangle \\(ABC\\).\n\nPlease output the final answer, enclosed withi... | math | {
"ground_truth": "243/2",
"style": "rule"
} | {
"index": 26603,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Let the function be $$f(x)= \\frac {2^{x}}{2^{x}+ \\sqrt {2}}$$. Calculate the sum of $f(-2016) + f(-2015) + \\ldots + f(0) + f(1) + \\ldots + f(2017)$.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOk... | math | {
"ground_truth": "2017",
"style": "rule"
} | {
"index": 22863,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Let \\( A \\) be a point on the parabola \\( y = x^2 - 4x \\), and let \\( B \\) be a point on the line \\( y = 2x - 3 \\). Find the shortest possible distance \\( AB \\).\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"con... | math | {
"ground_truth": "\\frac{6\\sqrt{5}}{5}",
"style": "rule"
} | {
"index": 21032,
"split": "train"
} |
deepscaler | [
{
"content": "Question: The base of the pyramid is an isosceles right triangle, where each leg measures 8. Each of the pyramid's lateral edges is 9. Find the volume of the pyramid.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>... | math | {
"ground_truth": "224/3",
"style": "rule"
} | {
"index": 12136,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Find the positive solution to\n\\[\\sqrt[3]{x + \\sqrt[3]{x + \\sqrt[3]{x + \\dotsb}}} = \\sqrt[3]{x \\sqrt[3]{x \\sqrt[3]{x \\dotsm}}}.\\]\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need... | math | {
"ground_truth": "\\frac{3 + \\sqrt{5}}{2}",
"style": "rule"
} | {
"index": 37324,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Given the function $f(x)=(a\\sin x+b\\cos x)\\cdot e^{x}$ has an extremum at $x= \\frac {\\pi}{3}$, determine the value of $\\frac {a}{b}$.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need... | math | {
"ground_truth": "2- \\sqrt {3}",
"style": "rule"
} | {
"index": 9578,
"split": "train"
} |
deepscaler | [
{
"content": "Question: 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 relativ... | math | {
"ground_truth": "515",
"style": "rule"
} | {
"index": 6974,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Suppose that $|x_i| < 1$ for $i = 1, 2, \\dots, n$. Suppose further that $|x_1| + |x_2| + \\dots + |x_n| = 19 + |x_1 + x_2 + \\dots + x_n|.$ What is the smallest possible value of $n$?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},... | math | {
"ground_truth": "20",
"style": "rule"
} | {
"index": 6494,
"split": "train"
} |
simplelr_math_35 | [
{
"content": "Question: What is the greatest common divisor of $2^{1001}-1$ and $2^{1012}-1$?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the greatest common divisor (GCD) of two numbers: 2^1001 - 1 ... | math | {
"ground_truth": "2047",
"style": "rule"
} | {
"index": 7671,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Following the concept of a healthy, low-carbon lifestyle, an increasing number of people are renting bicycles for cycling tours. A particular bicycle rental point charges no fee for rentals that do not exceed two hours, and for rentals that exceed two hours, the charging standard is 2 yu... | math | {
"ground_truth": "\\frac{7}{2}",
"style": "rule"
} | {
"index": 32904,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Compute the definite integral:\n\n$$\n\\int_{0}^{1} \\frac{x^{4}}{\\left(2-x^{2}\\right)^{3 / 2}} \\, dx\n$$\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to compute the definite integr... | math | {
"ground_truth": "\\frac{5}{2} - \\frac{3\\pi}{4}",
"style": "rule"
} | {
"index": 13380,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Given vectors $\\overrightarrow {m}=(\\sin x，-1)$ and $\\overrightarrow {n}=( \\sqrt {3}\\cos x，- \\frac {1}{2})$, and the function $f(x)= \\overrightarrow {m}^{2}+ \\overrightarrow {m}\\cdot \\overrightarrow {n}-2$.\n(I) Find the maximum value of $f(x)$ and the set of values of $x$ at w... | math | {
"ground_truth": "\\frac{2\\sqrt{3}}{3}",
"style": "rule"
} | {
"index": 26841,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Find the distance between the vertices of the hyperbola given by the equation $4x^2 + 16x - 9y^2 + 18y - 23 = 0.$\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the distance betw... | math | {
"ground_truth": "\\sqrt{30}",
"style": "rule"
} | {
"index": 22695,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Let $P(x) = x^2 - 3x - 7$, and let $Q(x)$ and $R(x)$ be two quadratic polynomials also with the coefficient of $x^2$ equal to $1$. David computes each of the three sums $P + Q$, $P + R$, and $Q + R$ and is surprised to find that each pair of these sums has a common root, and these three ... | math | {
"ground_truth": "71",
"style": "rule"
} | {
"index": 7296,
"split": "train"
} |
deepscaler | [
{
"content": "Question: The sequence of real numbers \\( a_1, a_2, \\cdots, a_n, \\cdots \\) is defined by the following equation: \\( a_{n+1} = 2^n - 3a_n \\) for \\( n = 0, 1, 2, \\cdots \\).\n1. Find an expression for \\( a_n \\) in terms of \\( a_0 \\) and \\( n \\).\n2. Find \\( a_0 \\) such that \\( a_{n+... | math | {
"ground_truth": "\\frac{1}{5}",
"style": "rule"
} | {
"index": 14132,
"split": "train"
} |
deepscaler | [
{
"content": "Question: How many five-digit positive integers have the product of their digits equal to 1000?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to figure out how many five-digit numbers have the pr... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"index": 26469,
"split": "train"
} |
deepscaler | [
{
"content": "Question: A food factory processes mushrooms, with a cost of 20 yuan per kilogram of mushrooms, and a processing fee of t yuan per kilogram (t is a constant, and $2 \\leq t \\leq 5$). Assume the factory price per kilogram of mushrooms is x yuan ($25 \\leq x \\leq 40$). According to market research... | math | {
"ground_truth": "100e^4",
"style": "rule"
} | {
"index": 30334,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Define a function $g :\\mathbb{N} \\rightarrow \\mathbb{R}$ Such that $g(x)=\\sqrt{4^x+\\sqrt {4^{x+1}+\\sqrt{4^{x+2}+...}}}$ .\nFind the last 2 digits in the decimal representation of $g(2021)$ .\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"rol... | math | {
"ground_truth": "53",
"style": "rule"
} | {
"index": 14880,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Each of the eight vertices of a rectangular prism is truncated, and each face of the prism is divided by a diagonal cut into two triangles. Calculate the total number of edges of the altered shape.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role"... | math | {
"ground_truth": "42",
"style": "rule"
} | {
"index": 14564,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Compute the sum of all positive integers $a \\leq 26$ for which there exist integers $b$ and $c$ such that $a+23 b+15 c-2$ and $2 a+5 b+14 c-8$ are both multiples of 26.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"conte... | math | {
"ground_truth": "31",
"style": "rule"
} | {
"index": 4954,
"split": "train"
} |
deepscaler | [
{
"content": "Question: If $\\angle \\text{CBD}$ is a right angle, then this protractor indicates that the measure of $\\angle \\text{ABC}$ is approximately\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to fig... | math | {
"ground_truth": "20^{\\circ}",
"style": "rule"
} | {
"index": 1300,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Given that $α$ is an angle in the third quadrant and $\\cos(α+π)=\\frac{4}{5}$, find the value of $\\tan 2α$.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, let's see. I need to find the value of ... | math | {
"ground_truth": "\\frac{24}{7}",
"style": "rule"
} | {
"index": 12139,
"split": "train"
} |
deepscaler | [
{
"content": "Question: In a country there are two-way non-stopflights between some pairs of cities. Any city can be reached from any other by a sequence of at most $100$ flights. Moreover, any city can be reached from any other by a sequence of an even number of flights. What is the smallest $d$ for which ... | math | {
"ground_truth": "200",
"style": "rule"
} | {
"index": 31281,
"split": "train"
} |
deepscaler | [
{
"content": "Question: If the random variable $X$ follows a Bernoulli distribution with a success probability of $0.7$, and the random variable $Y$ follows a binomial distribution with $Y \\sim B(10, 0.8)$, then $EX$, $DX$, $EY$, $DY$ are respectively ........, ........, ........, ........\n\nPlease output the... | math | {
"ground_truth": "1.6",
"style": "rule"
} | {
"index": 28278,
"split": "train"
} |
simplelr_math_35 | [
{
"content": "Question: Let $h(4x-1) = 2x + 7$. For what value of $x$ is $h(x) = x$?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the value of x where h(x) equals x, given that h(4x - 1) equals 2x + ... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"index": 3182,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Consider a dodecahedron, which is made up of 12 pentagonal faces. An ant starts at one of the top vertices and walks to one of the three adjacent vertices (vertex A). From vertex A, the ant walks again to one of its adjacent vertices (vertex B). What is the probability that vertex B is o... | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"index": 23825,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Find the largest real number $k$ , such that for any positive real numbers $a,b$ , $$ (a+b)(ab+1)(b+1)\\geq kab^2 $$\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the largest... | math | {
"ground_truth": "27/4",
"style": "rule"
} | {
"index": 31750,
"split": "train"
} |
deepscaler | [
{
"content": "Question: What digit $B$ will make the number $527B$ divisible by $5$?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to figure out what digit B will make the number 527B divisible by 5. Hmm, let ... | math | {
"ground_truth": "0 \\text{ or } 5",
"style": "rule"
} | {
"index": 32934,
"split": "train"
} |
deepscaler | [
{
"content": "Question: What is the least possible value of\n\\[(x+1)(x+2)(x+3)(x+4)+2019\\]where $x$ is a real number?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the least possible value of this ex... | math | {
"ground_truth": "2018",
"style": "rule"
} | {
"index": 2877,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Solve for $x:\\ \\log_2 x+\\log_4 x= 6.$\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to solve the equation log base 2 of x plus log base 4 of x equals 6. Hmm, let me think about how t... | math | {
"ground_truth": "16",
"style": "rule"
} | {
"index": 36923,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Cut a 3-meter-long rope into 7 equal segments. Each segment accounts for \\_\\_\\_\\_\\_\\_ of the total length, and each segment is \\_\\_\\_\\_\\_\\_ meters long.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": ... | math | {
"ground_truth": "\\frac{3}{7}",
"style": "rule"
} | {
"index": 22308,
"split": "train"
} |
deepscaler | [
{
"content": "Question: In the Cartesian coordinate system, O is the origin. Given vector $\\overrightarrow{a}=(2,1)$, point $A(1,0)$, and point $B(\\cos\\theta,t)$, \n(1) If $\\overrightarrow{a} \\parallel \\overrightarrow{AB}$ and $|\\overrightarrow{AB}| = \\sqrt{5}|\\overrightarrow{OA}|$, find the coordinat... | math | {
"ground_truth": "-\\frac{1}{5}",
"style": "rule"
} | {
"index": 18758,
"split": "train"
} |
deepscaler | [
{
"content": "Question: The complex numbers \\( \\alpha_{1}, \\alpha_{2}, \\alpha_{3}, \\) and \\( \\alpha_{4} \\) are the four distinct roots of the equation \\( x^{4}+2 x^{3}+2=0 \\). Determine the unordered set \\( \\left\\{\\alpha_{1} \\alpha_{2}+\\alpha_{3} \\alpha_{4}, \\alpha_{1} \\alpha_{3}+\\alpha_{2} ... | math | {
"ground_truth": "\\{1 \\pm \\sqrt{5},-2\\}",
"style": "rule"
} | {
"index": 3977,
"split": "train"
} |
simplelr_math_35 | [
{
"content": "Question: What is the domain of the function $$j(x) = \\frac{1}{x+8} + \\frac{1}{x^2+8} + \\frac{1}{x^3+8}~?$$Express your answer as a union of intervals.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I... | math | {
"ground_truth": "(-\\infty,-8)\\cup (-8,-2)\\cup (-2,\\infty)",
"style": "rule"
} | {
"index": 3270,
"split": "train"
} |
deepscaler | [
{
"content": "Question: 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.\n\nPlease o... | math | {
"ground_truth": "18.67",
"style": "rule"
} | {
"index": 32541,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Given that all three vertices of \\(\\triangle ABC\\) lie on the parabola defined by \\(y = 4x^2\\), with \\(A\\) at the origin and \\(\\overline{BC}\\) parallel to the \\(x\\)-axis, calculate the length of \\(BC\\), given that the area of the triangle is 128.\n\nPlease output the final ... | math | {
"ground_truth": "4\\sqrt[3]{4}",
"style": "rule"
} | {
"index": 30796,
"split": "train"
} |
simplelr_math_35 | [
{
"content": "Question: A cylindrical glass is half full of lemonade. The ratio of lemon juice to water in the lemonade is 1:11. If the glass is 6 inches tall and has a diameter of 2 inches, what is the volume of lemon juice in the glass? Express your answer as a decimal to the nearest hundredth.\n\nPlease outp... | math | {
"ground_truth": ".79",
"style": "rule"
} | {
"index": 3931,
"split": "train"
} |
deepscaler | [
{
"content": "Question: The cards in a stack are numbered consecutively from 1 to $2n$ from top to bottom. The top $n$ cards are removed to form pile $A$ and the remaining cards form pile $B$. The cards are restacked by alternating cards from pile $B$ and $A$, starting with a card from $B$. Given this process, ... | math | {
"ground_truth": "402",
"style": "rule"
} | {
"index": 29590,
"split": "train"
} |
simplelr_math_35 | [
{
"content": "Question: An acute isosceles triangle, $ABC$, is inscribed in a circle. Through $B$ and $C$, tangents to the circle are drawn, meeting at point $D$. If $\\angle ABC = \\angle ACB = 2 \\angle D$ and $\\angle BAC = k \\pi$ in radians, then find $k$.\n\n[asy]\nimport graph;\n\nunitsize(2 cm);\n\npa... | math | {
"ground_truth": "3/7",
"style": "rule"
} | {
"index": 1531,
"split": "train"
} |
deepscaler | [
{
"content": "Question: The rules for a race require that all runners start at $A$, touch any part of the 1200-meter wall, and stop at $B$. What is the number of meters in the minimum distance a participant must run? Express your answer to the nearest meter. [asy]\nimport olympiad; import geometry; size(250);\n... | math | {
"ground_truth": "1442",
"style": "rule"
} | {
"index": 36288,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Cameron writes down the smallest positive multiple of 30 that is a perfect square, the smallest positive multiple of 30 that is a perfect cube, and all the multiples of 30 between them. How many integers are in Cameron's list?\n\nPlease output the final answer, enclosed within \\boxed{} ... | math | {
"ground_truth": "871",
"style": "rule"
} | {
"index": 7626,
"split": "train"
} |
deepscaler | [
{
"content": "Question: If $\\lceil{\\sqrt{x}}\\rceil=20$, how many possible integer values of $x$ are there?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to figure out how many integer values of x satisfy th... | math | {
"ground_truth": "39",
"style": "rule"
} | {
"index": 17921,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Given the function $f(x)= e^{-2x}+1$, find the area of the triangle formed by the tangent line to the curve $y=f(x)$ at the point $(0,f(0))$ and the lines $y=0$ and $y=x$.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"con... | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"index": 11504,
"split": "train"
} |
deepscaler | [
{
"content": "Question: At a meeting with $25$ businessmen, twelve businessmen drank coffee, and ten businessmen drank tea. Five businessmen drank both coffee and tea. How many businessmen drank neither coffee nor tea?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role":... | math | {
"ground_truth": "8",
"style": "rule"
} | {
"index": 39065,
"split": "train"
} |
simplelr_math_35 | [
{
"content": "Question: The quadratic $x^2 + 5x + c$ has roots in the form of $x = \\frac{-5 \\pm \\sqrt{c}}{2}$. What is the value of $c$?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find the value of c ... | math | {
"ground_truth": "5",
"style": "rule"
} | {
"index": 4292,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Ten elves are sitting around a circular table, each with a basket of nuts. Each elf is asked, \"How many nuts do your two neighbors have together?\" and the answers, going around the circle, are 110, 120, 130, 140, 150, 160, 170, 180, 190, and 200. How many nuts does the elf who answered... | math | {
"ground_truth": "55",
"style": "rule"
} | {
"index": 15030,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Camilla had twice as many blueberry jelly beans as cherry jelly beans. After eating 10 pieces of each kind, she now has three times as many blueberry jelly beans as cherry jelly beans. How many blueberry jelly beans did she originally have?\n\nPlease output the final answer, enclosed wit... | math | {
"ground_truth": "40",
"style": "rule"
} | {
"index": 1504,
"split": "train"
} |
deepscaler | [
{
"content": "Question: A track and field team has three sprinters. According to the statistics from their usual training sessions, the probabilities of sprinters A, B, and C finishing a 100m dash within 13 seconds (considered qualified) are $\\frac{2}{5}$, $\\frac{3}{4}$, and $\\frac{1}{3}$, respectively. If t... | math | {
"ground_truth": "\\frac{9}{10}",
"style": "rule"
} | {
"index": 10773,
"split": "train"
} |
deepscaler | [
{
"content": "Question: Four friends do yardwork for their neighbors over the weekend, earning $15, $20, $25, and $40, respectively. They decide to split their earnings equally among themselves. In total, how much will the friend who earned $40 give to the others?\n\nPlease output the final answer, enclosed wit... | math | {
"ground_truth": "15",
"style": "rule"
} | {
"index": 2339,
"split": "train"
} |
deepscaler | [
{
"content": "Question: If the six digits 1, 2, 3, 5, 5 and 8 are randomly arranged into a six-digit positive integer, what is the probability that the integer is divisible by 15? Express your answer as a common fraction.\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role"... | math | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"index": 34920,
"split": "train"
} |
simplelr_math_35 | [
{
"content": "Question: The expression $x^2 + 13x + 30$ can be written as $(x + a)(x + b),$ and the expression $x^2 + 5x - 50$ written as $(x + b)(x - c)$, where $a$, $b$, and $c$ are integers. What is the value of $a + b + c$?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
... | math | {
"ground_truth": "18",
"style": "rule"
} | {
"index": 3528,
"split": "train"
} |
deepscaler | [
{
"content": "Question: The sum of the squares of four consecutive positive integers is 9340. What is the sum of the cubes of these four integers?\n\nPlease output the final answer, enclosed within \\boxed{} in LaTeX format.",
"role": "user"
},
{
"content": "<think>\nOkay, so I need to find four con... | math | {
"ground_truth": "457064",
"style": "rule"
} | {
"index": 32569,
"split": "train"
} |
deepscaler | [
{
"content": "Question: In the Cartesian coordinate system $xOy$, the parametric equation of line $l$ is\n$$\n\\begin{cases}\nx = -1 + \\frac {\\sqrt {2}}{2}t \\\\\ny = 1 + \\frac {\\sqrt {2}}{2}t\n\\end{cases}\n(t \\text{ is the parameter}),\n$$\nand the equation of circle $C$ is $(x-2)^{2} + (y-1)^{2} = 5$. E... | math | {
"ground_truth": "\\frac{3\\sqrt{10}}{10}",
"style": "rule"
} | {
"index": 17742,
"split": "train"
} |
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