data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
deepscaler | [
{
"role": "user",
"content": "Express 0.0000006 in scientific notation. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6 \\times 10^{-7}"
} | {
"split": "train",
"index": 17149,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer $n$ for which $11n-8$ and $5n + 9$ share a common factor greater than $1$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "165"
} | {
"split": "train",
"index": 17150,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Schools A and B are having a sports competition with three events. In each event, the winner gets 10 points and the loser gets 0 points, with no draws. The school with the highest total score after the three events wins the championship. It is known that the probabilities of sc... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 17151,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the remainder when (99)(101) is divided by 9? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0"
} | {
"split": "train",
"index": 17152,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, if $\\sin^{2}A + \\sin^{2}B = \\sin^{2}C - \\sqrt{2}\\sin A\\sin B$, find the maximum value of $\\sin 2A\\tan^{2}B$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3 - 2\\sqrt{2}"
} | {
"split": "train",
"index": 17153,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the minimum value of\n\\[\\frac{x^2}{x - 8}\\]for $x > 8.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 17154,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A club has between 300 and 400 members. The members gather every weekend and are divided into eight distinct groups. If two members are absent, the groups can all have the same number of members. What is the sum of all possible numbers of members in the club? Let's think step b... | math | {
"style": "rule",
"ground_truth": "4200"
} | {
"split": "train",
"index": 17155,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Of the following complex numbers $z$, which one has the property that $z^5$ has the greatest real part? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-\\sqrt{3} + i"
} | {
"split": "train",
"index": 17156,
"solution": "We evaluate the fifth power of each answer choice and determine the real part of each result.\n\n1. **For $\\textbf{(A)}$:**\n - $z = -2$\n - $z^5 = (-2)^5 = -32$\n - $\\operatorname{Re}(z^5) = -32$\n\n2. **For $\\textbf{(E)}$:**\n - $z = 2i$\n - $z^5 = (... |
deepscaler | [
{
"role": "user",
"content": "What is the smallest possible perimeter, in units, of a triangle whose side-length measures are consecutive integer values? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 17157,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Which of the following integers is equal to a perfect square: $2^{3}$, $3^{5}$, $4^{7}$, $5^{9}$, $6^{11}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "4^{7}"
} | {
"split": "train",
"index": 17158,
"solution": "Since $4 = 2^{2}$, then $4^{7} = (2^{2})^{7} = 2^{14} = (2^{7})^{2}$, which means that $4^{7}$ is a perfect square. We can check, for example using a calculator, that the square root of each of the other four choices is not an integer, and so each of these four cho... |
deepscaler | [
{
"role": "user",
"content": "The king called two wise men. He gave the first one 100 blank cards and ordered him to write a positive number on each (the numbers do not have to be different) without showing them to the second wise man. Then, the first wise man can communicate several different numbers to th... | math | {
"style": "rule",
"ground_truth": "101"
} | {
"split": "train",
"index": 17159,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A teacher wants to arrange 3 copies of Introduction to Geometry and 4 copies of Introduction to Number Theory on a bookshelf. In how many ways can he do that? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "35"
} | {
"split": "train",
"index": 17160,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Evaluate the expression \\((25 + 15)^2 - (25^2 + 15^2 + 150)\\). Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "600"
} | {
"split": "train",
"index": 17161,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Right triangle $ABC$ is inscribed in circle $W$ . $\\angle{CAB}=65$ degrees, and $\\angle{CBA}=25$ degrees. The median from $C$ to $AB$ intersects $W$ and line $D$ . Line $l_1$ is drawn tangent to $W$ at $A$ . Line $l_2$ is drawn tangent to $W$ at $D$ . ... | math | {
"style": "rule",
"ground_truth": "50"
} | {
"split": "train",
"index": 17162,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In base $b$, there are exactly one hundred three-digit numbers whose digits are all distinct. (That's \"one hundred\" in the ordinary sense, $100_{10}$.)\n\nWhat is $b$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "6"
} | {
"split": "train",
"index": 17163,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Alice starts to make a list, in increasing order, of the positive integers that have a first digit of 2. She writes $2, 20, 21, 22, \\ldots$ but by the 1000th digit she (finally) realizes that the list would contain an infinite number of elements. Find the three-digit number fo... | math | {
"style": "rule",
"ground_truth": "216"
} | {
"split": "train",
"index": 17164,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given the ellipse \\(3x^{2} + y^{2} = 6\\) and the point \\(P\\) with coordinates \\((1, \\sqrt{3})\\). Find the maximum area of triangle \\(PAB\\) formed by point \\(P\\) and two points \\(A\\) and \\(B\\) on the ellipse. Let's think step by step and put only the final answer ... | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 17165,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute\n\\[\\csc \\frac{\\pi}{14} - 4 \\cos \\frac{2 \\pi}{7}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "2"
} | {
"split": "train",
"index": 17166,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A school arranges five classes every morning from Monday to Friday, each lasting 40 minutes. The first class starts from 7:50 to 8:30, with a 10-minute break between classes. A student returns to school after taking leave. If he arrives at the classroom randomly between 8:50 an... | math | {
"style": "rule",
"ground_truth": "\\dfrac{1}{4}"
} | {
"split": "train",
"index": 17167,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the minimum value of\n$$\n\\begin{aligned}\nA & =\\sqrt{\\left(1264-z_{1}-\\cdots-z_{n}\\right)^{2}+x_{n}^{2}+y_{n}^{2}}+ \\\\\n& \\sqrt{z_{n}^{2}+x_{n-1}^{2}+y_{n-1}^{2}}+\\cdots+\\sqrt{z_{2}^{2}+x_{1}^{2}+y_{1}^{2}}+ \\\\\n& \\sqrt{z_{1}^{2}+\\left(948-x_{1}-\\cdots-x_{n... | math | {
"style": "rule",
"ground_truth": "1975"
} | {
"split": "train",
"index": 17168,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Compute the product\n\\[\n\\prod_{n = 1}^{15} \\frac{n^2 + 5n + 6}{n+2}.\n\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{18!}{6}"
} | {
"split": "train",
"index": 17169,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $\\sec x + \\tan x = \\frac{4}{3},$ enter all possible values of $\\sin x.$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7}{25}"
} | {
"split": "train",
"index": 17170,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The stem-and-leaf plot shows the duration of songs (in minutes and seconds) played during a concert by a band. There are 15 songs listed in the plot. In the stem-and-leaf plot, $3 \\ 15$ represents $3$ minutes, $15$ seconds, which is the same as $195$ seconds. Find the median d... | math | {
"style": "rule",
"ground_truth": "170"
} | {
"split": "train",
"index": 17171,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A rectangular metal plate measuring \\(10\\) cm by \\(8\\) cm has a circular piece of maximum size cut out, followed by cutting a rectangular piece of maximum size from the circular piece. Calculate the total metal wasted in this process. Let's think step by step and put only t... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 17172,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the coefficient of $x^3$ when \n$$x^5 - 4x^3 + 3x^2 - 2x + 5$$\nis multiplied by \n$$3x^2 - 2x + 4$$ \nand further multiplied by\n$$1 - x$$ \nand the like terms are combined? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-3"
} | {
"split": "train",
"index": 17173,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When two fair dice are rolled once each, what is the probability that one of the upward-facing numbers is 2, given that the two numbers are not the same? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{3}"
} | {
"split": "train",
"index": 17174,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What is the smallest positive integer $n$ for which $9n-2$ and $7n + 3$ share a common factor greater than $1$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 17175,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given is a regular tetrahedron of volume 1. We obtain a second regular tetrahedron by reflecting the given one through its center. What is the volume of their intersection? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 17176,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the number of quadruples $(a, b, c, d)$ of integers with absolute value at most 5 such that $\\left(a^{2}+b^{2}+c^{2}+d^{2}\\right)^{2}=(a+b+c+d)(a-b+c-d)\\left((a-c)^{2}+(b-d)^{2}\\right)$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "49"
} | {
"split": "train",
"index": 17177,
"solution": "Let $x=a+c, y=a-c, w=b+d$, and $z=b-d$. Then $$\\left(w^{2}+x^{2}+y^{2}+z^{2}\\right)^{2}=4\\left(x^{2}-w^{2}\\right)\\left(y^{2}+z^{2}\\right)$$ and since $\\left|x^{2}+w^{2}\\right| \\geq\\left|x^{2}-w^{2}\\right|$ it follows that $w=0$ or $y=z=0$. Now $y=z=0$ im... |
deepscaler | [
{
"role": "user",
"content": "The eccentricity of the hyperbola defined by the equation $\\frac {x^{2}}{a^{2}} - \\frac {y^{2}}{b^{2}} = 1$ given that a line with a slope of -1 passes through its right vertex A and intersects the two asymptotes of the hyperbola at points B and C, and if $\\overrightarrow {A... | math | {
"style": "rule",
"ground_truth": "\\sqrt{5}"
} | {
"split": "train",
"index": 17178,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A sphere with center $O$ has radius $6$. A triangle with sides of length $15, 15,$ and $24$ is situated in space so that each of its sides is tangent to the sphere. What is the distance between $O$ and the plane determined by the triangle? Let's think step by step and put only ... | math | {
"style": "rule",
"ground_truth": "2\\sqrt{5}"
} | {
"split": "train",
"index": 17179,
"solution": "1. **Understanding the Problem Setup**: We have a sphere with radius $6$ and a triangle with sides $15, 15, 24$ that is tangent to the sphere along each side. The triangle forms a plane that is tangent to the sphere.\n\n2. **Identifying the Incircle**: Since the tr... |
deepscaler | [
{
"role": "user",
"content": "Let $P_1^{}$ be a regular $r~\\mbox{gon}$ and $P_2^{}$ be a regular $s~\\mbox{gon}$ $(r\\geq s\\geq 3)$ such that each interior angle of $P_1^{}$ is $\\frac{59}{58}$ as large as each interior angle of $P_2^{}$. What's the largest possible value of $s_{}^{}$? Let's think step by... | math | {
"style": "rule",
"ground_truth": "117"
} | {
"split": "train",
"index": 17180,
"solution": "As in above, we have $rs = 118r - 116s.$ This means that $rs + 116s - 118r = 0.$ Using SFFT we obtain $s(r+116) - 118(r+116) = -118 \\cdot 116 \\implies (s-118)(r+116) = -118 \\cdot 116.$ Since $r+116$ is always positive, we know thta $s-118$ must be negative. Ther... |
deepscaler | [
{
"role": "user",
"content": "For how many integers $n$ between 1 and 150 is the greatest common divisor of 18 and $n$ equal to 6? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "17"
} | {
"split": "train",
"index": 17181,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Triangle $ABC$ has $\\angle C = 60^{\\circ}$ and $BC = 4$. Point $D$ is the midpoint of $BC$. What is the largest possible value of $\\tan{\\angle BAD}$?\n$\\mathrm{(A)}\\ \\frac{\\sqrt{3}}{6}\\qquad\\mathrm{(B)}\\ \\frac{\\sqrt{3}}{3}\\qquad\\mathrm{(C)}\\ \\frac{\\sqrt{3}}{2\... | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{3}}{4\\sqrt{2}-3}"
} | {
"split": "train",
"index": 17182,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are 3 complex numbers $a+bi$, $c+di$, and $e+fi$. If $b=3$, $e=-a-c$, and the sum of the numbers is $2i$, find $d+f$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 17183,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The Grunters play the Screamers 4 times. The Grunters are the much better team, and are $75\\%$ likely to win any given game. What is the probability that the Grunters will win all 4 games? Express your answer as a common fraction. Let's think step by step and put only the fi... | math | {
"style": "rule",
"ground_truth": "\\frac{81}{256}"
} | {
"split": "train",
"index": 17184,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The circles \\(O_{1}\\) and \\(O_{2}\\) touch the circle \\(O_{3}\\) with radius 13 at points \\(A\\) and \\(B\\) respectively and pass through its center \\(O\\). These circles intersect again at point \\(C\\). It is known that \\(OC = 12\\). Find \\(AB\\). Let's think step by... | math | {
"style": "rule",
"ground_truth": "10"
} | {
"split": "train",
"index": 17185,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "There are five students: A, B, C, D, and E.\n\n1. In how many different ways can they line up in a row such that A and B must be adjacent, and C and D cannot be adjacent?\n2. In how many different ways can these five students be distributed into three classes, with each class h... | math | {
"style": "rule",
"ground_truth": "150"
} | {
"split": "train",
"index": 17186,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $A B C$ be a triangle and $\\omega$ be its circumcircle. The point $M$ is the midpoint of arc $B C$ not containing $A$ on $\\omega$ and $D$ is chosen so that $D M$ is tangent to $\\omega$ and is on the same side of $A M$ as $C$. It is given that $A M=A C$ and $\\angle D M C... | math | {
"style": "rule",
"ground_truth": "33^{\\circ}"
} | {
"split": "train",
"index": 17187,
"solution": "By inscribed angles, we know that $\\angle B A C=38^{\\circ} \\cdot 2=76^{\\circ}$ which means that $\\angle C=104^{\\circ}-\\angle B$. Since $A M=A C$, we have $\\angle A C M=\\angle A M C=90^{\\circ}-\\frac{\\angle M A C}{2}=71^{\\circ}$. Once again by inscribed ... |
deepscaler | [
{
"role": "user",
"content": "Solve the inequalities:\n(1) $(2x - 4)(x - 5) < 0$;\n(2) $3x^{2} + 5x + 1 > 0$;\n(3) $-x^{2} + x < 2$;\n(4) $7x^{2} + 5x + 1 \\leq 0$;\n(5) $4x \\geq 4x^{2} + 1$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\left\\{\\frac{1}{2}\\right\\}"
} | {
"split": "train",
"index": 17188,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose we flip five coins simultaneously: a penny, a nickel, a dime, a quarter, and a half dollar. What is the probability that at least 65 cents worth of coins come up heads? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{5}{16}"
} | {
"split": "train",
"index": 17189,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a geometric sequence with positive terms $\\{a_n\\}$, let $S_n$ be the sum of the first $n$ terms. If $S_3 + a_2 = 9a_3$, determine the common ratio. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 17190,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three points are chosen uniformly at random on a circle. What is the probability that no two of these points form an obtuse triangle with the circle's center? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{16}"
} | {
"split": "train",
"index": 17191,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given vectors $\\overrightarrow {a}=(\\sqrt{3}\\sin x,\\sin x)$ and $\\overrightarrow {b}=(\\cos x,\\sin x)$, where $x \\in (0, \\frac{\\pi}{2})$,\n1. If $\\overrightarrow{a}$ is parallel to $\\overrightarrow{b}$, find the value of $x$;\n2. Let the function $f(x) = (\\overright... | math | {
"style": "rule",
"ground_truth": "\\frac{5}{2}"
} | {
"split": "train",
"index": 17192,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Four distinct points are arranged on a plane so that the segments connecting them have lengths $a$, $a$, $a$, $a$, $2a$, and $b$. What is the ratio of $b$ to $a$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3}"
} | {
"split": "train",
"index": 17193,
"solution": "1. **Identify the possible configurations of the points**: Given that there are four segments of length $a$, one of length $2a$, and one of length $b$, we need to determine how these points can be arranged. \n\n2. **Check the triangle inequality**: The triangle ine... |
deepscaler | [
{
"role": "user",
"content": "Let $x,$ $y,$ and $z$ be positive real numbers such that $x + y + z = 1.$ Find the minimum value of\n\\[\\frac{1}{x} + \\frac{1}{y} + \\frac{1}{z}.\\] Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "9"
} | {
"split": "train",
"index": 17194,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A shepherd uses 15 segments of fencing, each 2 meters long, to form a square or rectangular sheep pen with one side against a wall. What is the maximum area of the sheep pen in square meters? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "112"
} | {
"split": "train",
"index": 17195,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "When the square root of $x$ is cubed, the answer is 64. What is the value of $x$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 17196,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Two reals $a$ and $b$ are such that $a+b=7$ and $a^3+b^3=91$. Compute $ab$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"split": "train",
"index": 17197,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Alice has 10 green marbles and 5 purple marbles in a bag. She removes a marble at random, records the color, puts it back, and then repeats this process until she has withdrawn 8 marbles. What is the probability that exactly four of the marbles that she removes are green? Expre... | math | {
"style": "rule",
"ground_truth": "0.171"
} | {
"split": "train",
"index": 17198,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find the smallest natural number that begins with the digit five, which is reduced by four times if this five is removed from the beginning of its decimal representation and appended to its end. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "512820"
} | {
"split": "train",
"index": 17199,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a geometric progression $\\{a_n\\}$ with the first term $a_1=2$ and the sum of the first $n$ terms as $S_n$, and the equation $S_5 + 4S_3 = 5S_4$ holds, find the maximum term of the sequence $\\left\\{ \\frac{2\\log_{2}a_n + 1}{\\log_{2}a_n - 6} \\right\\}$. Let's think s... | math | {
"style": "rule",
"ground_truth": "15"
} | {
"split": "train",
"index": 17200,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $f$ be a quadratic function which satisfies the following condition. Find the value of $\\frac{f(8)-f(2)}{f(2)-f(1)}$ .\n\nFor two distinct real numbers $a,b$ , if $f(a)=f(b)$ , then $f(a^2-6b-1)=f(b^2+8)$ . Let's think step by step and put only the final answer withi... | math | {
"style": "rule",
"ground_truth": "13"
} | {
"split": "train",
"index": 17201,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "In triangle $ABC$, $AB=15$ and $AC=8$. The angle bisector of $\\angle A$ intersects $BC$ at point $D$, and the incenter $I$ of triangle $ABC$ is on the segment $AD$. Let the midpoint of $AD$ be $M$. Find the ratio of $IP$ to $PD$ where $P$ is the intersection of $AI$ and $BM$. ... | math | {
"style": "rule",
"ground_truth": "1:1"
} | {
"split": "train",
"index": 17202,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A regular pentagon \\(Q_1 Q_2 \\dotsb Q_5\\) is drawn in the coordinate plane with \\(Q_1\\) at \\((1,0)\\) and \\(Q_3\\) at \\((5,0)\\). If \\(Q_n\\) is the point \\((x_n,y_n)\\), compute the numerical value of the product\n\\[(x_1 + y_1 i)(x_2 + y_2 i)(x_3 + y_3 i) \\dotsm (x... | math | {
"style": "rule",
"ground_truth": "242"
} | {
"split": "train",
"index": 17203,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "What work is required to stretch a spring by \\(0.06 \\, \\text{m}\\), if a force of \\(1 \\, \\text{N}\\) stretches it by \\(0.01 \\, \\text{m}\\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0.18"
} | {
"split": "train",
"index": 17204,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A ball inside a rectangular container of width 7 and height 12 is launched from the lower-left vertex of the container. It first strikes the right side of the container after traveling a distance of $\\sqrt{53}$ (and strikes no other sides between its launch and its impact with... | math | {
"style": "rule",
"ground_truth": "5"
} | {
"split": "train",
"index": 17205,
"solution": "Every segment the ball traverses between bounces takes it 7 units horizontally and 2 units up. Thus, after 5 bounces it has traveled up 10 units, and the final segment traversed takes it directly to the upper right vertex of the rectangle."
} |
deepscaler | [
{
"role": "user",
"content": "The 8 eyelets for the lace of a sneaker all lie on a rectangle, four equally spaced on each of the longer sides. The rectangle has a width of 50 mm and a length of 80 mm. There is one eyelet at each vertex of the rectangle. The lace itself must pass between the vertex eyelets a... | math | {
"style": "rule",
"ground_truth": "790"
} | {
"split": "train",
"index": 17206,
"solution": "The rectangle is divided into three smaller rectangles with a width of 50 mm and a length of $\\dfrac{80}{3}$mm. According to the Pythagorean Theorem (or by noticing the 8-15-17 Pythagorean triple), the diagonal of the rectangle is $\\sqrt{50^2+\\left(\\frac{80}{3}... |
deepscaler | [
{
"role": "user",
"content": "The sequence $\\left\\{ a_n \\right\\}$ is a geometric sequence with a common ratio of $q$, its sum of the first $n$ terms is $S_n$, and the product of the first $n$ terms is $T_n$. Given that $0 < a_1 < 1, a_{2012}a_{2013} = 1$, the correct conclusion(s) is(are) ______.\n\n$(1... | math | {
"style": "rule",
"ground_truth": "(1)(3)(4)(5)"
} | {
"split": "train",
"index": 17207,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many nonnegative integers can be represented in the form \\[\na_7 \\cdot 4^7 + a_6 \\cdot 4^6 + a_5 \\cdot 4^5 + a_4 \\cdot 4^4 + a_3 \\cdot 4^3 + a_2 \\cdot 4^2 + a_1 \\cdot 4^1 + a_0 \\cdot 4^0,\n\\]\nwhere $a_i \\in \\{0, 1, 2\\}$ for $0 \\leq i \\leq 7$? Let's think ste... | math | {
"style": "rule",
"ground_truth": "6561"
} | {
"split": "train",
"index": 17208,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $x \\cdot (x+y) = x^2 + 8$, what is the value of $xy$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "8"
} | {
"split": "train",
"index": 17209,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that $a, b$ and $c$ are integers with $(x-a)(x-6)+3=(x+b)(x+c)$ for all real numbers $x$. What is the sum of all possible values of $b$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-24"
} | {
"split": "train",
"index": 17210,
"solution": "We are told that $(x-a)(x-6)+3=(x+b)(x+c)$ for all real numbers $x$. In particular, this equation holds when $x=6$. Substituting $x=6$ gives $(6-a)(6-6)+3=(6+b)(6+c)$ or $3=(6+b)(6+c)$. Since $b$ and $c$ are integers, then $6+b$ and $6+c$ are integers, which means ... |
deepscaler | [
{
"role": "user",
"content": "Yvan and Zoé play the following game. Let \\( n \\in \\mathbb{N} \\). The integers from 1 to \\( n \\) are written on \\( n \\) cards arranged in order. Yvan removes one card. Then, Zoé removes 2 consecutive cards. Next, Yvan removes 3 consecutive cards. Finally, Zoé removes 4 ... | math | {
"style": "rule",
"ground_truth": "14"
} | {
"split": "train",
"index": 17211,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a fair coin is tossed, the probability of heads or tails is both $\\frac{1}{2}$. Construct a sequence $\\{a_n\\}$, where $a_n = \\begin{cases} 1, \\text{if heads on the nth toss} \\\\ -1, \\text{if tails on the nth toss} \\end{cases}$. Let $S_n = a_1 + a_2 + ... + a_n$. F... | math | {
"style": "rule",
"ground_truth": "\\frac{13}{128}"
} | {
"split": "train",
"index": 17212,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that the sum of the first $n$ terms of the sequence ${a_n}$ is $S_n$, and $S_{n}=n^{2}+n+1$. In the positive geometric sequence ${b_n}$, $b_3=a_2$, $b_4=a_4$. Find:\n1. The general term formulas for ${a_n}$ and ${b_n}$;\n2. If $c_n$ is defined as $c_n=\\begin{cases} a_{n}... | math | {
"style": "rule",
"ground_truth": "733"
} | {
"split": "train",
"index": 17213,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Every time these two wheels are spun, two numbers are selected by the pointers. What is the probability that the sum of the two selected numbers is even? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 17214,
"solution": "1. **Understanding the Problem**: We need to find the probability that the sum of the numbers selected by spinning two wheels is even. For the sum to be even, both numbers must either be both even or both odd.\n\n2. **Determining the Probabilities**:\n - **Probab... |
deepscaler | [
{
"role": "user",
"content": "The zeroes of the function $f(x)=x^2-ax+2a$ are integers. What is the sum of the possible values of $a?$\n$\\textbf{(A)}\\ 7\\qquad\\textbf{(B)}\\ 8\\qquad\\textbf{(C)}\\ 16\\qquad\\textbf{(D)}\\ 17\\qquad\\textbf{(E)}\\ 18$\n Let's think step by step and put only the final ans... | math | {
"style": "rule",
"ground_truth": "16"
} | {
"split": "train",
"index": 17215,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $2014$ points in the plane, no three of which are collinear, what is the minimum number of line segments that can be drawn connecting pairs of points in such a way that adding a single additional line segment of the same sort will always produce a triangle of three conn... | math | {
"style": "rule",
"ground_truth": "2013"
} | {
"split": "train",
"index": 17216,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Find all the solutions to\n\\[\\sqrt[3]{15x - 1} + \\sqrt[3]{13x + 1} = 4 \\sqrt[3]{x}.\\]Enter all the solutions, separated by commas. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "0, \\frac{1}{14}, -\\frac{1}{12}"
} | {
"split": "train",
"index": 17217,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given $0\\leqslant x\\_0 < 1$, for all integers $n > 0$, let $x\\_n= \\begin{cases} 2x_{n-1}, & 2x_{n-1} < 1 \\\\ 2x_{n-1}-1, & 2x_{n-1} \\geqslant 1 \\end{cases}$. Find the number of $x\\_0$ that makes $x\\_0=x\\_6$ true. Let's think step by step and put only the final answer ... | math | {
"style": "rule",
"ground_truth": "64"
} | {
"split": "train",
"index": 17218,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A wholesaler bought 500 kilograms of a certain type of fruit at a price of 40 yuan per kilogram. According to market forecasts, the selling price $y$ (yuan per kilogram) of this fruit is a function of the storage time $x$ (days), given by $y=60+2x$. However, an average of 10 ki... | math | {
"style": "rule",
"ground_truth": "11600"
} | {
"split": "train",
"index": 17219,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $S = \\{r_1, r_2, \\ldots, r_n\\} \\subseteq \\{1, 2, 3, \\ldots, 50\\}$, and the sum of any two numbers in $S$ cannot be divisible by 7. The maximum value of $n$ is ____. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "23"
} | {
"split": "train",
"index": 17220,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Natural numbers are arranged according to the following pattern:\n\\begin{tabular}{cccc}\n$1-2$ & 5 & 10 & 17 \\\\\n$\\mid$ & $\\mid$ & $\\mid$ & $\\mid$ \\\\\n$4-3$ & 6 & 11 & 18 \\\\\n& $\\mid$ & $\\mid$ & $\\mid$ \\\\\n$9-8-7$ & 12 & 19 \\\\\n& $\\mid$ & $\\mid$ \\\\\n$16-15... | math | {
"style": "rule",
"ground_truth": "2002 \\times 2003"
} | {
"split": "train",
"index": 17221,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Consider the function \\( g(x) = \\sum_{k=3}^{12} (\\lfloor kx \\rfloor - k \\lfloor x \\rfloor) \\) where \\( \\lfloor r \\rfloor \\) denotes the greatest integer less than or equal to \\( r \\). Determine how many distinct values \\( g(x) \\) can take for \\( x \\ge 0 \\).\nA... | math | {
"style": "rule",
"ground_truth": "45"
} | {
"split": "train",
"index": 17222,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": " $O$ and $I$ are the circumcentre and incentre of $\\vartriangle ABC$ respectively. Suppose $O$ lies in the interior of $\\vartriangle ABC$ and $I$ lies on the circle passing through $B, O$ , and $C$ . What is the magnitude of $\\angle B AC$ in degrees? Let's t... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 17223,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "How many integers $n$ (with $1 \\le n \\le 2021$ ) have the property that $8n + 1$ is a perfect square? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "63"
} | {
"split": "train",
"index": 17224,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A bag contains 4 tan, 3 pink, and 5 violet chips. If the 12 chips are randomly drawn from the bag, one at a time and without replacement, what is the probability that the chips are drawn such that the 4 tan chips are drawn consecutively, the 3 pink chips are drawn consecutively... | math | {
"style": "rule",
"ground_truth": "\\frac{1}{4620}"
} | {
"split": "train",
"index": 17225,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Suppose that $f(x)=4x+5$. What is $f^{-1}(f^{-1}(9))$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"split": "train",
"index": 17226,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Starting at $(0,0),$ an object moves in the coordinate plane via a sequence of steps, each of length one. Each step is to the left, right, up, or down, all four equally likely. Let $q$ be the probability that the object reaches $(3,3)$ in eight or fewer steps. Write $q$ in the ... | math | {
"style": "rule",
"ground_truth": "4151"
} | {
"split": "train",
"index": 17227,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "For the graph $y = mx + 3$, determine the maximum value of $a$ such that the line does not pass through any lattice points for $0 < x \\leq 50$ when $\\frac{1}{3} < m < a$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{17}{51}"
} | {
"split": "train",
"index": 17228,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given that $α, β ∈ (0, \\frac{π}{2})$, and $\\frac{\\sin β}{\\sin α} = \\cos(α + β)$, \n(1) If $α = \\frac{π}{6}$, then $\\tan β =$ _______; \n(2) The maximum value of $\\tan β$ is _______. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{\\sqrt{2}}{4}"
} | {
"split": "train",
"index": 17229,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Under normal circumstances, for people aged between 18 and 38, the regression equation of weight $y$ (kg) to height $x$ (cm) is $\\overset{\\land }{y} = 0.72x - 58.2$. Zhang Hong, who is 20 years old and has a height of 178 cm, should have a weight of approximately \\_\\_\\_\\_... | math | {
"style": "rule",
"ground_truth": "69.96"
} | {
"split": "train",
"index": 17230,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Design a computer operation program:\n1. Initial values \\( x = 3 \\), \\( y = 0 \\).\n2. \\( x = x + 2 \\).\n3. \\( y = y + x \\).\n4. If \\( y \\geqslant 10000 \\), proceed to (5); otherwise, go back to (2).\n5. Print \\( x \\).\n6. Stop running. What will be the printed resu... | math | {
"style": "rule",
"ground_truth": "201"
} | {
"split": "train",
"index": 17231,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Ten gangsters are standing on a flat surface, and the distances between them are all distinct. At twelve o’clock, when the church bells start chiming, each of them fatally shoots the one among the other nine gangsters who is the nearest. At least how many gangsters will be kill... | math | {
"style": "rule",
"ground_truth": "7"
} | {
"split": "train",
"index": 17232,
"solution": "\nIn this problem, we need to determine the minimum number of gangsters who will be killed when each gangster shoots the nearest of the other nine gangsters. As all distances between the gangsters are distinct, each gangster has a unique nearest neighbor.\n\nConsid... |
deepscaler | [
{
"role": "user",
"content": "Find $c$ if $a$, $b$, and $c$ are positive integers which satisfy $c=(a + bi)^3 - 107i$, where $i^2 = -1$. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "198"
} | {
"split": "train",
"index": 17233,
"solution": "Expanding out both sides of the given equation we have $c + 107i = (a^3 - 3ab^2) + (3a^2b - b^3)i$. Two complex numbers are equal if and only if their real parts and imaginary parts are equal, so $c = a^3 - 3ab^2$ and $107 = 3a^2b - b^3 = (3a^2 - b^2)b$. Since $a, ... |
deepscaler | [
{
"role": "user",
"content": "A cylindrical tank with radius 6 feet and height 7 feet is lying on its side. The tank is filled with water to a depth of 3 feet. Find the volume of water in the tank, in cubic feet. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "84\\pi - 63\\sqrt{3}"
} | {
"split": "train",
"index": 17234,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Kevin writes down the positive integers $1,2, \\ldots, 15$ on a blackboard. Then, he repeatedly picks two random integers $a, b$ on the blackboard, erases them, and writes down $\\operatorname{gcd}(a, b)$ and $\\operatorname{lcm}(a, b)$. He does this until he is no longer able ... | math | {
"style": "rule",
"ground_truth": "360864"
} | {
"split": "train",
"index": 17235,
"solution": "Since $v_{p}(\\operatorname{gcd}(a, b))=\\min \\left(v_{p}(a), v_{p}(b)\\right)$ and $v_{p}(\\operatorname{lcm}(a, b))=\\max \\left(v_{p}(a), v_{p}(b)\\right)$, we may show the following: Claim. For any prime $p$ and non-negative integer $k$, the number of numbers ... |
deepscaler | [
{
"role": "user",
"content": "If \\( a < b < c < d \\) are distinct positive integers such that \\( a+b+c+d \\) is a square, what is the minimum value of \\( c+d \\)? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"split": "train",
"index": 17236,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The center of a circle with a radius of 5, circumscribed around an isosceles trapezoid, lies on the longer base, and the shorter base is equal to 6. Find the area of the trapezoid. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "32"
} | {
"split": "train",
"index": 17237,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Petya and Vasya took a math test. Petya answered $80\\%$ of all the questions correctly, while Vasya answered exactly 35 questions correctly. The number of questions both answered correctly is exactly half the total number of questions. No one answered 7 questions. How many que... | math | {
"style": "rule",
"ground_truth": "60"
} | {
"split": "train",
"index": 17238,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Let $ABC$ be an equilateral triangle of side length 6 inscribed in a circle $\\omega$. Let $A_{1}, A_{2}$ be the points (distinct from $A$) where the lines through $A$ passing through the two trisection points of $BC$ meet $\\omega$. Define $B_{1}, B_{2}, C_{1}, C_{2}$ similarl... | math | {
"style": "rule",
"ground_truth": "\\frac{846\\sqrt{3}}{49}"
} | {
"split": "train",
"index": 17239,
"solution": "Let $A^{\\prime}$ be the point on $BC$ such that $2BA^{\\prime}=A^{\\prime}C$. By law of cosines on triangle $AA^{\\prime}B$, we find that $AA^{\\prime}=2\\sqrt{7}$. By power of a point, $A^{\\prime}A_{1}=\\frac{2 \\cdot 4}{2\\sqrt{7}}=\\frac{4}{\\sqrt{7}}$. Using ... |
deepscaler | [
{
"role": "user",
"content": "Find the sum $$\\frac{3^1}{9^1 - 1} + \\frac{3^2}{9^2 - 1} + \\frac{3^4}{9^4 - 1} + \\frac{3^8}{9^8 - 1} + \\cdots.$$ Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2}"
} | {
"split": "train",
"index": 17240,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "A certain company, in response to the national call for garbage classification, has launched a project with the support of the research department to innovate technologies. The project processes kitchen waste into reusable chemical products. It is known that the daily processin... | math | {
"style": "rule",
"ground_truth": "1800"
} | {
"split": "train",
"index": 17241,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Given a finite sequence $D$: $a\\_1$, $a\\_2$, ..., $a\\_n$, where $S\\_n$ represents the sum of the first $n$ terms of the sequence $D$, define $\\frac{S\\_1 + S\\_2 + ... + S\\_n}{n}$ as the \"De-Guang sum\" of $D$. If a 99-term sequence $a\\_1$, $a\\_2$, ..., $a\\_99$ has a ... | math | {
"style": "rule",
"ground_truth": "998"
} | {
"split": "train",
"index": 17242,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "If $7=x^2+\\frac{1}{x^2}$, then what is the greatest possible value of $x+\\frac{1}{x}$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "3"
} | {
"split": "train",
"index": 17243,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Determine the number of different arrangements for assigning 6 repatriated international students to work in Jinan and Qingdao, given that at least 2 students must be assigned to Jinan and at least 3 students must be assigned to Qingdao. Let's think step by step and put only th... | math | {
"style": "rule",
"ground_truth": "35"
} | {
"split": "train",
"index": 17244,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "Three flower beds overlap as shown. Bed A has 500 plants, bed B has 450 plants, and bed C has 350 plants. Beds A and B share 50 plants, while beds A and C share 100. The total number of plants is Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1150"
} | {
"split": "train",
"index": 17245,
"solution": "\n#### Method 1: Using the Principle of Inclusion-Exclusion\nWe are given:\n- Total plants in Bed A, $|A| = 500$\n- Total plants in Bed B, $|B| = 450$\n- Total plants in Bed C, $|C| = 350$\n- Plants shared between Bed A and Bed B, $|A \\cap B| = 50$\n- Plants share... |
deepscaler | [
{
"role": "user",
"content": "The Elvish language consists of 4 words: \"elara\", \"quen\", \"silva\", and \"nore\". In a sentence, \"elara\" cannot come directly before \"quen\", and \"silva\" cannot come directly before \"nore\"; all other word combinations are grammatically correct (including sentences w... | math | {
"style": "rule",
"ground_truth": "48"
} | {
"split": "train",
"index": 17246,
"solution": ""
} |
deepscaler | [
{
"role": "user",
"content": "The parabolas $y=ax^2 - 2$ and $y=4 - bx^2$ intersect the coordinate axes in exactly four points, and these four points are the vertices of a kite of area $12$. What is $a+b$? Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "1.5"
} | {
"split": "train",
"index": 17247,
"solution": "\n#### Step 1: Understand the problem\nWe are given two parabolas, \\(y = ax^2 - 2\\) and \\(y = 4 - bx^2\\), and we know they intersect the coordinate axes in exactly four points. These points form the vertices of a kite with an area of 12. We need to find the sum... |
deepscaler | [
{
"role": "user",
"content": "Maria buys computer disks at a price of 5 for $6 and sells them at a price of 4 for $7. Find how many computer disks Maria must sell to make a profit of $120. Let's think step by step and put only the final answer within \\boxed{}."
}
] | math | {
"style": "rule",
"ground_truth": "219"
} | {
"split": "train",
"index": 17248,
"solution": ""
} |
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