idx int64 0 7.5k | first_round bool 2
classes | gt stringlengths 1 139 | rewards sequencelengths 4 8 | my_solu sequencelengths 1 1 | flag bool 1
class | turn int64 4 4 | conversations listlengths 4 6 |
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1,696 | false | 1024 | [
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nWhat is the value of \\[\\frac{x^1\\cdot x^2\\cdot x^3\\cdots x^{15}}{x^2\\cdot x^4 \\cdot x^6 \\cdots x^{20}}\\]if $x=2$?\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n... | true | 4 | [
{
"content": "What is the value of \\[\\frac{x^1\\cdot x^2\\cdot x^3\\cdots x^{15}}{x^2\\cdot x^4 \\cdot x^6 \\cdots x^{20}}\\]if $x=2$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "\\begin{align*}\n\\frac{x^1\\cdot x^2\\cdot x^3\\cdots x... |
1,843 | false | 36 | [
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nIn how many different ways can 3 men and 4 women be placed into two groups of two people and one group of three people if there must be at least one man and one woman in each group? Note that identically sized groups are indistinguishable.\nPlease reaso... | true | 4 | [
{
"content": "In how many different ways can 3 men and 4 women be placed into two groups of two people and one group of three people if there must be at least one man and one woman in each group? Note that identically sized groups are indistinguishable.\nPlease reason step by step, and put your final answer wi... |
3,450 | false | 8 | [
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nA square is inscribed in the ellipse\n\\[\\frac{x^2}{3} + \\frac{y^2}{6} = 1,\\]so that its sides are parallel to the coordinate axes. Find the area of the square.\n\n[asy]\nunitsize(1 cm);\n\ndraw(xscale(sqrt(3))*yscale(sqrt(6))*Circle((0,0),1));\ndraw... | true | 4 | [
{
"content": "A square is inscribed in the ellipse\n\\[\\frac{x^2}{3} + \\frac{y^2}{6} = 1,\\]so that its sides are parallel to the coordinate axes. Find the area of the square.\n\n[asy]\nunitsize(1 cm);\n\ndraw(xscale(sqrt(3))*yscale(sqrt(6))*Circle((0,0),1));\ndraw((sqrt(2),sqrt(2))--(-sqrt(2),sqrt(2))--(-sq... |
2,485 | true | 70 | [
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true
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nFor a certain weekend, the weatherman predicts that it will rain with a $40\\%$ probability on Saturday and a $50\\%$ probability on Sunday. Assuming these probabilities are independent, what is the probability that it rains over the weekend (that is, on... | true | 4 | [
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"content": "For a certain weekend, the weatherman predicts that it will rain with a $40\\%$ probability on Saturday and a $50\\%$ probability on Sunday. Assuming these probabilities are independent, what is the probability that it rains over the weekend (that is, on at least one of the days)? Express your ans... |
1,115 | false | -5 | [
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nThe lines $y=5x+3$, $y=-2x-25$ and $y=3x+k$ intersect at the same point. What is the value of $k$?\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\nSince the lines intersec... | true | 4 | [
{
"content": "The lines $y=5x+3$, $y=-2x-25$ and $y=3x+k$ intersect at the same point. What is the value of $k$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
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"content": "Since the lines intersect at the same point, their $y$-coordinates are equal at ... |
6,376 | false | \frac{1}{14} | [
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nSimplify this expression to a common fraction: $\\frac{1}{\\frac{1}{(\\frac{1}{2})^{1}}+\\frac{1}{(\\frac{1}{2})^{2}}+\\frac{1}{(\\frac{1}{2})^{3}}}$\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>as... | true | 4 | [
{
"content": "Simplify this expression to a common fraction: $\\frac{1}{\\frac{1}{(\\frac{1}{2})^{1}}+\\frac{1}{(\\frac{1}{2})^{2}}+\\frac{1}{(\\frac{1}{2})^{3}}}$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "The key idea here is to use ... |
7,496 | true | 0 | [
true,
false,
true,
true
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nLet $A,$ $B,$ $C$ be the angles of a triangle. Evaluate\n\\[\\begin{vmatrix} \\sin^2 A & \\cot A & 1 \\\\ \\sin^2 B & \\cot B & 1 \\\\ \\sin^2 C & \\cot C & 1 \\end{vmatrix}.\\]\nPlease reason step by step, and put your final answer within \\boxed{}.<|e... | true | 4 | [
{
"content": "Let $A,$ $B,$ $C$ be the angles of a triangle. Evaluate\n\\[\\begin{vmatrix} \\sin^2 A & \\cot A & 1 \\\\ \\sin^2 B & \\cot B & 1 \\\\ \\sin^2 C & \\cot C & 1 \\end{vmatrix}.\\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "... |
3,748 | true | 1152 | [
true,
true,
false,
false
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nLet $x$ and $y$ be positive real numbers such that $3x + 4y < 72.$ Find the maximum value of\n\\[xy (72 - 3x - 4y).\\]\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n## ... | true | 4 | [
{
"content": "Let $x$ and $y$ be positive real numbers such that $3x + 4y < 72.$ Find the maximum value of\n\\[xy (72 - 3x - 4y).\\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
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"content": "## Step 1: Recognize the problem as an optimization problem... |
3,858 | false | (-3,2) | [
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nSolve the inequality\n\\[|x - 1| + |x + 2| < 5.\\]\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\nLet's solve the given inequality step by step. We are given that:\n\\[|x... | true | 4 | [
{
"content": "Solve the inequality\n\\[|x - 1| + |x + 2| < 5.\\]\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "Let's solve the given inequality step by step. We are given that:\n\\[|x - 1| + |x + 2| < 5.\\]\nLet's split the given inequalit... |
2,316 | true | 6 | [
true,
true,
true,
true
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nWhat is the value of $\\sqrt{3! \\cdot 3!}$ expressed as a positive integer?\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n## Step 1: Calculate the value of 3!\n3! = 3 x... | true | 4 | [
{
"content": "What is the value of $\\sqrt{3! \\cdot 3!}$ expressed as a positive integer?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "## Step 1: Calculate the value of 3!\n3! = 3 x 2 x 1 = 6.\n\n## Step 2: Multiply the result by itself ... |
1,949 | false | \frac{7}{16} | [
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nAllen and Bethany each arrive at a party at a random time between 1:00 and 2:00. Each stays for 15 minutes, then leaves. What is the probability that Allen and Bethany see each other at the party?\nPlease reason step by step, and put your final answer ... | true | 4 | [
{
"content": "Allen and Bethany each arrive at a party at a random time between 1:00 and 2:00. Each stays for 15 minutes, then leaves. What is the probability that Allen and Bethany see each other at the party?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
... |
7,444 | false | 2x-y+2z-18=0 | [
false,
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nLet $\\mathbf{w} = \\begin{pmatrix} 2 \\\\ -1 \\\\ 2 \\end{pmatrix}.$ The set of vectors $\\mathbf{v}$ such that\n\\[\\operatorname{proj}_{\\mathbf{w}} \\mathbf{v} = \\begin{pmatrix} 4 \\\\ -2 \\\\ 4 \\end{pmatrix}\\]lie on a plane. Enter the equation ... | true | 4 | [
{
"content": "Let $\\mathbf{w} = \\begin{pmatrix} 2 \\\\ -1 \\\\ 2 \\end{pmatrix}.$ The set of vectors $\\mathbf{v}$ such that\n\\[\\operatorname{proj}_{\\mathbf{w}} \\mathbf{v} = \\begin{pmatrix} 4 \\\\ -2 \\\\ 4 \\end{pmatrix}\\]lie on a plane. Enter the equation of this plane in the form\n\\[Ax + By + Cz +... |
6,498 | false | 70 | [
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false,
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true,
false,
true
] | [
"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nIn parallelogram $ABCD$, angle $B$ measures $110^\\circ$. What is the number of degrees in the measure of angle $C$?\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\nBecaus... | true | 4 | [
{
"content": "In parallelogram $ABCD$, angle $B$ measures $110^\\circ$. What is the number of degrees in the measure of angle $C$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "Because opposite sides of a parallelogram are parallel, angles... |
6,741 | false | 30 | [
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false
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nIn a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|... | true | 4 | [
{
"content": "In a right-angled triangle, the sum of the squares of the three side lengths is 1800. What is the length of the hypotenuse of this triangle?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "Let the three sides of the triangle b... |
4,461 | true | -1,\;-5 | [
true,
true,
false,
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nFind all real values of $x$ that satisfy $x + \\frac{45}{x-4} = -10.$\n\nEnter all the solutions, separated by commas.\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n## S... | true | 4 | [
{
"content": "Find all real values of $x$ that satisfy $x + \\frac{45}{x-4} = -10.$\n\nEnter all the solutions, separated by commas.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "## Step 1: To find the real values of x that satisfy the equ... |
4,850 | false | 6 | [
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nWhat is the greatest whole number that must be a divisor of the product of any three consecutive positive integers?\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\nWe can ... | true | 4 | [
{
"content": "What is the greatest whole number that must be a divisor of the product of any three consecutive positive integers?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We can first assume that the three consecutive positive integer... |
1,149 | false | 2 | [
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nFind $\\left \\lceil \\frac{12}{7} \\cdot \\frac{-29}{3}\\right\\rceil - \\left\\lfloor \\frac{12}{7} \\cdot \\left \\lfloor \\frac{-29}{3}\\right \\rfloor \\right \\rfloor$.\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_i... | true | 4 | [
{
"content": "Find $\\left \\lceil \\frac{12}{7} \\cdot \\frac{-29}{3}\\right\\rceil - \\left\\lfloor \\frac{12}{7} \\cdot \\left \\lfloor \\frac{-29}{3}\\right \\rfloor \\right \\rfloor$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We f... |
5,583 | true | 9 | [
true,
false,
true,
true
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nThe product of two positive integers is 18. The positive difference of these two integers is 3. What is the sum of the two integers?\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_heade... | true | 4 | [
{
"content": "The product of two positive integers is 18. The positive difference of these two integers is 3. What is the sum of the two integers?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "## Step 1: To solve this problem, we can star... |
3,229 | true | 8 | [
true,
true,
false,
false
] | [
"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nIn the diagram, triangles $ABC$ and $CBD$ are isosceles. The perimeter of $\\triangle CBD$ is $19,$ the perimeter of $\\triangle ABC$ is $20,$ and the length of $BD$ is $7.$ What is the length of $AB?$ [asy]\n\nsize(7cm);\ndefaultpen(fontsize(11));\n\npa... | true | 4 | [
{
"content": "In the diagram, triangles $ABC$ and $CBD$ are isosceles. The perimeter of $\\triangle CBD$ is $19,$ the perimeter of $\\triangle ABC$ is $20,$ and the length of $BD$ is $7.$ What is the length of $AB?$ [asy]\n\nsize(7cm);\ndefaultpen(fontsize(11));\n\npair b = (0, 0);\npair d = 7 * dir(-30);\npair... |
1,425 | true | 4 | [
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nEvaluate $\\log_2 (4^2)$.\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n## Step 1: Recall the definition of a logarithm\nTo solve this problem, we first need to recall t... | true | 4 | [
{
"content": "Evaluate $\\log_2 (4^2)$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "## Step 1: Recall the definition of a logarithm\nTo solve this problem, we first need to recall that a logarithm is the inverse operation of exponentiati... |
361 | false | 1 | [
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nLine $a$ is parallel to line $y=2x+4$ and passes through the point $(2,5)$. What is the y-intercept of line $a$?\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\nIf line $a... | true | 4 | [
{
"content": "Line $a$ is parallel to line $y=2x+4$ and passes through the point $(2,5)$. What is the y-intercept of line $a$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "If line $a$ is parallel to the line $y = 2x + 4$, then it has the ... |
4,678 | false | 15 | [
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false
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nThe function $f(x)$ satisfies\n\\[f(xy) = \\frac{f(x)}{y}\\]for all positive real numbers $x$ and $y.$ If $f(30) = 20,$ find $f(40).$\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_hea... | true | 4 | [
{
"content": "The function $f(x)$ satisfies\n\\[f(xy) = \\frac{f(x)}{y}\\]for all positive real numbers $x$ and $y.$ If $f(30) = 20,$ find $f(40).$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We first plug in $x=30$ and $y=40/3$ to get:... |
2,368 | false | \frac{1}{52} | [
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false,
false,
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false,
false,
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false
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nTwo cards are chosen at random from a standard 52-card deck. What is the probability that the first card is a heart and the second card is a 10?\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assista... | true | 4 | [
{
"content": "Two cards are chosen at random from a standard 52-card deck. What is the probability that the first card is a heart and the second card is a 10?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "There are $13$ hearts and 52 tota... |
3,647 | true | 5 | [
false,
false,
true,
false
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nIf $x$ and $y$ are positive real numbers such that $5x^2 + 10xy = x^3 + 2x^2 y,$ what is the value of $x$?\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n## Step 1: Ident... | true | 4 | [
{
"content": "If $x$ and $y$ are positive real numbers such that $5x^2 + 10xy = x^3 + 2x^2 y,$ what is the value of $x$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "## Step 1: Identify and write down the given equation\nThe equation give... |
95 | false | 6 | [
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nSolve for $x$: $(x-4)^3=\\left(\\frac18\\right)^{-1}$\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\nWe begin by rewriting the equation as $$x^3-4x^2-24x+64=1$$Then we us... | true | 4 | [
{
"content": "Solve for $x$: $(x-4)^3=\\left(\\frac18\\right)^{-1}$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "We begin by rewriting the equation as $$x^3-4x^2-24x+64=1$$Then we use the difference of cubes to rewrite the equation as$$\\... |
5,030 | false | 29 | [
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false,
true
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nWhat integer $n$ satisfies $0\\le n<{101}$ and $$100n\\equiv 72\\pmod {101}~?$$\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n100n ≡ 72 (mod 101) 100n ≡ 72 + 101k for so... | true | 4 | [
{
"content": "What integer $n$ satisfies $0\\le n<{101}$ and $$100n\\equiv 72\\pmod {101}~?$$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "100n ≡ 72 (mod 101) 100n ≡ 72 + 101k for some integer k. In simpler notation, 100n ≡ 25 + 101k, sin... |
3,797 | false | x^3-3x^2+3x-3 | [
false,
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false,
false,
false,
false,
true,
true
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nFind a monic cubic polynomial $P(x)$ with integer coefficients such that\n\\[P(\\sqrt[3]{2} + 1) = 0.\\](A polynomial is monic if its leading coefficient is 1.)\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_hea... | true | 4 | [
{
"content": "Find a monic cubic polynomial $P(x)$ with integer coefficients such that\n\\[P(\\sqrt[3]{2} + 1) = 0.\\](A polynomial is monic if its leading coefficient is 1.)\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "If $P(x)=x^3+ax^2+... |
6,745 | false | 19 | [
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false
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nHow many numbers are in the list $ -33, -28, -23, \\ldots, 52, 57?$\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\nThe list consists of numbers which are 5 apart.\n\nThe ... | true | 4 | [
{
"content": "How many numbers are in the list $ -33, -28, -23, \\ldots, 52, 57?$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "The list consists of numbers which are 5 apart.\n\nThe list starts with -33 and the last number is 57.\n\nFind ... |
4,865 | false | 36 | [
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true,
true
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nWhat is the largest perfect square factor of 1512?\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\nA nice problem!\n\nLet's start by factoring 1512:\n\n1512 = 2 × 2 × 2 × ... | true | 4 | [
{
"content": "What is the largest perfect square factor of 1512?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
{
"content": "A nice problem!\n\nLet's start by factoring 1512:\n\n1512 = 2 × 2 × 2 × 3 × 3 × 7\n\nA perfect square must have only even powers... |
5,661 | true | \frac{5}{4} | [
false,
false,
true,
false
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nSimplify $\\frac{180}{16}\\cdot \\frac{5}{120}\\cdot \\frac{8}{3}$.\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n## Step 1: To simplify the given expression $\\frac{180... | true | 4 | [
{
"content": "Simplify $\\frac{180}{16}\\cdot \\frac{5}{120}\\cdot \\frac{8}{3}$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
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"content": "## Step 1: To simplify the given expression $\\frac{180}{16}\\cdot \\frac{5}{120}\\cdot \\frac{8}{3}$, first we... |
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nWhat is the greatest common divisor of $2^{1998}-1$ and $2^{1989}-1$?\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\nLet $a_n = 2^{n}-1$. We wish to find the GCD of $a_{1... | true | 4 | [
{
"content": "What is the greatest common divisor of $2^{1998}-1$ and $2^{1989}-1$?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
},
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"content": "Let $a_n = 2^{n}-1$. We wish to find the GCD of $a_{1998}$ and $a_{1989}$. Notice that $a_{1998} = (2^{1989})... |
755 | true | 16 | [
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nSeven identical bowling balls weigh the same as four identical canoes. If three of the canoes weigh a total of 84 pounds, how many pounds does one of the bowling balls weigh?\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_i... | true | 4 | [
{
"content": "Seven identical bowling balls weigh the same as four identical canoes. If three of the canoes weigh a total of 84 pounds, how many pounds does one of the bowling balls weigh?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
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{
"content": "## S... |
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nHow many non-congruent triangles with only integer side lengths have a perimeter of 15 units?\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\nSince the perimeter of the tr... | true | 4 | [
{
"content": "How many non-congruent triangles with only integer side lengths have a perimeter of 15 units?\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
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"content": "Since the perimeter of the triangle is 15, the sum of its three sides is 15. If two o... |
764 | false | \frac{225}{16} | [
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nFind $a$ such that $ax^2+15x+4$ is the square of a binomial.\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\nWe wish to find $a$ such that\n\n$$ax^2+15x+4=(bx+c)^2.$$Expan... | true | 4 | [
{
"content": "Find $a$ such that $ax^2+15x+4$ is the square of a binomial.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
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"content": "We wish to find $a$ such that\n\n$$ax^2+15x+4=(bx+c)^2.$$Expanding the right-hand side, we have\n\n$$(bx+c)^2=b^2x^2+2... |
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nDetermine the residue of $-811\\pmod{24}$. Your answer should be an integer in the range $0,1,2,\\ldots,22,23$.\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\nFirst, dete... | true | 4 | [
{
"content": "Determine the residue of $-811\\pmod{24}$. Your answer should be an integer in the range $0,1,2,\\ldots,22,23$.\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
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"content": "First, determine the greatest common factor of $811$ and $24$, usin... |
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nCompute $1-2+3-4+ \\dots -98+99$ .\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assistant<|end_header_id|>\n\n$1+(-1)+2+(-2)+ \\dots +98+(-98)+99=(1-1)+(2-2)+ \\dots +(98-98)+99=\\boxed{100}$.\nFina... | true | 4 | [
{
"content": "Compute $1-2+3-4+ \\dots -98+99$ .\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
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{
"content": "$1+(-1)+2+(-2)+ \\dots +98+(-98)+99=(1-1)+(2-2)+ \\dots +(98-98)+99=\\boxed{100}$.\nFinal Answer: The final answer is \\boxed{100}. I hope it is... |
2,480 | true | 15 | [
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"<|begin_of_text|><|start_header_id|>user<|end_header_id|>\n\nHow many different positive integers can be represented as a difference of two distinct members of the set $\\{1, 2, 3, \\ldots, 14, 15, 16 \\}?$\nPlease reason step by step, and put your final answer within \\boxed{}.<|eot_id|><|start_header_id|>assista... | true | 4 | [
{
"content": "How many different positive integers can be represented as a difference of two distinct members of the set $\\{1, 2, 3, \\ldots, 14, 15, 16 \\}?$\nPlease reason step by step, and put your final answer within \\boxed{}.",
"role": "user"
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{
"content": "## Step 1: Understand the set giv... |
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