answers listlengths 1 1 | datasets listlengths 1 1 | id stringlengths 64 64 | messages listlengths 1 1 | prompt stringlengths 10 2.99k | reference_answer_raw stringlengths 3 1.22k | source stringclasses 1
value | source_records stringlengths 116 1.08k | verifiability dict |
|---|---|---|---|---|---|---|---|---|
[
"50"
] | [
"deepscaler"
] | 318fe464389971eaccaa99d884e330042c1d76ba3867694e8c66a0e11e63fee8 | [
{
"content": "How many squares whose sides are parallel to the axes and whose vertices have coordinates that are integers lie entirely within the region bounded by the line $y=\\pi x$, the line $y=-0.1$ and the line $x=5.1?$",
"role": "user"
}
] | How many squares whose sides are parallel to the axes and whose vertices have coordinates that are integers lie entirely within the region bounded by the line $y=\pi x$, the line $y=-0.1$ and the line $x=5.1?$ | "50" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:318"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:676"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"17"
] | [
"deepscaler"
] | 22ae20b81e6ca4a4bdb688157ae5f3096917cd68cca47a55a17d1d62cdc09991 | [
{
"content": "Quadrilateral $ABCD$ is inscribed in circle $O$ and has side lengths $AB=3, BC=2, CD=6$, and $DA=8$. Let $X$ and $Y$ be points on $\\overline{BD}$ such that $\\frac{DX}{BD} = \\frac{1}{4}$ and $\\frac{BY}{BD} = \\frac{11}{36}$.\nLet $E$ be the intersection of line $AX$ and the line through $Y$ par... | Quadrilateral $ABCD$ is inscribed in circle $O$ and has side lengths $AB=3, BC=2, CD=6$, and $DA=8$. Let $X$ and $Y$ be points on $\overline{BD}$ such that $\frac{DX}{BD} = \frac{1}{4}$ and $\frac{BY}{BD} = \frac{11}{36}$.
Let $E$ be the intersection of line $AX$ and the line through $Y$ parallel to $\overline{AD}$. Le... | "17" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:319"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"deepscaler"
] | a495d5f80794c61e88d4ada9e5ab6050d5ac26d4cd4b4173ac6265af8a83e474 | [
{
"content": "-15 + 9 \\times (6 \\div 3) =",
"role": "user"
}
] | -15 + 9 \times (6 \div 3) = | "3" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:320"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"deepscaler"
] | ef3f5e266fbd763b0593dd25b18bd85113ace4b08c877ea8c93643ababfed7ae | [
{
"content": "How many ordered triples $(a, b, c)$ of non-zero real numbers have the property that each number is the product of the other two?",
"role": "user"
}
] | How many ordered triples $(a, b, c)$ of non-zero real numbers have the property that each number is the product of the other two? | "4" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:321"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"492"
] | [
"deepscaler"
] | 90354c7f74a1e614e3e820ad16ced0d71839df00ef05db25ecce40bb20c60ec2 | [
{
"content": "Suppose $a$, $b$ and $c$ are positive integers with $a+b+c=2006$, and $a!b!c!=m\\cdot 10^n$, where $m$ and $n$ are integers and $m$ is not divisible by $10$. What is the smallest possible value of $n$?",
"role": "user"
}
] | Suppose $a$, $b$ and $c$ are positive integers with $a+b+c=2006$, and $a!b!c!=m\cdot 10^n$, where $m$ and $n$ are integers and $m$ is not divisible by $10$. What is the smallest possible value of $n$? | "492" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:322"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"$y^x=x^y$"
] | [
"deepscaler"
] | 3da32fd74731f7708fcca1659a7d3b820bff4eaa1299a95ef973e56fc82a4e6b | [
{
"content": "If $x=t^{\\frac{1}{t-1}}$ and $y=t^{\\frac{t}{t-1}},t>0,t \\ne 1$, a relation between $x$ and $y$ is:",
"role": "user"
}
] | If $x=t^{\frac{1}{t-1}}$ and $y=t^{\frac{t}{t-1}},t>0,t \ne 1$, a relation between $x$ and $y$ is: | "$y^x=x^y$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:324"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"deepscaler"
] | 4972a7c98cfa35f1f15d36faa7660f900428a56cf6f4bbd9e1a29109f4da9ade | [
{
"content": "The figure below shows line $\\ell$ with a regular, infinite, recurring pattern of squares and line segments.\n\nHow many of the following four kinds of rigid motion transformations of the plane in which this figure is drawn, other than the identity transformation, will transform this figure into ... | The figure below shows line $\ell$ with a regular, infinite, recurring pattern of squares and line segments.
How many of the following four kinds of rigid motion transformations of the plane in which this figure is drawn, other than the identity transformation, will transform this figure into itself?
some rotation ar... | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:325"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"26"
] | [
"deepscaler"
] | cef245c505c0c6716ed104feee48f6074f131624fae33c3586d4b09759e62976 | [
{
"content": "A driver travels for $2$ hours at $60$ miles per hour, during which her car gets $30$ miles per gallon of gasoline. She is paid $\\$0.50$ per mile, and her only expense is gasoline at $\\$2.00$ per gallon. What is her net rate of pay, in dollars per hour, after this expense?",
"role": "user"
... | A driver travels for $2$ hours at $60$ miles per hour, during which her car gets $30$ miles per gallon of gasoline. She is paid $\$0.50$ per mile, and her only expense is gasoline at $\$2.00$ per gallon. What is her net rate of pay, in dollars per hour, after this expense? | "26" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:326"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1931"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{15}{8}"
] | [
"deepscaler"
] | ca703d3f7483c12d18e532cdfd9004384b7cc723030b56ae22b613b5c21084b9 | [
{
"content": "Andy and Bethany have a rectangular array of numbers with $40$ rows and $75$ columns. Andy adds the numbers in each row. The average of his $40$ sums is $A$. Bethany adds the numbers in each column. The average of her $75$ sums is $B$. What is the value of $\\frac{A}{B}$?",
"role": "user"
}
... | Andy and Bethany have a rectangular array of numbers with $40$ rows and $75$ columns. Andy adds the numbers in each row. The average of his $40$ sums is $A$. Bethany adds the numbers in each column. The average of her $75$ sums is $B$. What is the value of $\frac{A}{B}$? | "\\frac{15}{8}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:327"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"$20\\%$"
] | [
"deepscaler"
] | 2b6a5d82c6914f6871b2bd3ef74df3082dce0c43738803e60cf7882358b19403 | [
{
"content": "Liliane has $50\\%$ more soda than Jacqueline, and Alice has $25\\%$ more soda than Jacqueline. What is the relationship between the amounts of soda that Liliane and Alice have?",
"role": "user"
}
] | Liliane has $50\%$ more soda than Jacqueline, and Alice has $25\%$ more soda than Jacqueline. What is the relationship between the amounts of soda that Liliane and Alice have? | "$20\\%$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:328"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"deepscaler"
] | bfbf20c86f991f484e238dbe3b3ee9e5f7d64b1d90380421ec89ec0f84157b6a | [
{
"content": "If $\\left(a + \\frac{1}{a}\\right)^2 = 3$, then $a^3 + \\frac{1}{a^3}$ equals:",
"role": "user"
}
] | If $\left(a + \frac{1}{a}\right)^2 = 3$, then $a^3 + \frac{1}{a^3}$ equals: | "0" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:329"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"397"
] | [
"deepscaler"
] | 492192941b60444ed14d82d3904adea18de9448c09c7972fce1b70a7231dff84 | [
{
"content": "What is the $100\\text{th}$ number in the arithmetic sequence: $1,5,9,13,17,21,25,...$?",
"role": "user"
}
] | What is the $100\text{th}$ number in the arithmetic sequence: $1,5,9,13,17,21,25,...$? | "397" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:330"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"deepscaler"
] | 8fba16f114255b5ff3b9d3b95ecd5b619f5427d6153040c4c2a99eee086e0b1c | [
{
"content": "The nine squares in the table shown are to be filled so that every row and every column contains each of the numbers $1,2,3$. Then $A+B=$ \\begin{tabular}{|c|c|c|}\\hline 1 & &\\\\ \\hline & 2 & A\\\\ \\hline & & B\\\\ \\hline\\end{tabular}",
"role": "user"
}
] | The nine squares in the table shown are to be filled so that every row and every column contains each of the numbers $1,2,3$. Then $A+B=$ \begin{tabular}{|c|c|c|}\hline 1 & &\\ \hline & 2 & A\\ \hline & & B\\ \hline\end{tabular} | "4" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:331"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"279"
] | [
"deepscaler"
] | b8158f536d222f6b629ef8ef7849cf031660f7c49db4bcdc1d9c1030687b9c28 | [
{
"content": "The number $5^{867}$ is between $2^{2013}$ and $2^{2014}$. How many pairs of integers $(m,n)$ are there such that $1\\leq m\\leq 2012$ and $5^n<2^m<2^{m+2}<5^{n+1}$?",
"role": "user"
}
] | The number $5^{867}$ is between $2^{2013}$ and $2^{2014}$. How many pairs of integers $(m,n)$ are there such that $1\leq m\leq 2012$ and $5^n<2^m<2^{m+2}<5^{n+1}$? | "279" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:332"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1001"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"256"
] | [
"deepscaler"
] | 56de1e6cfa04b0949bcfeaba6158f7e008fa4b03ab6fff67165cc340c322d7cd | [
{
"content": "Evaluate $(x^x)^{(x^x)}$ at $x = 2$.",
"role": "user"
}
] | Evaluate $(x^x)^{(x^x)}$ at $x = 2$. | "256" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:333"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{5}{12}"
] | [
"deepscaler"
] | 85089034508956e219ec4f3a1038b2b8d5ac1a84b1c99def4f99d6eebd277d65 | [
{
"content": "Diana and Apollo each roll a standard die obtaining a number at random from $1$ to $6$. What is the probability that Diana's number is larger than Apollo's number?",
"role": "user"
}
] | Diana and Apollo each roll a standard die obtaining a number at random from $1$ to $6$. What is the probability that Diana's number is larger than Apollo's number? | "\\frac{5}{12}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:334"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"64"
] | [
"deepscaler"
] | c868183f6a2f555c161c1927b4d5bb1a27c6a7c1983e56bbe06d405e82f35fe7 | [
{
"content": "A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total of $280$ pieces of fruit. There are twice as many raspberries as blueberries, three times as many grapes as cherries, and four times as many cherries as raspberries. How many cherries are there... | A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total of $280$ pieces of fruit. There are twice as many raspberries as blueberries, three times as many grapes as cherries, and four times as many cherries as raspberries. How many cherries are there in the fruit salad? | "64" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:335"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{5}{19} < \\frac{7}{21} < \\frac{9}{23}"
] | [
"deepscaler"
] | 208e07537b5b0e065e68ec487cb5be52323619e070300aabc25a89e825dea7a6 | [
{
"content": "What is the correct ordering of the three numbers $\\frac{5}{19}$, $\\frac{7}{21}$, and $\\frac{9}{23}$, in increasing order?",
"role": "user"
}
] | What is the correct ordering of the three numbers $\frac{5}{19}$, $\frac{7}{21}$, and $\frac{9}{23}$, in increasing order? | "\\frac{5}{19} < \\frac{7}{21} < \\frac{9}{23}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:336"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"81"
] | [
"deepscaler"
] | 4525e2b72f5bfa5c6052ad27cb7599235699030e5e6b0aa63ca542b560baf315 | [
{
"content": "The numbers on the faces of this cube are consecutive whole numbers. The sum of the two numbers on each of the three pairs of opposite faces are equal. The sum of the six numbers on this cube is",
"role": "user"
}
] | The numbers on the faces of this cube are consecutive whole numbers. The sum of the two numbers on each of the three pairs of opposite faces are equal. The sum of the six numbers on this cube is | "81" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:337"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"15"
] | [
"deepscaler"
] | af66f10e5d43d9d37746b4fd3546d028f93f46cacf9f6a6707af48b9b40aacac | [
{
"content": "Paula the painter had just enough paint for 30 identically sized rooms. Unfortunately, on the way to work, three cans of paint fell off her truck, so she had only enough paint for 25 rooms. How many cans of paint did she use for the 25 rooms?",
"role": "user"
}
] | Paula the painter had just enough paint for 30 identically sized rooms. Unfortunately, on the way to work, three cans of paint fell off her truck, so she had only enough paint for 25 rooms. How many cans of paint did she use for the 25 rooms? | "15" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:338"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"100"
] | [
"deepscaler"
] | 20ee934b91d9f967e05f224115de6dfa5a37f33417933cc531f65c62575700cd | [
{
"content": "At Megapolis Hospital one year, multiple-birth statistics were as follows: Sets of twins, triplets, and quadruplets accounted for $1000$ of the babies born. There were four times as many sets of triplets as sets of quadruplets, and there was three times as many sets of twins as sets of triplets. H... | At Megapolis Hospital one year, multiple-birth statistics were as follows: Sets of twins, triplets, and quadruplets accounted for $1000$ of the babies born. There were four times as many sets of triplets as sets of quadruplets, and there was three times as many sets of twins as sets of triplets. How many of these $1000... | "100" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:339"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{32}{3}"
] | [
"deepscaler"
] | 0c75a5deb0fc0e9672cc05844bb5e0fa61cb94c9915d8cd8f09afeacb6e5ccf9 | [
{
"content": "A triangle with vertices $(6, 5)$, $(8, -3)$, and $(9, 1)$ is reflected about the line $x=8$ to create a second triangle. What is the area of the union of the two triangles?",
"role": "user"
}
] | A triangle with vertices $(6, 5)$, $(8, -3)$, and $(9, 1)$ is reflected about the line $x=8$ to create a second triangle. What is the area of the union of the two triangles? | "\\frac{32}{3}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:340"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"500"
] | [
"deepscaler"
] | 6e26ac2bf072aed350be167f68b347e3f5134e27095378838138bd986e6df94d | [
{
"content": "$\\frac{1000^2}{252^2-248^2}$ equals",
"role": "user"
}
] | $\frac{1000^2}{252^2-248^2}$ equals | "500" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:341"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"13"
] | [
"deepscaler"
] | 00251c57c882163572766e08a0487290fb427f2a28e781bc085a44ec77eb0001 | [
{
"content": "Jamal wants to save 30 files onto disks, each with 1.44 MB space. 3 of the files take up 0.8 MB, 12 of the files take up 0.7 MB, and the rest take up 0.4 MB. It is not possible to split a file onto 2 different disks. What is the smallest number of disks needed to store all 30 files?",
"role": ... | Jamal wants to save 30 files onto disks, each with 1.44 MB space. 3 of the files take up 0.8 MB, 12 of the files take up 0.7 MB, and the rest take up 0.4 MB. It is not possible to split a file onto 2 different disks. What is the smallest number of disks needed to store all 30 files? | "13" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:342"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2617"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"60"
] | [
"deepscaler"
] | 3f118e3c138b6d9f040780a3d19bcc0a2cbe4a5e1121b2add3939fdd33ffb574 | [
{
"content": "How many three-digit numbers are not divisible by $5$, have digits that sum to less than $20$, and have the first digit equal to the third digit?",
"role": "user"
}
] | How many three-digit numbers are not divisible by $5$, have digits that sum to less than $20$, and have the first digit equal to the third digit? | "60" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:343"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{7}{12}"
] | [
"deepscaler"
] | 98065a2243530fe9fbb200f45e3b69bf62221206c02ba46ad84f929c6ea2ab6a | [
{
"content": "A fair $6$ sided die is rolled twice. What is the probability that the first number that comes up is greater than or equal to the second number?",
"role": "user"
}
] | A fair $6$ sided die is rolled twice. What is the probability that the first number that comes up is greater than or equal to the second number? | "\\frac{7}{12}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:344"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"15"
] | [
"deepscaler"
] | 15e6e6af2673d252c9d8484cee2efa504e7311a8aed29f93307f53f5549fd152 | [
{
"content": "If $r$ is the remainder when each of the numbers $1059$, $1417$, and $2312$ is divided by $d$, where $d$ is an integer greater than $1$, then $d-r$ equals",
"role": "user"
}
] | If $r$ is the remainder when each of the numbers $1059$, $1417$, and $2312$ is divided by $d$, where $d$ is an integer greater than $1$, then $d-r$ equals | "15" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:345"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2.4"
] | [
"deepscaler"
] | e825ae647fe5943d609109eeea8265ac431cf7b229a209d002f8dfb25b93140b | [
{
"content": "A flagpole is originally $5$ meters tall. A hurricane snaps the flagpole at a point $x$ meters above the ground so that the upper part, still attached to the stump, touches the ground $1$ meter away from the base. What is $x$?",
"role": "user"
}
] | A flagpole is originally $5$ meters tall. A hurricane snaps the flagpole at a point $x$ meters above the ground so that the upper part, still attached to the stump, touches the ground $1$ meter away from the base. What is $x$? | "2.4" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:346"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"19"
] | [
"deepscaler"
] | da8bde9c12a2583470f7275a191bb8ff037250ac4140e8e87e580530590bd4c5 | [
{
"content": "Let $B$ be a right rectangular prism (box) with edges lengths $1,$ $3,$ and $4$, together with its interior. For real $r\\geq0$, let $S(r)$ be the set of points in $3$-dimensional space that lie within a distance $r$ of some point in $B$. The volume of $S(r)$ can be expressed as $ar^{3} + br^{2} +... | Let $B$ be a right rectangular prism (box) with edges lengths $1,$ $3,$ and $4$, together with its interior. For real $r\geq0$, let $S(r)$ be the set of points in $3$-dimensional space that lie within a distance $r$ of some point in $B$. The volume of $S(r)$ can be expressed as $ar^{3} + br^{2} + cr +d$, where $a,$ $b,... | "19" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:347"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"170"
] | [
"deepscaler"
] | 6eef0e43d389b2d4b8267e01e693b0a7d31b0fee524209c15583956ae644c982 | [
{
"content": "Adam, Benin, Chiang, Deshawn, Esther, and Fiona have internet accounts. Some, but not all, of them are internet friends with each other, and none of them has an internet friend outside this group. Each of them has the same number of internet friends. In how many different ways can this happen?"... | Adam, Benin, Chiang, Deshawn, Esther, and Fiona have internet accounts. Some, but not all, of them are internet friends with each other, and none of them has an internet friend outside this group. Each of them has the same number of internet friends. In how many different ways can this happen? | "170" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:348"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1811"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2} s(2-\\sqrt{3})"
] | [
"deepscaler"
] | 62dd7c41d68dca090b424d247b4111a5d73798341c4a8f686536a57e8cddbf3f | [
{
"content": "Inside square $ABCD$ with side $s$, quarter-circle arcs with radii $s$ and centers at $A$ and $B$ are drawn. These arcs intersect at a point $X$ inside the square. How far is $X$ from the side of $CD$?",
"role": "user"
}
] | Inside square $ABCD$ with side $s$, quarter-circle arcs with radii $s$ and centers at $A$ and $B$ are drawn. These arcs intersect at a point $X$ inside the square. How far is $X$ from the side of $CD$? | "\\frac{1}{2} s(2-\\sqrt{3})" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:349"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"31 \\text{ and } 32"
] | [
"deepscaler"
] | 61ba926e63760783020657f7f2153107bbde1f347f6af2787c320d5d1fcee90d | [
{
"content": "Point $B$ is due east of point $A$. Point $C$ is due north of point $B$. The distance between points $A$ and $C$ is $10\\sqrt 2$, and $\\angle BAC = 45^\\circ$. Point $D$ is $20$ meters due north of point $C$. The distance $AD$ is between which two integers?",
"role": "user"
}
] | Point $B$ is due east of point $A$. Point $C$ is due north of point $B$. The distance between points $A$ and $C$ is $10\sqrt 2$, and $\angle BAC = 45^\circ$. Point $D$ is $20$ meters due north of point $C$. The distance $AD$ is between which two integers? | "31 \\text{ and } 32" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:350"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"3722"
] | [
"deepscaler"
] | 5518b4a227d3c53724452b9c62ca1661b05cb2019196fc2c235b9a33eca84fa1 | [
{
"content": "Let $1$; $4$; $\\ldots$ and $9$; $16$; $\\ldots$ be two arithmetic progressions. The set $S$ is the union of the first $2004$ terms of each sequence. How many distinct numbers are in $S$?",
"role": "user"
}
] | Let $1$; $4$; $\ldots$ and $9$; $16$; $\ldots$ be two arithmetic progressions. The set $S$ is the union of the first $2004$ terms of each sequence. How many distinct numbers are in $S$? | "3722" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:351"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"16"
] | [
"deepscaler"
] | 7d8b28ec67993f2c29a720fc2132690e858e33e609dae8e832dd550e687e660e | [
{
"content": "Consider the figure consisting of a square, its diagonals, and the segments joining the midpoints of opposite sides. The total number of triangles of any size in the figure is",
"role": "user"
}
] | Consider the figure consisting of a square, its diagonals, and the segments joining the midpoints of opposite sides. The total number of triangles of any size in the figure is | "16" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:352"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"1"
] | [
"deepscaler"
] | 19e79e17fcb926c782e9bfa8dcde511fb6ffcc7bdb164a6cad57903582df8f62 | [
{
"content": "The first three terms of a geometric progression are $\\sqrt{2}, \\sqrt[3]{2}, \\sqrt[6]{2}$. Find the fourth term.",
"role": "user"
}
] | The first three terms of a geometric progression are $\sqrt{2}, \sqrt[3]{2}, \sqrt[6]{2}$. Find the fourth term. | "1" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:353"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"0.73r"
] | [
"deepscaler"
] | 6ebb59d7bdd08457f14cc7f4b0e0d67e9d200f4ed4eb2e6796cd12a87ba2f57f | [
{
"content": "The ratio of the areas of two concentric circles is $1: 3$. If the radius of the smaller is $r$, then the difference between the radii is best approximated by:",
"role": "user"
}
] | The ratio of the areas of two concentric circles is $1: 3$. If the radius of the smaller is $r$, then the difference between the radii is best approximated by: | "0.73r" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:354"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{(n-2)180}{n}"
] | [
"deepscaler"
] | c655688e04f66c3c067e1fbb15ca45223dd84806129ec4a649ede41d29d4f39e | [
{
"content": "The sides of a regular polygon of $n$ sides, $n>4$, are extended to form a star. The number of degrees at each point of the star is:",
"role": "user"
}
] | The sides of a regular polygon of $n$ sides, $n>4$, are extended to form a star. The number of degrees at each point of the star is: | "\\frac{(n-2)180}{n}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:355"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"64"
] | [
"deepscaler"
] | 044ca67118b83f07ae5bbad726e4fbbf143bc98a79a19690890e9cdc81e67b83 | [
{
"content": "Each of the $100$ students in a certain summer camp can either sing, dance, or act. Some students have more than one talent, but no student has all three talents. There are $42$ students who cannot sing, $65$ students who cannot dance, and $29$ students who cannot act. How many students have two o... | Each of the $100$ students in a certain summer camp can either sing, dance, or act. Some students have more than one talent, but no student has all three talents. There are $42$ students who cannot sing, $65$ students who cannot dance, and $29$ students who cannot act. How many students have two of these talents? | "64" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:356"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"36"
] | [
"deepscaler"
] | a6abeaf93a479496ce6bc690e2ca0bb5697f6b83f4218835656177577a40a7b6 | [
{
"content": "Three generations of the Wen family are going to the movies, two from each generation. The two members of the youngest generation receive a $50$% discount as children. The two members of the oldest generation receive a $25\\%$ discount as senior citizens. The two members of the middle generation r... | Three generations of the Wen family are going to the movies, two from each generation. The two members of the youngest generation receive a $50$% discount as children. The two members of the oldest generation receive a $25\%$ discount as senior citizens. The two members of the middle generation receive no discount. Gra... | "36" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:357"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"432"
] | [
"deepscaler"
] | d5cbe3567c25168135945897cf45493299c8bfdf0f56212ac7096546a54f5b58 | [
{
"content": "How many ways are there to paint each of the integers $2, 3, \\cdots , 9$ either red, green, or blue so that each number has a different color from each of its proper divisors?",
"role": "user"
}
] | How many ways are there to paint each of the integers $2, 3, \cdots , 9$ either red, green, or blue so that each number has a different color from each of its proper divisors? | "432" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:358"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"100"
] | [
"deepscaler"
] | 6ba693a76c577133e47a243fb1309f013c3065622706c51901088bc3ba20010c | [
{
"content": "A store normally sells windows at $100 each. This week the store is offering one free window for each purchase of four. Dave needs seven windows and Doug needs eight windows. How many dollars will they save if they purchase the windows together rather than separately?",
"role": "user"
}
] | A store normally sells windows at $100 each. This week the store is offering one free window for each purchase of four. Dave needs seven windows and Doug needs eight windows. How many dollars will they save if they purchase the windows together rather than separately? | "100" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:359"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"$x^2-2x+2$"
] | [
"deepscaler"
] | 7015beeaa4f202e56232a5ebe5c8db6f3f77258b6a5e694e1b3762bb6de775e2 | [
{
"content": "One of the factors of $x^4+4$ is:",
"role": "user"
}
] | One of the factors of $x^4+4$ is: | "$x^2-2x+2$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:360"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"deepscaler"
] | 4d2b1a790a1efa1badff4b9b5ecafff3f1b60b0375a9daca75cc5b6fb1cbf5a1 | [
{
"content": "How many ordered pairs $(m,n)$ of positive integers, with $m \\ge n$, have the property that their squares differ by $96$?",
"role": "user"
}
] | How many ordered pairs $(m,n)$ of positive integers, with $m \ge n$, have the property that their squares differ by $96$? | "4" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:361"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"40"
] | [
"deepscaler"
] | 7f6d1afd651378675b155e3d24053152ed62fb3f6d92321653a869415d6ec3af | [
{
"content": "Four students take an exam. Three of their scores are $70, 80,$ and $90$. If the average of their four scores is $70$, then what is the remaining score?",
"role": "user"
}
] | Four students take an exam. Three of their scores are $70, 80,$ and $90$. If the average of their four scores is $70$, then what is the remaining score? | "40" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:362"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"686"
] | [
"deepscaler"
] | 03b426ddd8a5f795e9c47ef90e246a6ad990ce02835fef688c483671df6be785 | [
{
"content": "The number of positive integers less than $1000$ divisible by neither $5$ nor $7$ is:",
"role": "user"
}
] | The number of positive integers less than $1000$ divisible by neither $5$ nor $7$ is: | "686" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:363"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{3}{16}"
] | [
"deepscaler"
] | 18b9c6758a8421ddbf947b6579a50610a3651440d213d5f008df77b27940aca2 | [
{
"content": "First $a$ is chosen at random from the set $\\{1,2,3,\\cdots,99,100\\}$, and then $b$ is chosen at random from the same set. The probability that the integer $3^a+7^b$ has units digit $8$ is",
"role": "user"
}
] | First $a$ is chosen at random from the set $\{1,2,3,\cdots,99,100\}$, and then $b$ is chosen at random from the same set. The probability that the integer $3^a+7^b$ has units digit $8$ is | "\\frac{3}{16}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:364"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{4}{15}"
] | [
"deepscaler"
] | eed73c11d1b21d9cd19ee71960fd363e8c5f365acacb435c5d83f0301c84c1e1 | [
{
"content": "The fraction halfway between $\\frac{1}{5}$ and $\\frac{1}{3}$ (on the number line) is",
"role": "user"
}
] | The fraction halfway between $\frac{1}{5}$ and $\frac{1}{3}$ (on the number line) is | "\\frac{4}{15}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:365"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{4}{3}"
] | [
"deepscaler"
] | 3629a39bed2752a82780fca939fbf00460f2a6cbc905b6c91f8d59858ac1ac24 | [
{
"content": "Given the equation $3x^2 - 4x + k = 0$ with real roots. The value of $k$ for which the product of the roots of the equation is a maximum is:",
"role": "user"
}
] | Given the equation $3x^2 - 4x + k = 0$ with real roots. The value of $k$ for which the product of the roots of the equation is a maximum is: | "\\frac{4}{3}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:366"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"240"
] | [
"deepscaler"
] | c1ef0a35435d78d2aca291da4efc09a8c0be28db1c926a852ecf3cba3cf4c555 | [
{
"content": "Hui is an avid reader. She bought a copy of the best seller Math is Beautiful. On the first day, Hui read $1/5$ of the pages plus $12$ more, and on the second day she read $1/4$ of the remaining pages plus $15$ pages. On the third day she read $1/3$ of the remaining pages plus $18$ pages. She then... | Hui is an avid reader. She bought a copy of the best seller Math is Beautiful. On the first day, Hui read $1/5$ of the pages plus $12$ more, and on the second day she read $1/4$ of the remaining pages plus $15$ pages. On the third day she read $1/3$ of the remaining pages plus $18$ pages. She then realized that there w... | "240" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:367"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"112"
] | [
"deepscaler"
] | fa55eeaff57087e7be10648543f950313aa5838a86ff0a9acaa540f9bcec0ebc | [
{
"content": "Let $D(n)$ denote the number of ways of writing the positive integer $n$ as a product\n\\[n = f_1\\cdot f_2\\cdots f_k,\\]where $k\\ge1$, the $f_i$ are integers strictly greater than $1$, and the order in which the factors are listed matters (that is, two representations that differ only in the or... | Let $D(n)$ denote the number of ways of writing the positive integer $n$ as a product
\[n = f_1\cdot f_2\cdots f_k,\]where $k\ge1$, the $f_i$ are integers strictly greater than $1$, and the order in which the factors are listed matters (that is, two representations that differ only in the order of the factors are count... | "112" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:368"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:971"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3120"
] | [
"deepscaler"
] | f954faa5d63e1f6c6d88470ff23667accc89461e2dd6879107588ff06706adcb | [
{
"content": "Each vertex of convex pentagon $ABCDE$ is to be assigned a color. There are $6$ colors to choose from, and the ends of each diagonal must have different colors. How many different colorings are possible?",
"role": "user"
}
] | Each vertex of convex pentagon $ABCDE$ is to be assigned a color. There are $6$ colors to choose from, and the ends of each diagonal must have different colors. How many different colorings are possible? | "3120" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:369"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2158"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"deepscaler"
] | 231bb3db0a74544a8d8aac215179f1577850ec0649a36f85f38b7d635cde5f0a | [
{
"content": "John scores 93 on this year's AHSME. Had the old scoring system still been in effect, he would score only 84 for the same answers. \nHow many questions does he leave unanswered?",
"role": "user"
}
] | John scores 93 on this year's AHSME. Had the old scoring system still been in effect, he would score only 84 for the same answers.
How many questions does he leave unanswered? | "9" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:370"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"8"
] | [
"deepscaler"
] | 3e65d268cd933d920939a5403fab2f590b60e271b730a719202b1ee28c430286 | [
{
"content": "A picture $3$ feet across is hung in the center of a wall that is $19$ feet wide. How many feet from the end of the wall is the nearest edge of the picture?",
"role": "user"
}
] | A picture $3$ feet across is hung in the center of a wall that is $19$ feet wide. How many feet from the end of the wall is the nearest edge of the picture? | "8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:371"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{7}{24}"
] | [
"deepscaler"
] | dfea32a979aaf0c0612d3792b2c2fa7dfde056e8c8de0f053ce05688bb7093b0 | [
{
"content": "On circle $O$, points $C$ and $D$ are on the same side of diameter $\\overline{AB}$, $\\angle AOC = 30^\\circ$, and $\\angle DOB = 45^\\circ$. What is the ratio of the area of the smaller sector $COD$ to the area of the circle?",
"role": "user"
}
] | On circle $O$, points $C$ and $D$ are on the same side of diameter $\overline{AB}$, $\angle AOC = 30^\circ$, and $\angle DOB = 45^\circ$. What is the ratio of the area of the smaller sector $COD$ to the area of the circle? | "\\frac{7}{24}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:373"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"deepscaler"
] | c5a47c864f7f99ec83061d4b33fb6683f8f5c9355f2f8b05b137c7561f3a948d | [
{
"content": "The base three representation of $x$ is $12112211122211112222$. The first digit (on the left) of the base nine representation of $x$ is",
"role": "user"
}
] | The base three representation of $x$ is $12112211122211112222$. The first digit (on the left) of the base nine representation of $x$ is | "5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:375"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"80"
] | [
"deepscaler"
] | fe2860aec77e17c9750f5a4832857dab292ba3697356e79f2a245ed3aedb138d | [
{
"content": "The average cost of a long-distance call in the USA in $1985$ was\n$41$ cents per minute, and the average cost of a long-distance\ncall in the USA in $2005$ was $7$ cents per minute. Find the\napproximate percent decrease in the cost per minute of a long-\ndistance call.",
"role": "user"
}
] | The average cost of a long-distance call in the USA in $1985$ was
$41$ cents per minute, and the average cost of a long-distance
call in the USA in $2005$ was $7$ cents per minute. Find the
approximate percent decrease in the cost per minute of a long-
distance call. | "80" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:376"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"441"
] | [
"deepscaler"
] | a79e77eaff1e3dbc4b963a67b28a9aad7ba3ab56c3205ccc27f84f3ee4b09067 | [
{
"content": "At a twins and triplets convention, there were $9$ sets of twins and $6$ sets of triplets, all from different families. Each twin shook hands with all the twins except his/her siblings and with half the triplets. Each triplet shook hands with all the triplets except his/her siblings and with half ... | At a twins and triplets convention, there were $9$ sets of twins and $6$ sets of triplets, all from different families. Each twin shook hands with all the twins except his/her siblings and with half the triplets. Each triplet shook hands with all the triplets except his/her siblings and with half the twins. How many ha... | "441" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:377"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"24\\sqrt{5}"
] | [
"deepscaler"
] | 3b14226936f9af55ee32a0ac8641b05e5ae84fe863814e0f5574eb8bdcccb3d2 | [
{
"content": "Let $ABCD$ be a rectangle and let $\\overline{DM}$ be a segment perpendicular to the plane of $ABCD$. Suppose that $\\overline{DM}$ has integer length, and the lengths of $\\overline{MA}, \\overline{MC},$ and $\\overline{MB}$ are consecutive odd positive integers (in this order). What is the volum... | Let $ABCD$ be a rectangle and let $\overline{DM}$ be a segment perpendicular to the plane of $ABCD$. Suppose that $\overline{DM}$ has integer length, and the lengths of $\overline{MA}, \overline{MC},$ and $\overline{MB}$ are consecutive odd positive integers (in this order). What is the volume of pyramid $MABCD?$ | "24\\sqrt{5}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:378"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"0"
] | [
"deepscaler"
] | 5d3f8bb4ddd508d8b5a84ef91e61ac9ffcec21569118a30567edaa65210b4d04 | [
{
"content": "The arithmetic mean of the nine numbers in the set $\\{9, 99, 999, 9999, \\ldots, 999999999\\}$ is a $9$-digit number $M$, all of whose digits are distinct. The number $M$ doesn't contain the digit",
"role": "user"
}
] | The arithmetic mean of the nine numbers in the set $\{9, 99, 999, 9999, \ldots, 999999999\}$ is a $9$-digit number $M$, all of whose digits are distinct. The number $M$ doesn't contain the digit | "0" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:379"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1187"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{3}"
] | [
"deepscaler"
] | c1e788ecdbeaa40c1f9a336de24334559e4008cfe10dec9642e3804db48404b3 | [
{
"content": "In the adjoining plane figure, sides $AF$ and $CD$ are parallel, as are sides $AB$ and $EF$, \nand sides $BC$ and $ED$. Each side has length $1$. Also, $\\angle FAB = \\angle BCD = 60^\\circ$. \nThe area of the figure is",
"role": "user"
}
] | In the adjoining plane figure, sides $AF$ and $CD$ are parallel, as are sides $AB$ and $EF$,
and sides $BC$ and $ED$. Each side has length $1$. Also, $\angle FAB = \angle BCD = 60^\circ$.
The area of the figure is | "\\sqrt{3}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:380"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"37"
] | [
"deepscaler"
] | 347c5f5e3e8433f8532765bf122a37b1c4431b295c7db85ff3ec74bf5682ee2c | [
{
"content": "$\\diamondsuit$ and $\\Delta$ are whole numbers and $\\diamondsuit \\times \\Delta =36$. The largest possible value of $\\diamondsuit + \\Delta$ is",
"role": "user"
}
] | $\diamondsuit$ and $\Delta$ are whole numbers and $\diamondsuit \times \Delta =36$. The largest possible value of $\diamondsuit + \Delta$ is | "37" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:381"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2003"
] | [
"deepscaler"
] | bd4363eba8e22dad780e680697d3269c9c65df5d205b49d0ba4fd1f8f3f7ee3d | [
{
"content": "What is the difference between the sum of the first $2003$ even counting numbers and the sum of the first $2003$ odd counting numbers?",
"role": "user"
}
] | What is the difference between the sum of the first $2003$ even counting numbers and the sum of the first $2003$ odd counting numbers? | "2003" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:382"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:670"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{5}{24}"
] | [
"deepscaler"
] | b8b54274aa1c3492609c4668dcef8ed06ae73cf12c4bebcebe5fcab3e828a38e | [
{
"content": "Three fair six-sided dice are rolled. What is the probability that the values shown on two of the dice sum to the value shown on the remaining die?",
"role": "user"
}
] | Three fair six-sided dice are rolled. What is the probability that the values shown on two of the dice sum to the value shown on the remaining die? | "\\frac{5}{24}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:383"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"8"
] | [
"deepscaler"
] | c132eee2097f08d50446a75c082cc7fe9a349f83d7568bf0a9211cb8f7435da5 | [
{
"content": "In the base ten number system the number $526$ means $5 \\times 10^2+2 \\times 10 + 6$. In the Land of Mathesis, however, numbers are written in the base $r$. Jones purchases an automobile there for $440$ monetary units (abbreviated m.u). He gives the salesman a $1000$ m.u bill, and receives, in c... | In the base ten number system the number $526$ means $5 \times 10^2+2 \times 10 + 6$. In the Land of Mathesis, however, numbers are written in the base $r$. Jones purchases an automobile there for $440$ monetary units (abbreviated m.u). He gives the salesman a $1000$ m.u bill, and receives, in change, $340$ m.u. The ba... | "8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:384"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"15"
] | [
"deepscaler"
] | b12df5989754520543a7184a70f34976b3850344aee63e60587bbc5402b29c32 | [
{
"content": "A large rectangle is partitioned into four rectangles by two segments parallel to its sides. The areas of three of the resulting rectangles are shown. What is the area of the fourth rectangle?",
"role": "user"
}
] | A large rectangle is partitioned into four rectangles by two segments parallel to its sides. The areas of three of the resulting rectangles are shown. What is the area of the fourth rectangle? | "15" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:385"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"88"
] | [
"deepscaler"
] | 6605f3ef8d5369f4f8ccadad283524de775094e6de02daf711a961a782909ed7 | [
{
"content": "The \"Middle School Eight\" basketball conference has $8$ teams. Every season, each team plays every other conference team twice (home and away), and each team also plays $4$ games against non-conference opponents. What is the total number of games in a season involving the \"Middle School Eight\"... | The "Middle School Eight" basketball conference has $8$ teams. Every season, each team plays every other conference team twice (home and away), and each team also plays $4$ games against non-conference opponents. What is the total number of games in a season involving the "Middle School Eight" teams? | "88" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:386"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"x(y-1)=0"
] | [
"deepscaler"
] | 706bdacc556d9e18d65d58a828f365232f29cefc04b72e49c6fb32187c60d987 | [
{
"content": "If $|x-\\log y|=x+\\log y$ where $x$ and $\\log y$ are real, then",
"role": "user"
}
] | If $|x-\log y|=x+\log y$ where $x$ and $\log y$ are real, then | "x(y-1)=0" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:387"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{n^2+3n}{4}"
] | [
"deepscaler"
] | e18b61d674ced0da80f7d85bf2397d995df98d806fbb0c471317acfb999959ca | [
{
"content": "If $x_{k+1} = x_k + \\frac{1}{2}$ for $k=1, 2, \\dots, n-1$ and $x_1=1$, find $x_1 + x_2 + \\dots + x_n$.",
"role": "user"
}
] | If $x_{k+1} = x_k + \frac{1}{2}$ for $k=1, 2, \dots, n-1$ and $x_1=1$, find $x_1 + x_2 + \dots + x_n$. | "\\frac{n^2+3n}{4}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:388"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"h"
] | [
"deepscaler"
] | 66eb18a13a05f7bb6a6aeaf138922d6fa49dbc77e34421c0d8f3e32570777ee4 | [
{
"content": "Define $x\\otimes y=x^3-y$. What is $h\\otimes (h\\otimes h)$?",
"role": "user"
}
] | Define $x\otimes y=x^3-y$. What is $h\otimes (h\otimes h)$? | "h" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:389"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:623"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"4"
] | [
"deepscaler"
] | 3cd33adf5ce3897014f440622ae24035c007f5a4376150df266aa4bf681a2476 | [
{
"content": "Laura added two three-digit positive integers. All six digits in these numbers are different. Laura's sum is a three-digit number $S$. What is the smallest possible value for the sum of the digits of $S$?",
"role": "user"
}
] | Laura added two three-digit positive integers. All six digits in these numbers are different. Laura's sum is a three-digit number $S$. What is the smallest possible value for the sum of the digits of $S$? | "4" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:391"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"$3x + y = 10$"
] | [
"deepscaler"
] | 03be216e30589b6ecc72eb83968a711f47525e2f90c6f07dbd6beb650728d839 | [
{
"content": "Indicate in which one of the following equations $y$ is neither directly nor inversely proportional to $x$:",
"role": "user"
}
] | Indicate in which one of the following equations $y$ is neither directly nor inversely proportional to $x$: | "$3x + y = 10$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:392"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"-0.25"
] | [
"deepscaler"
] | 3535c0b1719b3d830e4a266bb92257ff7e9c23f65dfc93a88c26dbc6bb9e90e5 | [
{
"content": "Suppose there is a special key on a calculator that replaces the number $x$ currently displayed with the number given by the formula $1/(1-x)$. For example, if the calculator is displaying 2 and the special key is pressed, then the calculator will display -1 since $1/(1-2)=-1$. Now suppose that th... | Suppose there is a special key on a calculator that replaces the number $x$ currently displayed with the number given by the formula $1/(1-x)$. For example, if the calculator is displaying 2 and the special key is pressed, then the calculator will display -1 since $1/(1-2)=-1$. Now suppose that the calculator is displa... | "-0.25" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:393"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{7}{9}"
] | [
"deepscaler"
] | a7a8b48308a5d5cdff9c350a84f7ba644275a01d9fad24fc408ae62b95057a2e | [
{
"content": "The two spinners shown are spun once and each lands on one of the numbered sectors. What is the probability that the sum of the numbers in the two sectors is prime?",
"role": "user"
}
] | The two spinners shown are spun once and each lands on one of the numbered sectors. What is the probability that the sum of the numbers in the two sectors is prime? | "\\frac{7}{9}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:394"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
".246"
] | [
"deepscaler"
] | 7baba35987a2bad77b93fcb865b877b0be217980cb658a36a864c8cb7de763c1 | [
{
"content": "$\\frac{2}{10}+\\frac{4}{100}+\\frac{6}{1000}=$",
"role": "user"
}
] | $\frac{2}{10}+\frac{4}{100}+\frac{6}{1000}=$ | ".246" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:395"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"1+\\sqrt{3(r^2-1)}"
] | [
"deepscaler"
] | 1da34acd29049f906da7e520f51a149c861b565af893fbe594798738b181ec85 | [
{
"content": "Circles with centers $A$, $B$, and $C$ each have radius $r$, where $1 < r < 2$. The distance between each pair of centers is $2$. If $B'$ is the point of intersection of circle $A$ and circle $C$ which is outside circle $B$, and if $C'$ is the point of intersection of circle $A$ and circle $B$ whi... | Circles with centers $A$, $B$, and $C$ each have radius $r$, where $1 < r < 2$. The distance between each pair of centers is $2$. If $B'$ is the point of intersection of circle $A$ and circle $C$ which is outside circle $B$, and if $C'$ is the point of intersection of circle $A$ and circle $B$ which is outside circle $... | "1+\\sqrt{3(r^2-1)}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:396"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"16"
] | [
"deepscaler"
] | f68b7fe52192bc4d7e661df7a01cb7150950886692472f8b016050127960c00d | [
{
"content": "For some positive integer $k$, the repeating base-$k$ representation of the (base-ten) fraction $\\frac{7}{51}$ is $0.\\overline{23}_k = 0.232323..._k$. What is $k$?",
"role": "user"
}
] | For some positive integer $k$, the repeating base-$k$ representation of the (base-ten) fraction $\frac{7}{51}$ is $0.\overline{23}_k = 0.232323..._k$. What is $k$? | "16" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:397"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1900"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"97"
] | [
"deepscaler"
] | 15ec1fa6f7a5fc306510f640aa8d74fbe47db54defdb36518a3dda4f92fd0a69 | [
{
"content": "A positive number is mistakenly divided by $6$ instead of being multiplied by $6.$ Based on the correct answer, the error thus committed, to the nearest percent, is",
"role": "user"
}
] | A positive number is mistakenly divided by $6$ instead of being multiplied by $6.$ Based on the correct answer, the error thus committed, to the nearest percent, is | "97" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:398"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"271"
] | [
"deepscaler"
] | 7c814f4e22b8a7f11c8c1c2ab863b7f85dc8076534c01941234c57f42862d84f | [
{
"content": "The domain of the function $f(x)=\\log_{\\frac{1}{2}}(\\log_4(\\log_{\\frac{1}{4}}(\\log_{16}(\\log_{\\frac{1}{16}}x))))$ is an interval of length $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?",
"role": "user"
}
] | The domain of the function $f(x)=\log_{\frac{1}{2}}(\log_4(\log_{\frac{1}{4}}(\log_{16}(\log_{\frac{1}{16}}x))))$ is an interval of length $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$? | "271" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:399"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"5"
] | [
"deepscaler"
] | 9092a8468be15e266b390f084b261e4729a36dd6fc55a92a8fd2ba534a11f229 | [
{
"content": "A rising number, such as $34689$, is a positive integer each digit of which is larger than each of the digits to its left. There are $\\binom{9}{5} = 126$ five-digit rising numbers. When these numbers are arranged from smallest to largest, the $97^{\\text{th}}$ number in the list does not contain ... | A rising number, such as $34689$, is a positive integer each digit of which is larger than each of the digits to its left. There are $\binom{9}{5} = 126$ five-digit rising numbers. When these numbers are arranged from smallest to largest, the $97^{\text{th}}$ number in the list does not contain the digit | "5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:400"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"C"
] | [
"deepscaler"
] | 366f877764532d59905068d9937c95d97dcd5487eaeab5d87ceaf22a613c35ea | [
{
"content": "What is the $1992^{\\text{nd}}$ letter in this sequence?\n\\[\\text{ABCDEDCBAABCDEDCBAABCDEDCBAABCDEDC}\\cdots\\]",
"role": "user"
}
] | What is the $1992^{\text{nd}}$ letter in this sequence?
\[\text{ABCDEDCBAABCDEDCBAABCDEDCBAABCDEDC}\cdots\] | "C" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:401"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"20"
] | [
"deepscaler"
] | a4d67a31c87b54be4de9acf44d970129a02366e9304a4979bc48e664d337acf9 | [
{
"content": "Each of the $12$ edges of a cube is labeled $0$ or $1$. Two labelings are considered different even if one can be obtained from the other by a sequence of one or more rotations and/or reflections. For how many such labelings is the sum of the labels on the edges of each of the $6$ faces of the cub... | Each of the $12$ edges of a cube is labeled $0$ or $1$. Two labelings are considered different even if one can be obtained from the other by a sequence of one or more rotations and/or reflections. For how many such labelings is the sum of the labels on the edges of each of the $6$ faces of the cube equal to $2$? | "20" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:402"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"n(\\sqrt{2} + 1)"
] | [
"deepscaler"
] | 0cfd6426bff39dedae146179470c5398640d4c947d025adfe536b0e8ed0f68a5 | [
{
"content": "The area of a circle is doubled when its radius $r$ is increased by $n$. Then $r$ equals:",
"role": "user"
}
] | The area of a circle is doubled when its radius $r$ is increased by $n$. Then $r$ equals: | "n(\\sqrt{2} + 1)" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:403"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{\\frac{2160}{\\pi}}"
] | [
"deepscaler"
] | 0be263d434aebf257b478bda2b4a3bf11644e59a431ced382821902a770d7066 | [
{
"content": "Liquid $X$ does not mix with water. Unless obstructed, it spreads out on the surface of water to form a circular film $0.1$cm thick. A rectangular box measuring $6$cm by $3$cm by $12$cm is filled with liquid $X$. Its contents are poured onto a large body of water. What will be the radius, in centi... | Liquid $X$ does not mix with water. Unless obstructed, it spreads out on the surface of water to form a circular film $0.1$cm thick. A rectangular box measuring $6$cm by $3$cm by $12$cm is filled with liquid $X$. Its contents are poured onto a large body of water. What will be the radius, in centimeters, of the resulti... | "\\sqrt{\\frac{2160}{\\pi}}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:404"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\pi}{4}"
] | [
"deepscaler"
] | e92d756c1e3736c8cb25f25d00bfbd00084842e478b2335e7d73360b31da20a4 | [
{
"content": "If $a=\\frac{1}{2}$ and $(a+1)(b+1)=2$ then the radian measure of $\\arctan a + \\arctan b$ equals",
"role": "user"
}
] | If $a=\frac{1}{2}$ and $(a+1)(b+1)=2$ then the radian measure of $\arctan a + \arctan b$ equals | "\\frac{\\pi}{4}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:405"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"22"
] | [
"deepscaler"
] | 430a27e6bce29692e12512382c52da1b9e2a88d0d020cae719beb2b40d6fb2ee | [
{
"content": "Barney Schwinn notices that the odometer on his bicycle reads $1441$, a palindrome, because it reads the same forward and backward. After riding $4$ more hours that day and $6$ the next, he notices that the odometer shows another palindrome, $1661$. What was his average speed in miles per hour?",
... | Barney Schwinn notices that the odometer on his bicycle reads $1441$, a palindrome, because it reads the same forward and backward. After riding $4$ more hours that day and $6$ the next, he notices that the odometer shows another palindrome, $1661$. What was his average speed in miles per hour? | "22" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:406"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"$2 + \\sqrt{2}$"
] | [
"deepscaler"
] | 0cd333cabd310d3c842bca8486874804a96284f1300f659a45883c3087006ca9 | [
{
"content": "A point $P$ lies in the same plane as a given square of side $1$. Let the vertices of the square, taken counterclockwise, be $A, B, C$ and $D$. Also, let the distances from $P$ to $A, B$ and $C$, respectively, be $u, v$ and $w$. What is the greatest distance that $P$ can be from $D$ if $u^2 + v^2 ... | A point $P$ lies in the same plane as a given square of side $1$. Let the vertices of the square, taken counterclockwise, be $A, B, C$ and $D$. Also, let the distances from $P$ to $A, B$ and $C$, respectively, be $u, v$ and $w$. What is the greatest distance that $P$ can be from $D$ if $u^2 + v^2 = w^2$? | "$2 + \\sqrt{2}$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:407"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2:3"
] | [
"deepscaler"
] | 874f8667624d505827fdf1cf3e9f11ee48ef6ac838be605e4b1c748c0c8ccfb4 | [
{
"content": "A painting $18$\" X $24$\" is to be placed into a wooden frame with the longer dimension vertical. The wood at the top and bottom is twice as wide as the wood on the sides. If the frame area equals that of the painting itself, the ratio of the smaller to the larger dimension of the framed painting... | A painting $18$" X $24$" is to be placed into a wooden frame with the longer dimension vertical. The wood at the top and bottom is twice as wide as the wood on the sides. If the frame area equals that of the painting itself, the ratio of the smaller to the larger dimension of the framed painting is: | "2:3" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:408"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"50^\\circ"
] | [
"deepscaler"
] | cd2313cc58980ffd163cae229474a49c86e3865851300047063db56078527905 | [
{
"content": "In triangle $ABC$, $AB=AC$ and $\\measuredangle A=80^\\circ$. If points $D, E$, and $F$ lie on sides $BC, AC$ and $AB$, respectively, and $CE=CD$ and $BF=BD$, then $\\measuredangle EDF$ equals",
"role": "user"
}
] | In triangle $ABC$, $AB=AC$ and $\measuredangle A=80^\circ$. If points $D, E$, and $F$ lie on sides $BC, AC$ and $AB$, respectively, and $CE=CD$ and $BF=BD$, then $\measuredangle EDF$ equals | "50^\\circ" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:409"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"18"
] | [
"deepscaler"
] | 740d2c887597defe0e31ec0010cf0e719b98a82baf14d916495160278d2d7535 | [
{
"content": "A set of tiles numbered 1 through 100 is modified repeatedly by the following operation: remove all tiles numbered with a perfect square, and renumber the remaining tiles consecutively starting with 1. How many times must the operation be performed to reduce the number of tiles in the set to one?"... | A set of tiles numbered 1 through 100 is modified repeatedly by the following operation: remove all tiles numbered with a perfect square, and renumber the remaining tiles consecutively starting with 1. How many times must the operation be performed to reduce the number of tiles in the set to one? | "18" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:410"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{88}{7}"
] | [
"deepscaler"
] | 70d2640ec2b48c77716906d84d922f3ab18d359d7e5469edfbc52d6462139484 | [
{
"content": "At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of $12$, $15$, and $10$ minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the average number of minute... | At an elementary school, the students in third grade, fourth grade, and fifth grade run an average of $12$, $15$, and $10$ minutes per day, respectively. There are twice as many third graders as fourth graders, and twice as many fourth graders as fifth graders. What is the average number of minutes run per day by these... | "\\frac{88}{7}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:411"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:657"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"21"
] | [
"deepscaler"
] | 64950e57b8a15a5969916665a3d35f0aefa83a10b7d38207bb06476a8a42fc06 | [
{
"content": "How many terms are in the arithmetic sequence $13$, $16$, $19$, $\\dotsc$, $70$, $73$?",
"role": "user"
}
] | How many terms are in the arithmetic sequence $13$, $16$, $19$, $\dotsc$, $70$, $73$? | "21" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:412"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"81"
] | [
"deepscaler"
] | 683de5ca4afe93fd9406f40196bcb90ee43f0a99abc805376a9c514540146fbc | [
{
"content": "Let $ABCD$ be a parallelogram with area $15$. Points $P$ and $Q$ are the projections of $A$ and $C,$ respectively, onto the line $BD;$ and points $R$ and $S$ are the projections of $B$ and $D,$ respectively, onto the line $AC.$ See the figure, which also shows the relative locations of these point... | Let $ABCD$ be a parallelogram with area $15$. Points $P$ and $Q$ are the projections of $A$ and $C,$ respectively, onto the line $BD;$ and points $R$ and $S$ are the projections of $B$ and $D,$ respectively, onto the line $AC.$ See the figure, which also shows the relative locations of these points.
Suppose $PQ=6$ and... | "81" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:413"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"24"
] | [
"deepscaler"
] | 459ea02aa212a864dfe3b56f19444e629d5e72db2c20e4a376dab2129996ab45 | [
{
"content": "Problems 8, 9 and 10 use the data found in the accompanying paragraph and figures\nFour friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.\n$\\circ$ Art's cookies are trapezoids: \n\n$\\circ$ Roger's cookies are ... | Problems 8, 9 and 10 use the data found in the accompanying paragraph and figures
Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.
$\circ$ Art's cookies are trapezoids:
$\circ$ Roger's cookies are rectangles:
$\circ$ Paul's... | "24" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:414"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"17"
] | [
"deepscaler"
] | 90a5020eb461a40eee56f41761a92768d5ff44149515c430b8d2c322aa608b47 | [
{
"content": "Joy has $30$ thin rods, one each of every integer length from $1$ cm through $30$ cm. She places the rods with lengths $3$ cm, $7$ cm, and $15$ cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaini... | Joy has $30$ thin rods, one each of every integer length from $1$ cm through $30$ cm. She places the rods with lengths $3$ cm, $7$ cm, and $15$ cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose... | "17" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:415"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"14"
] | [
"deepscaler"
] | ef8bb0742ae0de126b48263eea930020ce1ed36d2370c0174363c306d2c848bd | [
{
"content": "A regular octahedron has side length $1$. A plane parallel to two of its opposite faces cuts the octahedron into the two congruent solids. The polygon formed by the intersection of the plane and the octahedron has area $\\frac {a\\sqrt {b}}{c}$, where $a$, $b$, and $c$ are positive integers, $a$ a... | A regular octahedron has side length $1$. A plane parallel to two of its opposite faces cuts the octahedron into the two congruent solids. The polygon formed by the intersection of the plane and the octahedron has area $\frac {a\sqrt {b}}{c}$, where $a$, $b$, and $c$ are positive integers, $a$ and $c$ are relatively pr... | "14" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:416"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"24"
] | [
"deepscaler"
] | ad0e81d9dfbe415fc0ff3a70414b976cc765a84317aa56077726f6ab7db127a9 | [
{
"content": "If one side of a triangle is $12$ inches and the opposite angle is $30^{\\circ}$, then the diameter of the circumscribed circle is:",
"role": "user"
}
] | If one side of a triangle is $12$ inches and the opposite angle is $30^{\circ}$, then the diameter of the circumscribed circle is: | "24" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:417"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"7: 23 and 7: 53"
] | [
"deepscaler"
] | c4359d018a5c30fa1aaf3dacfc88bad02f26cefd0c987f34e5bdd8e401d4866b | [
{
"content": "The times between $7$ and $8$ o'clock, correct to the nearest minute, when the hands of a clock will form an angle of $84^{\\circ}$ are:",
"role": "user"
}
] | The times between $7$ and $8$ o'clock, correct to the nearest minute, when the hands of a clock will form an angle of $84^{\circ}$ are: | "7: 23 and 7: 53" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:418"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"12"
] | [
"deepscaler"
] | 58ef7c6536cec00a6c91530aa195a456c46024b7c37653e266c77eca61999149 | [
{
"content": "Let $N$ be a positive multiple of $5$. One red ball and $N$ green balls are arranged in a line in random order. Let $P(N)$ be the probability that at least $\\frac{3}{5}$ of the green balls are on the same side of the red ball. Observe that $P(5)=1$ and that $P(N)$ approaches $\\frac{4}{5}$ as $N$... | Let $N$ be a positive multiple of $5$. One red ball and $N$ green balls are arranged in a line in random order. Let $P(N)$ be the probability that at least $\frac{3}{5}$ of the green balls are on the same side of the red ball. Observe that $P(5)=1$ and that $P(N)$ approaches $\frac{4}{5}$ as $N$ grows large. What is th... | "12" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:419"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2176"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"27"
] | [
"deepscaler"
] | 37112949dfb2b092553609c2e86108affe46aa8996126d912d3fa12dfdb36bbc | [
{
"content": "Terri produces a sequence of positive integers by following three rules. She starts with a positive integer, then applies the appropriate rule to the result, and continues in this fashion. \n\nRule 1: If the integer is less than 10, multiply it by 9.\nRule 2: If the integer is even and greater t... | Terri produces a sequence of positive integers by following three rules. She starts with a positive integer, then applies the appropriate rule to the result, and continues in this fashion.
Rule 1: If the integer is less than 10, multiply it by 9.
Rule 2: If the integer is even and greater than 9, divide it by 2.
Ru... | "27" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:420"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"6"
] | [
"deepscaler"
] | 97a8a22ebfbc42042a4a94628a8d2bfcf1cffac1d1c15fbae224cf9e47c51efe | [
{
"content": "$A$ can do a piece of work in $9$ days. $B$ is $50\\%$ more efficient than $A$. The number of days it takes $B$ to do the same piece of work is:",
"role": "user"
}
] | $A$ can do a piece of work in $9$ days. $B$ is $50\%$ more efficient than $A$. The number of days it takes $B$ to do the same piece of work is: | "6" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:421"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.