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 |
|---|---|---|---|---|---|---|---|---|
[
"[\\frac{5}{12},\\frac{2}{3}]"
] | [
"deepscaler"
] | 3dd555d0234e95f35a0f176bbe2b8a87d57a7d7ac211de46c6262b8f092c86f6 | [
{
"content": "The probability that event $A$ occurs is $\\frac{3}{4}$; the probability that event B occurs is $\\frac{2}{3}$. \nLet $p$ be the probability that both $A$ and $B$ occur. The smallest interval necessarily containing $p$ is the interval",
"role": "user"
}
] | The probability that event $A$ occurs is $\frac{3}{4}$; the probability that event B occurs is $\frac{2}{3}$.
Let $p$ be the probability that both $A$ and $B$ occur. The smallest interval necessarily containing $p$ is the interval | "[\\frac{5}{12},\\frac{2}{3}]" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:422"}] | {
"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
} |
[
"R"
] | [
"deepscaler"
] | 4a3fdb9f1428c9fbb5f11f6ac10efaa5632c4e54727be53c836fa4723685dec1 | [
{
"content": "If a number $N, N \\ne 0$, diminished by four times its reciprocal, equals a given real constant $R$, then, for this given $R$, the sum of all such possible values of $N$ is",
"role": "user"
}
] | If a number $N, N \ne 0$, diminished by four times its reciprocal, equals a given real constant $R$, then, for this given $R$, the sum of all such possible values of $N$ is | "R" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:423"}] | {
"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
} |
[
"380"
] | [
"deepscaler"
] | c2d35e69face37e36c15f6c32cb4ed9fcd4b53d8a561779bd115af44c415f787 | [
{
"content": "Ahn chooses a two-digit integer, subtracts it from 200, and doubles the result. What is the largest number Ahn can get?",
"role": "user"
}
] | Ahn chooses a two-digit integer, subtracts it from 200, and doubles the result. What is the largest number Ahn can get? | "380" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:424"}] | {
"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"
] | e13ebe400c0be50166a01e403572027ed81b699a0b6decffec2f5a0fe934c91f | [
{
"content": "How many positive integers $b$ have the property that $\\log_{b} 729$ is a positive integer?",
"role": "user"
}
] | How many positive integers $b$ have the property that $\log_{b} 729$ is a positive integer? | "4" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:425"}] | {
"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
} |
[
"$3\\sqrt{3}$"
] | [
"deepscaler"
] | dbbdc11ac396331ccc45fbab9ca7b34fe0dcabc761326cf226e56d601a0579f7 | [
{
"content": "Six regular hexagons surround a regular hexagon of side length $1$ as shown. What is the area of $\\triangle{ABC}$?",
"role": "user"
}
] | Six regular hexagons surround a regular hexagon of side length $1$ as shown. What is the area of $\triangle{ABC}$? | "$3\\sqrt{3}$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:426"}] | {
"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"
] | c5b185973083c9f1df84f4e63f01737b5fe9680fd40661e9f418bb763848dc45 | [
{
"content": "Arithmetic sequences $\\left(a_n\\right)$ and $\\left(b_n\\right)$ have integer terms with $a_1=b_1=1<a_2 \\le b_2$ and $a_n b_n = 2010$ for some $n$. What is the largest possible value of $n$?",
"role": "user"
}
] | Arithmetic sequences $\left(a_n\right)$ and $\left(b_n\right)$ have integer terms with $a_1=b_1=1<a_2 \le b_2$ and $a_n b_n = 2010$ for some $n$. What is the largest possible value of $n$? | "8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:427"}] | {
"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"
] | f64a7dc0199953fe9124e24e2a5acee357758e831bcc73b93f0a84e60b21fbd5 | [
{
"content": "Al and Barb start their new jobs on the same day. Al's schedule is 3 work-days followed by 1 rest-day. Barb's schedule is 7 work-days followed by 3 rest-days. On how many of their first 1000 days do both have rest-days on the same day?",
"role": "user"
}
] | Al and Barb start their new jobs on the same day. Al's schedule is 3 work-days followed by 1 rest-day. Barb's schedule is 7 work-days followed by 3 rest-days. On how many of their first 1000 days do both have rest-days on the same day? | "100" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:428"}] | {
"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"
] | d08eb4ecc886a1155a3d18a10bda1443d94851d44c7a5db40681a52551bddf0f | [
{
"content": "The fraction\n\\[\\frac{\\left(3^{2008}\\right)^2-\\left(3^{2006}\\right)^2}{\\left(3^{2007}\\right)^2-\\left(3^{2005}\\right)^2}\\]\nsimplifies to what?",
"role": "user"
}
] | The fraction
\[\frac{\left(3^{2008}\right)^2-\left(3^{2006}\right)^2}{\left(3^{2007}\right)^2-\left(3^{2005}\right)^2}\]
simplifies to what? | "9" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:429"}] | {
"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"
] | 34691992875ee7f49a2d910aa38ad0bb8ec687ee9d183e29318bdfde04997299 | [
{
"content": "Given two equiangular polygons $P_1$ and $P_2$ with different numbers of sides; each angle of $P_1$ is $x$ degrees and each angle of $P_2$ is $kx$ degrees, where $k$ is an integer greater than $1$. The number of possibilities for the pair $(x, k)$ is:",
"role": "user"
}
] | Given two equiangular polygons $P_1$ and $P_2$ with different numbers of sides; each angle of $P_1$ is $x$ degrees and each angle of $P_2$ is $kx$ degrees, where $k$ is an integer greater than $1$. The number of possibilities for the pair $(x, k)$ is: | "1" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:430"}] | {
"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
} |
[
"35^\\circ"
] | [
"deepscaler"
] | a3775e6e6040aa2e64982785bb7eb5d5b2344e01cfff18d6c62587366798d7b7 | [
{
"content": "\\angle 1 + \\angle 2 = 180^\\circ\n\\angle 3 = \\angle 4\nFind \\angle 4.",
"role": "user"
}
] | \angle 1 + \angle 2 = 180^\circ
\angle 3 = \angle 4
Find \angle 4. | "35^\\circ" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:431"}] | {
"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
} |
[
"6"
] | [
"deepscaler"
] | c1c9328bc60dcb3133e43a31b251d218b47f1a80c06662195143540b9d2d2c42 | [
{
"content": "A can of soup can feed $3$ adults or $5$ children. If there are $5$ cans of soup and $15$ children are fed, then how many adults would the remaining soup feed?",
"role": "user"
}
] | A can of soup can feed $3$ adults or $5$ children. If there are $5$ cans of soup and $15$ children are fed, then how many adults would the remaining soup feed? | "6" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:432"}] | {
"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"
] | 51d2804cbb11144895c276241b5896203f2899b064f22ae160830a64237d75e3 | [
{
"content": "Doug and Dave shared a pizza with $8$ equally-sized slices. Doug wanted a plain pizza, but Dave wanted anchovies on half the pizza. The cost of a plain pizza was $8$ dollars, and there was an additional cost of $2$ dollars for putting anchovies on one half. Dave ate all the slices of anchovy pizza... | Doug and Dave shared a pizza with $8$ equally-sized slices. Doug wanted a plain pizza, but Dave wanted anchovies on half the pizza. The cost of a plain pizza was $8$ dollars, and there was an additional cost of $2$ dollars for putting anchovies on one half. Dave ate all the slices of anchovy pizza and one plain slice. ... | "4" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:433"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:505"}] | {
"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
} |
[
"752"
] | [
"deepscaler"
] | 80e4930805b72f921d71908a33848a1fa6e217f6d2862931e32f5d95eeaf1bfc | [
{
"content": "Functions $f$ and $g$ are quadratic, $g(x) = - f(100 - x)$, and the graph of $g$ contains the vertex of the graph of $f$. The four $x$-intercepts on the two graphs have $x$-coordinates $x_1$, $x_2$, $x_3$, and $x_4$, in increasing order, and $x_3 - x_2 = 150$. Then $x_4 - x_1 = m + n\\sqrt p$, whe... | Functions $f$ and $g$ are quadratic, $g(x) = - f(100 - x)$, and the graph of $g$ contains the vertex of the graph of $f$. The four $x$-intercepts on the two graphs have $x$-coordinates $x_1$, $x_2$, $x_3$, and $x_4$, in increasing order, and $x_3 - x_2 = 150$. Then $x_4 - x_1 = m + n\sqrt p$, where $m$, $n$, and $p$ ar... | "752" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:434"}] | {
"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
} |
[
"90"
] | [
"deepscaler"
] | b76395baa3b7037f6f0d9d1f03d437f7a12568b960024b8ce4ba28bb6218b91c | [
{
"content": "The mean, median, and mode of the $7$ data values $60, 100, x, 40, 50, 200, 90$ are all equal to $x$. What is the value of $x$?",
"role": "user"
}
] | The mean, median, and mode of the $7$ data values $60, 100, x, 40, 50, 200, 90$ are all equal to $x$. What is the value of $x$? | "90" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:435"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2593"}] | {
"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 \\frac{3}{4}"
] | [
"deepscaler"
] | ee014ced5be83fa80308ead69f98ef02632d05df45843be5ad1eea0d0d8bbaf2 | [
{
"content": "Mr. Lopez has a choice of two routes to get to work. Route A is $6$ miles long, and his average speed along this route is $30$ miles per hour. Route B is $5$ miles long, and his average speed along this route is $40$ miles per hour, except for a $\\frac{1}{2}$-mile stretch in a school zone where h... | Mr. Lopez has a choice of two routes to get to work. Route A is $6$ miles long, and his average speed along this route is $30$ miles per hour. Route B is $5$ miles long, and his average speed along this route is $40$ miles per hour, except for a $\frac{1}{2}$-mile stretch in a school zone where his average speed is $20... | "3 \\frac{3}{4}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:436"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:510"}] | {
"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
} |
[
"3195"
] | [
"deepscaler"
] | 277d5d077b9282a3c4a6a14313cf7cc5652c2913ef1266fbc1d46b0a71f984ff | [
{
"content": "A cart rolls down a hill, travelling $5$ inches the first second and accelerating so that during each successive $1$-second time interval, it travels $7$ inches more than during the previous $1$-second interval. The cart takes $30$ seconds to reach the bottom of the hill. How far, in inches, does ... | A cart rolls down a hill, travelling $5$ inches the first second and accelerating so that during each successive $1$-second time interval, it travels $7$ inches more than during the previous $1$-second interval. The cart takes $30$ seconds to reach the bottom of the hill. How far, in inches, does it travel? | "3195" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:437"}] | {
"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}{5}"
] | [
"deepscaler"
] | fc6480b9748f6dc78763d388ef021ed27682a51e590fe5ba0c3255085bcd669c | [
{
"content": "What is the value of $(2^0 - 1 + 5^2 - 0)^{-1} \\times 5?$",
"role": "user"
}
] | What is the value of $(2^0 - 1 + 5^2 - 0)^{-1} \times 5?$ | "\\frac{1}{5}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:438"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1920"}] | {
"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"
] | [
"deepscaler"
] | 3e1852bfaa6b961567a8ff844ace10a93ebfffdf773f8a95b9040656f1e23a42 | [
{
"content": "What is the value of the following expression?\n\\[ \\frac{100^2-7^2}{70^2-11^2} \\cdot \\frac{(70-11)(70+11)}{(100-7)(100+7)} \\]",
"role": "user"
}
] | What is the value of the following expression?
\[ \frac{100^2-7^2}{70^2-11^2} \cdot \frac{(70-11)(70+11)}{(100-7)(100+7)} \] | "1" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:439"}] | {
"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}{12}"
] | [
"deepscaler"
] | f7690264a342a6152ceb4a523c8dba382285ddd4d37dda08c410fb49f58fad4a | [
{
"content": "What fraction of the large $12$ by $18$ rectangular region is shaded?",
"role": "user"
}
] | What fraction of the large $12$ by $18$ rectangular region is shaded? | "\\frac{1}{12}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:440"}] | {
"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
} |
[
"89"
] | [
"deepscaler"
] | afb0813d208820b2aa463140926b2a60d64a652eea91fe6bc1507aa14d7c5dda | [
{
"content": "Ten women sit in $10$ seats in a line. All of the $10$ get up and then reseat themselves using all $10$ seats, each sitting in the seat she was in before or a seat next to the one she occupied before. In how many ways can the women be reseated?",
"role": "user"
}
] | Ten women sit in $10$ seats in a line. All of the $10$ get up and then reseat themselves using all $10$ seats, each sitting in the seat she was in before or a seat next to the one she occupied before. In how many ways can the women be reseated? | "89" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:441"}] | {
"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{10}"
] | [
"deepscaler"
] | edfbe833a064b0387e2ec2bf134dcb545ab134f731665ed180974d1cf0c7e484 | [
{
"content": "Points $A$ and $B$ are on a circle of radius $5$ and $AB = 6$. Point $C$ is the midpoint of the minor arc $AB$. What is the length of the line segment $AC$?",
"role": "user"
}
] | Points $A$ and $B$ are on a circle of radius $5$ and $AB = 6$. Point $C$ is the midpoint of the minor arc $AB$. What is the length of the line segment $AC$? | "\\sqrt{10}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:442"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:694"}] | {
"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
} |
[
"7"
] | [
"deepscaler"
] | af62a26b0d098c047ff07344305e011d9879eb6d2f8e569d369892e77b3a84bc | [
{
"content": "Bernardo and Silvia play the following game. An integer between $0$ and $999$ inclusive is selected and given to Bernardo. Whenever Bernardo receives a number, he doubles it and passes the result to Silvia. Whenever Silvia receives a number, she adds $50$ to it and passes the result to Bernardo. T... | Bernardo and Silvia play the following game. An integer between $0$ and $999$ inclusive is selected and given to Bernardo. Whenever Bernardo receives a number, he doubles it and passes the result to Silvia. Whenever Silvia receives a number, she adds $50$ to it and passes the result to Bernardo. The winner is the last ... | "7" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:444"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1377"}] | {
"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
} |
[
"180(n-4)"
] | [
"deepscaler"
] | 3be39f9e060705fdfb43110ef505b5a11fecdbbb3b408c5d44b24c54d42d5fa3 | [
{
"content": "An \"$n$-pointed star\" is formed as follows: the sides of a convex polygon are numbered consecutively $1,2,\\cdots ,k,\\cdots,n,\\text{ }n\\ge 5$; for all $n$ values of $k$, sides $k$ and $k+2$ are non-parallel, sides $n+1$ and $n+2$ being respectively identical with sides $1$ and $2$; prolong th... | An "$n$-pointed star" is formed as follows: the sides of a convex polygon are numbered consecutively $1,2,\cdots ,k,\cdots,n,\text{ }n\ge 5$; for all $n$ values of $k$, sides $k$ and $k+2$ are non-parallel, sides $n+1$ and $n+2$ being respectively identical with sides $1$ and $2$; prolong the $n$ pairs of sides numbere... | "180(n-4)" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:445"}] | {
"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{1}{5}"
] | [
"deepscaler"
] | 084736df6854e0b297251703fbfec5fa522228b3f42bfea877d854bd31f379bd | [
{
"content": "If $10^{2y} = 25$, then $10^{ - y}$ equals:",
"role": "user"
}
] | If $10^{2y} = 25$, then $10^{ - y}$ equals: | "\\frac{1}{5}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:446"}] | {
"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
} |
[
"10"
] | [
"deepscaler"
] | 712c013e058874d6b921ec8887af0fe50f94119c0d9db722341275f74d3c0c92 | [
{
"content": "Points $A = (3,9)$, $B = (1,1)$, $C = (5,3)$, and $D=(a,b)$ lie in the first quadrant and are the vertices of quadrilateral $ABCD$. The quadrilateral formed by joining the midpoints of $\\overline{AB}$, $\\overline{BC}$, $\\overline{CD}$, and $\\overline{DA}$ is a square. What is the sum of the co... | Points $A = (3,9)$, $B = (1,1)$, $C = (5,3)$, and $D=(a,b)$ lie in the first quadrant and are the vertices of quadrilateral $ABCD$. The quadrilateral formed by joining the midpoints of $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, and $\overline{DA}$ is a square. What is the sum of the coordinates of point $D$? | "10" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:447"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"170"
] | [
"deepscaler"
] | f90a00f576f57997afc771c49a020da282655e699dc9e429dc2124ebff351cb9 | [
{
"content": "As shown in the figure below, point $E$ lies on the opposite half-plane determined by line $CD$ from point $A$ so that $\\angle CDE = 110^\\circ$. Point $F$ lies on $\\overline{AD}$ so that $DE=DF$, and $ABCD$ is a square. What is the degree measure of $\\angle AFE$?",
"role": "user"
}
] | As shown in the figure below, point $E$ lies on the opposite half-plane determined by line $CD$ from point $A$ so that $\angle CDE = 110^\circ$. Point $F$ lies on $\overline{AD}$ so that $DE=DF$, and $ABCD$ is a square. What is the degree measure of $\angle AFE$? | "170" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:448"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2092"}] | {
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"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{\\sqrt{6}}{2}"
] | [
"deepscaler"
] | 5daa603246573d8191745c7ca3450cd5c9bc72b9ad34dc79b537ec9541ee1ba6 | [
{
"content": "A cube with side length $1$ is sliced by a plane that passes through two diagonally opposite vertices $A$ and $C$ and the midpoints $B$ and $D$ of two opposite edges not containing $A$ or $C$, as shown. What is the area of quadrilateral $ABCD$?",
"role": "user"
}
] | A cube with side length $1$ is sliced by a plane that passes through two diagonally opposite vertices $A$ and $C$ and the midpoints $B$ and $D$ of two opposite edges not containing $A$ or $C$, as shown. What is the area of quadrilateral $ABCD$? | "\\frac{\\sqrt{6}}{2}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:449"}] | {
"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{p}{q^2}"
] | [
"deepscaler"
] | bd76969d2f664c44565943e33f6210315a6194443a390ea40591f315501824ec | [
{
"content": "If $\\tan{\\alpha}$ and $\\tan{\\beta}$ are the roots of $x^2 - px + q = 0$, and $\\cot{\\alpha}$ and $\\cot{\\beta}$ are the roots of $x^2 - rx + s = 0$, then $rs$ is necessarily",
"role": "user"
}
] | If $\tan{\alpha}$ and $\tan{\beta}$ are the roots of $x^2 - px + q = 0$, and $\cot{\alpha}$ and $\cot{\beta}$ are the roots of $x^2 - rx + s = 0$, then $rs$ is necessarily | "\\frac{p}{q^2}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:450"}] | {
"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{3}{10}"
] | [
"deepscaler"
] | c6c22a2b150398b96b1e45c4cdbce59f3423393cad28d34bec20e1a875ee5164 | [
{
"content": "A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards are selected randomly without replacement from the box. What is the probability that 4 is the largest value selected?",
"role": "user"
}
] | A box contains five cards, numbered 1, 2, 3, 4, and 5. Three cards are selected randomly without replacement from the box. What is the probability that 4 is the largest value selected? | "\\frac{3}{10}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:451"}] | {
"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{12\\sqrt{3}-9}{13}"
] | [
"deepscaler"
] | cddb6d29db991e56d34636857e07dd5f54c8bd62b0388c09debce6088972d4eb | [
{
"content": "Given right $\\triangle ABC$ with legs $BC=3, AC=4$. Find the length of the shorter angle trisector from $C$ to the hypotenuse:",
"role": "user"
}
] | Given right $\triangle ABC$ with legs $BC=3, AC=4$. Find the length of the shorter angle trisector from $C$ to the hypotenuse: | "\\frac{12\\sqrt{3}-9}{13}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:452"}] | {
"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"
] | c9e240f5c458928bec344643a8d166285f34a80a8e0de03f6622e0c64db348a6 | [
{
"content": "How many pairs $(m,n)$ of integers satisfy the equation $m+n=mn$?",
"role": "user"
}
] | How many pairs $(m,n)$ of integers satisfy the equation $m+n=mn$? | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:453"}] | {
"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
} |
[
"21"
] | [
"deepscaler"
] | 034b0a02a30f1fccff871e2f2f4c889b66d4788ade8f5a2bf67cc5f28f3cced4 | [
{
"content": "Hexadecimal (base-16) numbers are written using numeric digits $0$ through $9$ as well as the letters $A$ through $F$ to represent $10$ through $15$. Among the first $1000$ positive integers, there are $n$ whose hexadecimal representation contains only numeric digits. What is the sum of the digits... | Hexadecimal (base-16) numbers are written using numeric digits $0$ through $9$ as well as the letters $A$ through $F$ to represent $10$ through $15$. Among the first $1000$ positive integers, there are $n$ whose hexadecimal representation contains only numeric digits. What is the sum of the digits of $n$? | "21" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:454"}] | {
"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
} |
[
"86"
] | [
"deepscaler"
] | 47442795477b010404e526ce385c0e8583636efdec878e50f5f2575091b2194c | [
{
"content": "For how many integers $N$ between $1$ and $1990$ is the improper fraction $\\frac{N^2+7}{N+4}$ not in lowest terms?",
"role": "user"
}
] | For how many integers $N$ between $1$ and $1990$ is the improper fraction $\frac{N^2+7}{N+4}$ not in lowest terms? | "86" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:455"}] | {
"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"
] | 364751b84483d9580a51be928a5da952294c4b5ce01310f4d5fbf9835605d88a | [
{
"content": "Convex quadrilateral $ABCD$ has $AB = 9$ and $CD = 12$. Diagonals $AC$ and $BD$ intersect at $E$, $AC = 14$, and $\\triangle AED$ and $\\triangle BEC$ have equal areas. What is $AE$?",
"role": "user"
}
] | Convex quadrilateral $ABCD$ has $AB = 9$ and $CD = 12$. Diagonals $AC$ and $BD$ intersect at $E$, $AC = 14$, and $\triangle AED$ and $\triangle BEC$ have equal areas. What is $AE$? | "6" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:456"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:656"}] | {
"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
} |
[
"2021"
] | [
"deepscaler"
] | 79792550198f248a67f407ab9ff6cdd6afc87730a21d65829f0e04722b55a9d6 | [
{
"content": "The expression $\\frac{2021}{2020} - \\frac{2020}{2021}$ is equal to the fraction $\\frac{p}{q}$ in which $p$ and $q$ are positive integers whose greatest common divisor is 1. What is $p?$",
"role": "user"
}
] | The expression $\frac{2021}{2020} - \frac{2020}{2021}$ is equal to the fraction $\frac{p}{q}$ in which $p$ and $q$ are positive integers whose greatest common divisor is 1. What is $p?$ | "2021" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:457"}] | {
"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{4\\pi}{3}"
] | [
"deepscaler"
] | 0e698a3441c8fc0c23ea3ab488b0b425d201f7fdb8f97fdbe5eeaea2c910652e | [
{
"content": "The radius of the first circle is $1$ inch, that of the second $\\frac{1}{2}$ inch, that of the third $\\frac{1}{4}$ inch and so on indefinitely. The sum of the areas of the circles is:",
"role": "user"
}
] | The radius of the first circle is $1$ inch, that of the second $\frac{1}{2}$ inch, that of the third $\frac{1}{4}$ inch and so on indefinitely. The sum of the areas of the circles is: | "\\frac{4\\pi}{3}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:458"}] | {
"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
} |
[
"-2014"
] | [
"deepscaler"
] | 7d9268485478f557bdc9b5c32e880972802de93ae3cd39433b80f907303ff930 | [
{
"content": "For real numbers $w$ and $z$, $\\frac{\\frac{1}{w} + \\frac{1}{z}}{\\frac{1}{w} - \\frac{1}{z}} = 2014.$ What is $\\frac{w+z}{w-z}$?",
"role": "user"
}
] | For real numbers $w$ and $z$, $\frac{\frac{1}{w} + \frac{1}{z}}{\frac{1}{w} - \frac{1}{z}} = 2014.$ What is $\frac{w+z}{w-z}$? | "-2014" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:459"}] | {
"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
} |
[
"2.8"
] | [
"deepscaler"
] | 48277d68ebf886eaf08c42469ddc38a6191da6d6e9286ed09876d6606cbe08c5 | [
{
"content": "Samia set off on her bicycle to visit her friend, traveling at an average speed of $17$ kilometers per hour. When she had gone half the distance to her friend's house, a tire went flat, and she walked the rest of the way at $5$ kilometers per hour. In all it took her $44$ minutes to reach her frie... | Samia set off on her bicycle to visit her friend, traveling at an average speed of $17$ kilometers per hour. When she had gone half the distance to her friend's house, a tire went flat, and she walked the rest of the way at $5$ kilometers per hour. In all it took her $44$ minutes to reach her friend's house. In kilomet... | "2.8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:460"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1882"}] | {
"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"
] | 9947cae34f8ca7ebe641ac9154107cc87d899dae9ae84f2908b004252a75b118 | [
{
"content": "Michael walks at the rate of $5$ feet per second on a long straight path. Trash pails are located every $200$ feet along the path. A garbage truck traveling at $10$ feet per second in the same direction as Michael stops for $30$ seconds at each pail. As Michael passes a pail, he notices the truck ... | Michael walks at the rate of $5$ feet per second on a long straight path. Trash pails are located every $200$ feet along the path. A garbage truck traveling at $10$ feet per second in the same direction as Michael stops for $30$ seconds at each pail. As Michael passes a pail, he notices the truck ahead of him just leav... | "5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:461"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2658"}] | {
"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}{256}"
] | [
"deepscaler"
] | de725a08c2a8c4491a151dc78d7d592389827ce5104f34a3fee2088c98fc062b | [
{
"content": "There are lily pads in a row numbered $0$ to $11$, in that order. There are predators on lily pads $3$ and $6$, and a morsel of food on lily pad $10$. Fiona the frog starts on pad $0$, and from any given lily pad, has a $\\frac{1}{2}$ chance to hop to the next pad, and an equal chance to jump $2$ ... | There are lily pads in a row numbered $0$ to $11$, in that order. There are predators on lily pads $3$ and $6$, and a morsel of food on lily pad $10$. Fiona the frog starts on pad $0$, and from any given lily pad, has a $\frac{1}{2}$ chance to hop to the next pad, and an equal chance to jump $2$ pads. What is the proba... | "\\frac{15}{256}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:462"}] | {
"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
} |
[
"26"
] | [
"deepscaler"
] | 832a9decde32a9e3cc7c80f0f18154bc9bfccf1b7c708c945070d4c829ed791a | [
{
"content": "A teacher tells the class,\n\n\"Think of a number, add 1 to it, and double the result. Give the answer to your partner. Partner, subtract 1 from the number you are given and double the result to get your answer.\"\n\nBen thinks of $6$, and gives his answer to Sue. What should Sue's answer be?",... | A teacher tells the class,
"Think of a number, add 1 to it, and double the result. Give the answer to your partner. Partner, subtract 1 from the number you are given and double the result to get your answer."
Ben thinks of $6$, and gives his answer to Sue. What should Sue's answer be? | "26" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:463"}] | {
"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"
] | 3b7d3c169252f361c2085a81655f7f696a6846a796397a975b364a0fc7c8c06b | [
{
"content": "Mary divides a circle into 12 sectors. The central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. What is the degree measure of the smallest possible sector angle?",
"role": "user"
}
] | Mary divides a circle into 12 sectors. The central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. What is the degree measure of the smallest possible sector angle? | "8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:464"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2445"}] | {
"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
} |
[
"110"
] | [
"deepscaler"
] | 946666cfe513e7400e8646166dfbcc0bb46c0074288a7967473ec2892f5e9830 | [
{
"content": "Qiang drives $15$ miles at an average speed of $30$ miles per hour. How many additional miles will he have to drive at $55$ miles per hour to average $50$ miles per hour for the entire trip?",
"role": "user"
}
] | Qiang drives $15$ miles at an average speed of $30$ miles per hour. How many additional miles will he have to drive at $55$ miles per hour to average $50$ miles per hour for the entire trip? | "110" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:465"}] | {
"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
} |
[
"25"
] | [
"deepscaler"
] | 4a4260eadd8d043f90392d7b4aeb16ed4ab0ed9a9ba3f65f733a79cbb531ca7a | [
{
"content": "Makarla attended two meetings during her $9$-hour work day. The first meeting took $45$ minutes and the second meeting took twice as long. What percent of her work day was spent attending meetings?",
"role": "user"
}
] | Makarla attended two meetings during her $9$-hour work day. The first meeting took $45$ minutes and the second meeting took twice as long. What percent of her work day was spent attending meetings? | "25" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:466"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1873"}] | {
"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"
] | 417eac10a944aa44bcaaf72762f902ceb7f9a0b9ceae25d4e5a403685907bbf0 | [
{
"content": "Let $f(x)=x^2+3x+2$ and let $S$ be the set of integers $\\{0, 1, 2, \\dots , 25 \\}$. \nThe number of members $s$ of $S$ such that $f(s)$ has remainder zero when divided by $6$ is:",
"role": "user"
}
] | Let $f(x)=x^2+3x+2$ and let $S$ be the set of integers $\{0, 1, 2, \dots , 25 \}$.
The number of members $s$ of $S$ such that $f(s)$ has remainder zero when divided by $6$ is: | "17" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:467"}] | {
"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"
] | 7446b43a6f4d58f3085ea1075f5ee9061f9e22025c20ea94d074f8e8916e3880 | [
{
"content": "In a tournament there are six teams that play each other twice. A team earns $3$ points for a win, $1$ point for a draw, and $0$ points for a loss. After all the games have been played it turns out that the top three teams earned the same number of total points. What is the greatest possible numbe... | In a tournament there are six teams that play each other twice. A team earns $3$ points for a win, $1$ point for a draw, and $0$ points for a loss. After all the games have been played it turns out that the top three teams earned the same number of total points. What is the greatest possible number of total points for ... | "24" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:469"}] | {
"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"
] | [
"deepscaler"
] | b7176ff33abb72042eec5b1572b010ea0d672e88fddc8810261c6fc169013793 | [
{
"content": "The sums of three whole numbers taken in pairs are 12, 17, and 19. What is the middle number?",
"role": "user"
}
] | The sums of three whole numbers taken in pairs are 12, 17, and 19. What is the middle number? | "7" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:470"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1979"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"22"
] | [
"deepscaler"
] | d4e2d3a145fbf4e0cec328a38bb6e4efddf2cf5fa5a7d7288846614d92e8a092 | [
{
"content": "Anna enjoys dinner at a restaurant in Washington, D.C., where the sales tax on meals is 10%. She leaves a 15% tip on the price of her meal before the sales tax is added, and the tax is calculated on the pre-tip amount. She spends a total of 27.50 dollars for dinner. What is the cost of her dinner ... | Anna enjoys dinner at a restaurant in Washington, D.C., where the sales tax on meals is 10%. She leaves a 15% tip on the price of her meal before the sales tax is added, and the tax is calculated on the pre-tip amount. She spends a total of 27.50 dollars for dinner. What is the cost of her dinner without tax or tip in ... | "22" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:471"}] | {
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} |
[
"75"
] | [
"deepscaler"
] | d18adb0543b8b6dd210b9f71048881bb5c763c6051b4e415435a697780dc9122 | [
{
"content": "Triangle $ABC$ with $AB=50$ and $AC=10$ has area $120$. Let $D$ be the midpoint of $\\overline{AB}$, and let $E$ be the midpoint of $\\overline{AC}$. The angle bisector of $\\angle BAC$ intersects $\\overline{DE}$ and $\\overline{BC}$ at $F$ and $G$, respectively. What is the area of quadrilateral... | Triangle $ABC$ with $AB=50$ and $AC=10$ has area $120$. Let $D$ be the midpoint of $\overline{AB}$, and let $E$ be the midpoint of $\overline{AC}$. The angle bisector of $\angle BAC$ intersects $\overline{DE}$ and $\overline{BC}$ at $F$ and $G$, respectively. What is the area of quadrilateral $FDBG$? | "75" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:472"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2779"}] | {
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"reference_components": 1,
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} |
[
"y^2 + 2y - 1"
] | [
"deepscaler"
] | 7a584a916891c0468e237a4886a6697005270e1012a68b43c26a3ed0d7599280 | [
{
"content": "If $\\frac{x}{x-1} = \\frac{y^2 + 2y - 1}{y^2 + 2y - 2},$ then $x$ equals",
"role": "user"
}
] | If $\frac{x}{x-1} = \frac{y^2 + 2y - 1}{y^2 + 2y - 2},$ then $x$ equals | "y^2 + 2y - 1" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:473"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"37"
] | [
"deepscaler"
] | 943bdb849a31285ed8162f228160f18d2b9077a482b2458b90614e347ca3364a | [
{
"content": "How many positive integer divisors of $201^9$ are perfect squares or perfect cubes (or both)?",
"role": "user"
}
] | How many positive integer divisors of $201^9$ are perfect squares or perfect cubes (or both)? | "37" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:474"}] | {
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} |
[
"665"
] | [
"deepscaler"
] | 397263cb669184ae29f2f7961e0551747cf58f38afb9accc5eecd4ec6da6d9e0 | [
{
"content": "The longest professional tennis match ever played lasted a total of $11$ hours and $5$ minutes. How many minutes was this?",
"role": "user"
}
] | The longest professional tennis match ever played lasted a total of $11$ hours and $5$ minutes. How many minutes was this? | "665" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:475"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"19"
] | [
"deepscaler"
] | 6e95a7e1035e9a85c7d94ec6c4774726655984332c51c7316f256b95dc39a231 | [
{
"content": "In base $R_1$ the expanded fraction $F_1$ becomes $.373737\\cdots$, and the expanded fraction $F_2$ becomes $.737373\\cdots$. In base $R_2$ fraction $F_1$, when expanded, becomes $.252525\\cdots$, while the fraction $F_2$ becomes $.525252\\cdots$. The sum of $R_1$ and $R_2$, each written in the ba... | In base $R_1$ the expanded fraction $F_1$ becomes $.373737\cdots$, and the expanded fraction $F_2$ becomes $.737373\cdots$. In base $R_2$ fraction $F_1$, when expanded, becomes $.252525\cdots$, while the fraction $F_2$ becomes $.525252\cdots$. The sum of $R_1$ and $R_2$, each written in the base ten, is: | "19" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:476"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"deepscaler"
] | 500038d3e52e22f62ca0b5a46d8b5dfcd6e44e8f2b623260dd08866b5d22e121 | [
{
"content": "A line segment is divided so that the lesser part is to the greater part as the greater part is to the whole. If $R$ is the ratio of the lesser part to the greater part, then the value of\n\\[R^{\\left(R^{(R^2+R^{-1})}+R^{-1}\\right)}+R^{-1}\\]is",
"role": "user"
}
] | A line segment is divided so that the lesser part is to the greater part as the greater part is to the whole. If $R$ is the ratio of the lesser part to the greater part, then the value of
\[R^{\left(R^{(R^2+R^{-1})}+R^{-1}\right)}+R^{-1}\]is | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:477"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
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} |
[
"2\\sqrt{2}+2"
] | [
"deepscaler"
] | 4f2976682b9ca65e8a38aa1efa35201205e97b9dfa8c70a8125f33b41c4d6b30 | [
{
"content": "A paint brush is swept along both diagonals of a square to produce the symmetric painted area, as shown. Half the area of the square is painted. What is the ratio of the side length of the square to the brush width?",
"role": "user"
}
] | A paint brush is swept along both diagonals of a square to produce the symmetric painted area, as shown. Half the area of the square is painted. What is the ratio of the side length of the square to the brush width? | "2\\sqrt{2}+2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:478"}] | {
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} |
[
"(E,O,E)"
] | [
"deepscaler"
] | 678cb30519c9d13cd98a020e8bdda0dd721f21f21739aca8092e9728d2feb49a | [
{
"content": "A sequence of numbers is defined by $D_0=0,D_1=0,D_2=1$ and $D_n=D_{n-1}+D_{n-3}$ for $n\\ge 3$. What are the parities (evenness or oddness) of the triple of numbers $(D_{2021},D_{2022},D_{2023})$, where $E$ denotes even and $O$ denotes odd?",
"role": "user"
}
] | A sequence of numbers is defined by $D_0=0,D_1=0,D_2=1$ and $D_n=D_{n-1}+D_{n-3}$ for $n\ge 3$. What are the parities (evenness or oddness) of the triple of numbers $(D_{2021},D_{2022},D_{2023})$, where $E$ denotes even and $O$ denotes odd? | "(E,O,E)" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:479"}] | {
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"reference_components": 1,
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} |
[
"2"
] | [
"deepscaler"
] | 5440b9f4b012f13f2f93b87a5a9135b08353b6066a8ab32bc3178fdc800c0f32 | [
{
"content": "How many ordered pairs $(a, b)$ of positive integers satisfy the equation \n\\[a \\cdot b + 63 = 20 \\cdot \\text{lcm}(a, b) + 12 \\cdot \\text{gcd}(a,b),\\] where $\\text{gcd}(a,b)$ denotes the greatest common divisor of $a$ and $b$, and $\\text{lcm}(a,b)$ denotes their least common multiple?",
... | How many ordered pairs $(a, b)$ of positive integers satisfy the equation
\[a \cdot b + 63 = 20 \cdot \text{lcm}(a, b) + 12 \cdot \text{gcd}(a,b),\] where $\text{gcd}(a,b)$ denotes the greatest common divisor of $a$ and $b$, and $\text{lcm}(a,b)$ denotes their least common multiple? | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:480"}] | {
"all_reference_components_parse": true,
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"reference_components": 1,
"reference_present": true
} |
[
"115"
] | [
"deepscaler"
] | ce81bffd21f25869fde6cfdafde69e1d67c640eda06436886f075caade23e5dd | [
{
"content": "Using the letters $A$, $M$, $O$, $S$, and $U$, we can form five-letter \"words\". If these \"words\" are arranged in alphabetical order, then the \"word\" $USAMO$ occupies position",
"role": "user"
}
] | Using the letters $A$, $M$, $O$, $S$, and $U$, we can form five-letter "words". If these "words" are arranged in alphabetical order, then the "word" $USAMO$ occupies position | "115" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:481"}] | {
"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"
] | c82fd69af0c7d7ff71cf32603c84695da6b9a4ebb358f825bb8e2a146eef7727 | [
{
"content": "The number of ounces of water needed to reduce $9$ ounces of shaving lotion containing $50$ % alcohol to a lotion containing $30$ % alcohol is:",
"role": "user"
}
] | The number of ounces of water needed to reduce $9$ ounces of shaving lotion containing $50$ % alcohol to a lotion containing $30$ % alcohol is: | "6" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:482"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"76"
] | [
"deepscaler"
] | 9c1298c431efa203c1b9b1d5fedb8b8b81aacac7bbcfa0ca73b12c24c664ccfe | [
{
"content": "Ms. Blackwell gives an exam to two classes. The mean of the scores of the students in the morning class is $84$, and the afternoon class's mean score is $70$. The ratio of the number of students in the morning class to the number of students in the afternoon class is $\\frac{3}{4}$. What is the me... | Ms. Blackwell gives an exam to two classes. The mean of the scores of the students in the morning class is $84$, and the afternoon class's mean score is $70$. The ratio of the number of students in the morning class to the number of students in the afternoon class is $\frac{3}{4}$. What is the mean of the scores of all... | "76" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:483"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2886"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"36"
] | [
"deepscaler"
] | b5544f8016b9089b39aecb90cb2d012402e8cea2a3b116bc96a74fe55adf1900 | [
{
"content": "Convex quadrilateral $ABCD$ has $AB=3$, $BC=4$, $CD=13$, $AD=12$, and $\\angle ABC=90^{\\circ}$, as shown. What is the area of the quadrilateral?",
"role": "user"
}
] | Convex quadrilateral $ABCD$ has $AB=3$, $BC=4$, $CD=13$, $AD=12$, and $\angle ABC=90^{\circ}$, as shown. What is the area of the quadrilateral? | "36" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:484"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"19"
] | [
"deepscaler"
] | 3ddc2bd617de62a954c78143ca22bf2fa52b275081c4b45a9a08453c4dc24692 | [
{
"content": "Let $A$ be the set of positive integers that have no prime factors other than $2$, $3$, or $5$. The infinite sum \\[\\frac{1}{1} + \\frac{1}{2} + \\frac{1}{3} + \\frac{1}{4} + \\frac{1}{5} + \\frac{1}{6} + \\frac{1}{8} + \\frac{1}{9} + \\frac{1}{10} + \\frac{1}{12} + \\frac{1}{15} + \\frac{1}{16} ... | Let $A$ be the set of positive integers that have no prime factors other than $2$, $3$, or $5$. The infinite sum \[\frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{8} + \frac{1}{9} + \frac{1}{10} + \frac{1}{12} + \frac{1}{15} + \frac{1}{16} + \frac{1}{18} + \frac{1}{20} + \cd... | "19" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:485"}] | {
"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{a+b}{2} \\geq \\sqrt{ab}"
] | [
"deepscaler"
] | 93b8941098b1686355a70df4ff150c51c7ddd96955778f9c0adb63c2379c9d93 | [
{
"content": "The lengths of two line segments are $a$ units and $b$ units respectively. Then the correct relation between them is:",
"role": "user"
}
] | The lengths of two line segments are $a$ units and $b$ units respectively. Then the correct relation between them is: | "\\frac{a+b}{2} \\geq \\sqrt{ab}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:486"}] | {
"all_reference_components_parse": true,
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"reference_components": 1,
"reference_present": true
} |
[
"34"
] | [
"deepscaler"
] | 4747bcf5f1c6b39c9bb7c349ba86ee9025bf4c9f0c52af1ce406fd86a09cdbba | [
{
"content": "For how many integers $n$ between $1$ and $50$, inclusive, is $\\frac{(n^2-1)!}{(n!)^n}$ an integer?",
"role": "user"
}
] | For how many integers $n$ between $1$ and $50$, inclusive, is $\frac{(n^2-1)!}{(n!)^n}$ an integer? | "34" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:487"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2420"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"120"
] | [
"deepscaler"
] | ae2e19e2dc736bc287ff0dd94b2785ec24056459669a487c5898a41331449b0a | [
{
"content": "$\\frac{(3!)!}{3!} = $",
"role": "user"
}
] | $\frac{(3!)!}{3!} = $ | "120" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:488"}] | {
"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
} |
[
"all"
] | [
"deepscaler"
] | fc05a9ce31376f28bd513f4ef8d1129aa1baa51d1d2cb2982a89e07da728deb9 | [
{
"content": "Given a set $S$ consisting of two undefined elements \"pib\" and \"maa\", and the four postulates: $P_1$: Every pib is a collection of maas, $P_2$: Any two distinct pibs have one and only one maa in common, $P_3$: Every maa belongs to two and only two pibs, $P_4$: There are exactly four pibs. Con... | Given a set $S$ consisting of two undefined elements "pib" and "maa", and the four postulates: $P_1$: Every pib is a collection of maas, $P_2$: Any two distinct pibs have one and only one maa in common, $P_3$: Every maa belongs to two and only two pibs, $P_4$: There are exactly four pibs. Consider the three theorems: ... | "all" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:489"}] | {
"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
} |
[
"45"
] | [
"deepscaler"
] | 5be85c0e6f19002289558ab2026ae40f078ec7eb9c500ce9d9000cf0ef093a84 | [
{
"content": "Each of $2010$ boxes in a line contains a single red marble, and for $1 \\le k \\le 2010$, the box in the $k\\text{th}$ position also contains $k$ white marbles. Isabella begins at the first box and successively draws a single marble at random from each box, in order. She stops when she first draw... | Each of $2010$ boxes in a line contains a single red marble, and for $1 \le k \le 2010$, the box in the $k\text{th}$ position also contains $k$ white marbles. Isabella begins at the first box and successively draws a single marble at random from each box, in order. She stops when she first draws a red marble. Let $P(n)... | "45" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:490"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1526"}] | {
"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}{91}"
] | [
"deepscaler"
] | 26df6e551ec98cd0c79759b0b2014a4a9e600bb08af83203ab0370054ba80b6f | [
{
"content": "Six points on a circle are given. Four of the chords joining pairs of the six points are selected at random. What is the probability that the four chords form a convex quadrilateral?",
"role": "user"
}
] | Six points on a circle are given. Four of the chords joining pairs of the six points are selected at random. What is the probability that the four chords form a convex quadrilateral? | "\\frac{1}{91}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:491"}] | {
"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
} |
[
"420"
] | [
"deepscaler"
] | d85e54b881409770950b0b8af9e01d5818951e02b681fe392e025f3c8191ee48 | [
{
"content": "How many distinguishable arrangements are there of $1$ brown tile, $1$ purple tile, $2$ green tiles, and $3$ yellow tiles in a row from left to right? (Tiles of the same color are indistinguishable.)",
"role": "user"
}
] | How many distinguishable arrangements are there of $1$ brown tile, $1$ purple tile, $2$ green tiles, and $3$ yellow tiles in a row from left to right? (Tiles of the same color are indistinguishable.) | "420" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:492"}] | {
"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{\\sqrt{5}-1}{2}"
] | [
"deepscaler"
] | 209f66134addfe1ac0c41eae30d537f6fcf95d05ea66cbc5e75cf5237e7db1e9 | [
{
"content": "Eight semicircles line the inside of a square with side length 2 as shown. What is the radius of the circle tangent to all of these semicircles?",
"role": "user"
}
] | Eight semicircles line the inside of a square with side length 2 as shown. What is the radius of the circle tangent to all of these semicircles? | "\\frac{\\sqrt{5}-1}{2}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:493"}] | {
"all_reference_components_parse": true,
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} |
[
"1 or 5"
] | [
"deepscaler"
] | a602c90410518f73ee924a223355ed3ebc057880268aa9df30ad09ac37aa9a52 | [
{
"content": "If $3^{2x}+9=10\\left(3^{x}\\right)$, then the value of $(x^2+1)$ is",
"role": "user"
}
] | If $3^{2x}+9=10\left(3^{x}\right)$, then the value of $(x^2+1)$ is | "1 or 5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:494"}] | {
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} |
[
".3"
] | [
"deepscaler"
] | 0b67da1a75cdce659fb272956100004c11350605b4bfb65c1b7d392bfa012f8d | [
{
"content": "$\\frac{1}{10} + \\frac{2}{20} + \\frac{3}{30} = $",
"role": "user"
}
] | $\frac{1}{10} + \frac{2}{20} + \frac{3}{30} = $ | ".3" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:495"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"\\pi + 6\\sqrt{3}"
] | [
"deepscaler"
] | 27da4e69ddccad44d34c5c98ca7c326bddc575269ef46845eedd16466aa147bd | [
{
"content": "The closed curve in the figure is made up of 9 congruent circular arcs each of length $\\frac{2\\pi}{3}$, where each of the centers of the corresponding circles is among the vertices of a regular hexagon of side 2. What is the area enclosed by the curve?",
"role": "user"
}
] | The closed curve in the figure is made up of 9 congruent circular arcs each of length $\frac{2\pi}{3}$, where each of the centers of the corresponding circles is among the vertices of a regular hexagon of side 2. What is the area enclosed by the curve? | "\\pi + 6\\sqrt{3}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:496"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1230"}] | {
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} |
[
"8"
] | [
"deepscaler"
] | fac0b67595d8b5e22efd17e41d02f0a174cce319a7dcd93870bf355612dc194d | [
{
"content": "A line passes through $A\\ (1,1)$ and $B\\ (100,1000)$. How many other points with integer coordinates are on the line and strictly between $A$ and $B$?",
"role": "user"
}
] | A line passes through $A\ (1,1)$ and $B\ (100,1000)$. How many other points with integer coordinates are on the line and strictly between $A$ and $B$? | "8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:497"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"50"
] | [
"deepscaler"
] | 9349d266269daacce6e58c1d152e72d7929339d7e99bf4088a5de5193956e449 | [
{
"content": "While exploring a cave, Carl comes across a collection of $5$-pound rocks worth $\\$14$ each, $4$-pound rocks worth $\\$11$ each, and $1$-pound rocks worth $\\$2$ each. There are at least $20$ of each size. He can carry at most $18$ pounds. What is the maximum value, in dollars, of the rocks he ca... | While exploring a cave, Carl comes across a collection of $5$-pound rocks worth $\$14$ each, $4$-pound rocks worth $\$11$ each, and $1$-pound rocks worth $\$2$ each. There are at least $20$ of each size. He can carry at most $18$ pounds. What is the maximum value, in dollars, of the rocks he can carry out of the cave? | "50" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:498"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"64"
] | [
"deepscaler"
] | 1010c02128d2001bc10c4d1789b7b0c310f02cf51356fd6e3f2dc9bbc2606929 | [
{
"content": "Each third-grade classroom at Pearl Creek Elementary has $18$ students and $2$ pet rabbits. How many more students than rabbits are there in all $4$ of the third-grade classrooms?",
"role": "user"
}
] | Each third-grade classroom at Pearl Creek Elementary has $18$ students and $2$ pet rabbits. How many more students than rabbits are there in all $4$ of the third-grade classrooms? | "64" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:499"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:663"}] | {
"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"
] | [
"deepscaler"
] | 6b2c13f83b05d0cd2d52539a3876606060c732550db0f9d6197107dab3b74b1f | [
{
"content": "For real numbers $a$ and $b$, define $a * b=(a-b)^2$. What is $(x-y)^2*(y-x)^2$?",
"role": "user"
}
] | For real numbers $a$ and $b$, define $a * b=(a-b)^2$. What is $(x-y)^2*(y-x)^2$? | "0" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:500"}] | {
"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
} |
[
"26.9"
] | [
"deepscaler"
] | ab878e2446403dfcfae4c650365a4f2bb7a05ba6f61fa688769b7ef59758fcd9 | [
{
"content": "At the beginning of a trip, the mileage odometer read $56,200$ miles. The driver filled the gas tank with $6$ gallons of gasoline. During the trip, the driver filled his tank again with $12$ gallons of gasoline when the odometer read $56,560$. At the end of the trip, the driver filled his tank aga... | At the beginning of a trip, the mileage odometer read $56,200$ miles. The driver filled the gas tank with $6$ gallons of gasoline. During the trip, the driver filled his tank again with $12$ gallons of gasoline when the odometer read $56,560$. At the end of the trip, the driver filled his tank again with $20$ gallons o... | "26.9" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:501"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"$(1993)^2$"
] | [
"deepscaler"
] | 5b8d2dd3649fd87580a22bd965d295dd157943ff6451f6e15d4e95bdfdac9bcc | [
{
"content": "$1000 \\times 1993 \\times 0.1993 \\times 10 =$",
"role": "user"
}
] | $1000 \times 1993 \times 0.1993 \times 10 =$ | "$(1993)^2$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:502"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"300"
] | [
"deepscaler"
] | e95e2cbac37ab84e77cc63972f65dfd1d22786ff7972821bdc57bd1e31c49288 | [
{
"content": "If the sum of the first $3n$ positive integers is $150$ more than the sum of the first $n$ positive integers, then the sum of the first $4n$ positive integers is",
"role": "user"
}
] | If the sum of the first $3n$ positive integers is $150$ more than the sum of the first $n$ positive integers, then the sum of the first $4n$ positive integers is | "300" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:503"}] | {
"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 \\times 8"
] | [
"deepscaler"
] | 5c616e17d1683efbe3b2d5e501f9493937e4e17138013d017a7e86339fc2c666 | [
{
"content": "A square with side length 8 is cut in half, creating two congruent rectangles. What are the dimensions of one of these rectangles?",
"role": "user"
}
] | A square with side length 8 is cut in half, creating two congruent rectangles. What are the dimensions of one of these rectangles? | "4 \\times 8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:504"}] | {
"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{1}{4}"
] | [
"deepscaler"
] | 5b071c4e70ab9dbc5201f8526bfc10d53679551da5020b59ea5087ccff4af619 | [
{
"content": "Professor Gamble buys a lottery ticket, which requires that he pick six different integers from $1$ through $46$, inclusive. He chooses his numbers so that the sum of the base-ten logarithms of his six numbers is an integer. It so happens that the integers on the winning ticket have the same prope... | Professor Gamble buys a lottery ticket, which requires that he pick six different integers from $1$ through $46$, inclusive. He chooses his numbers so that the sum of the base-ten logarithms of his six numbers is an integer. It so happens that the integers on the winning ticket have the same property— the sum of the ba... | "\\frac{1}{4}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:506"}] | {
"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
} |
[
"7"
] | [
"deepscaler"
] | 8654987a991e222ebb048274f4d03d4e303124a097a4a85890e21f79a1758c36 | [
{
"content": "The five solutions to the equation\\[(z-1)(z^2+2z+4)(z^2+4z+6)=0\\] may be written in the form $x_k+y_ki$ for $1\\le k\\le 5,$ where $x_k$ and $y_k$ are real. Let $\\mathcal E$ be the unique ellipse that passes through the points $(x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4),$ and $(x_5,y_5)$. The ecce... | The five solutions to the equation\[(z-1)(z^2+2z+4)(z^2+4z+6)=0\] may be written in the form $x_k+y_ki$ for $1\le k\le 5,$ where $x_k$ and $y_k$ are real. Let $\mathcal E$ be the unique ellipse that passes through the points $(x_1,y_1),(x_2,y_2),(x_3,y_3),(x_4,y_4),$ and $(x_5,y_5)$. The eccentricity of $\mathcal E$ ca... | "7" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:507"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac {4004}{2003}"
] | [
"deepscaler"
] | 990cd2cf7c101ac76353167101e0be8b9c0ed0fe572017f1e7b22ef3d6edb437 | [
{
"content": "Let $t_n = \\frac{n(n+1)}{2}$ be the $n$th triangular number. Find\n\\[\\frac{1}{t_1} + \\frac{1}{t_2} + \\frac{1}{t_3} + ... + \\frac{1}{t_{2002}}\\]",
"role": "user"
}
] | Let $t_n = \frac{n(n+1)}{2}$ be the $n$th triangular number. Find
\[\frac{1}{t_1} + \frac{1}{t_2} + \frac{1}{t_3} + ... + \frac{1}{t_{2002}}\] | "\\frac {4004}{2003}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:508"}] | {
"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 < p \\le 41"
] | [
"deepscaler"
] | 0977f048e50686aa70b45deb74c402edb5d948e82e1905d06693f450ffc9e14c | [
{
"content": "If $p$ is a prime and both roots of $x^2+px-444p=0$ are integers, then",
"role": "user"
}
] | If $p$ is a prime and both roots of $x^2+px-444p=0$ are integers, then | "31 < p \\le 41" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:511"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"2"
] | [
"deepscaler"
] | 089ee7fb6ddfe2da915797261d702f457f19c9c7a46aa056fab06641e849367c | [
{
"content": "What is the smallest integral value of $k$ such that\n$2x(kx-4)-x^2+6=0$ has no real roots?",
"role": "user"
}
] | What is the smallest integral value of $k$ such that
$2x(kx-4)-x^2+6=0$ has no real roots? | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:512"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"407"
] | [
"deepscaler"
] | 945fedb104c7c450fb0155135215d86bf70a2756dd4d41de323d7e39299d2501 | [
{
"content": "Given that $3^8 \\cdot 5^2 = a^b,$ where both $a$ and $b$ are positive integers, find the smallest possible value for $a+b$.",
"role": "user"
}
] | Given that $3^8 \cdot 5^2 = a^b,$ where both $a$ and $b$ are positive integers, find the smallest possible value for $a+b$. | "407" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:513"}] | {
"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"
] | [
"deepscaler"
] | 304c23a3213999acb4f0791731b6288318bf502740793b70fad7c21063788659 | [
{
"content": "If $2137^{753}$ is multiplied out, the units' digit in the final product is:",
"role": "user"
}
] | If $2137^{753}$ is multiplied out, the units' digit in the final product is: | "7" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:514"}] | {
"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"
] | [
"deepscaler"
] | 774688a0898ac1a83bcda418aa5a8a332dbfe32be0c715a43d550512d887ff34 | [
{
"content": "The acute angles of a right triangle are $a^{\\circ}$ and $b^{\\circ}$, where $a>b$ and both $a$ and $b$ are prime numbers. What is the least possible value of $b$?",
"role": "user"
}
] | The acute angles of a right triangle are $a^{\circ}$ and $b^{\circ}$, where $a>b$ and both $a$ and $b$ are prime numbers. What is the least possible value of $b$? | "7" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:515"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:627"}] | {
"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
} |
[
"70"
] | [
"deepscaler"
] | 392a4dda0a67ab2a7c778d355eb0070f4612437c5250c3f8e9ef4d6302ce5ffe | [
{
"content": "Emily sees a ship traveling at a constant speed along a straight section of a river. She walks parallel to the riverbank at a uniform rate faster than the ship. She counts $210$ equal steps walking from the back of the ship to the front. Walking in the opposite direction, she counts $42$ steps of ... | Emily sees a ship traveling at a constant speed along a straight section of a river. She walks parallel to the riverbank at a uniform rate faster than the ship. She counts $210$ equal steps walking from the back of the ship to the front. Walking in the opposite direction, she counts $42$ steps of the same size from the... | "70" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:516"}] | {
"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}{6}"
] | [
"deepscaler"
] | 41f0878bcef5096493a074181fc04ca1c54a061f1ac1d70219582797f384bed0 | [
{
"content": "If $b>1$, $x>0$, and $(2x)^{\\log_b 2}-(3x)^{\\log_b 3}=0$, then $x$ is",
"role": "user"
}
] | If $b>1$, $x>0$, and $(2x)^{\log_b 2}-(3x)^{\log_b 3}=0$, then $x$ is | "\\frac{1}{6}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:517"}] | {
"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"
] | 5e68a1fd08c99b2436adcd936a3ad2219c7c549d3357cffd1aa1f009c3bd92e9 | [
{
"content": "Medians $BD$ and $CE$ of triangle $ABC$ are perpendicular, $BD=8$, and $CE=12$. The area of triangle $ABC$ is",
"role": "user"
}
] | Medians $BD$ and $CE$ of triangle $ABC$ are perpendicular, $BD=8$, and $CE=12$. The area of triangle $ABC$ is | "64" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:518"}] | {
"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
} |
[
"117"
] | [
"deepscaler"
] | 7cf595bc68e02043a0c131bdfa509015bff2b6a677694222624985cff8a2b395 | [
{
"content": "Let $S$ be the set of all positive integer divisors of $100,000.$ How many numbers are the product of two distinct elements of $S?$",
"role": "user"
}
] | Let $S$ be the set of all positive integer divisors of $100,000.$ How many numbers are the product of two distinct elements of $S?$ | "117" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:519"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1493"}] | {
"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
} |
[
"250"
] | [
"deepscaler"
] | 194c09d178d590f515b9df8e61e3e4bca3a1d448d4f17274b354b029642276d8 | [
{
"content": "You and five friends need to raise $1500$ dollars in donations for a charity, dividing the fundraising equally. How many dollars will each of you need to raise?",
"role": "user"
}
] | You and five friends need to raise $1500$ dollars in donations for a charity, dividing the fundraising equally. How many dollars will each of you need to raise? | "250" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:520"}] | {
"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"
] | 95b46d7d4aa72d41fcc70fd0c7c13dedb1b0bf50bae14d010be22b5ff52c4ac9 | [
{
"content": "What is $\\left(20 - \\left(2010 - 201\\right)\\right) + \\left(2010 - \\left(201 - 20\\right)\\right)$?",
"role": "user"
}
] | What is $\left(20 - \left(2010 - 201\right)\right) + \left(2010 - \left(201 - 20\right)\right)$? | "40" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:521"}] | {
"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
} |
[
"34"
] | [
"deepscaler"
] | d9debbbac8d4a328d7b205cdd67dd738f543eb407f3ccb3ed4cfdd8146cf42a6 | [
{
"content": "In trapezoid $ABCD$, the sides $AB$ and $CD$ are equal. The perimeter of $ABCD$ is",
"role": "user"
}
] | In trapezoid $ABCD$, the sides $AB$ and $CD$ are equal. The perimeter of $ABCD$ is | "34" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:523"}] | {
"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, 5, 6, 7, 8}"
] | [
"deepscaler"
] | dce12e654d6911da261f4adfb55a53c1710bbfeaf9fa248922183cf7498c1f62 | [
{
"content": "A non-zero digit is chosen in such a way that the probability of choosing digit $d$ is $\\log_{10}{(d+1)}-\\log_{10}{d}$. The probability that the digit $2$ is chosen is exactly $\\frac{1}{2}$ the probability that the digit chosen is in the set",
"role": "user"
}
] | A non-zero digit is chosen in such a way that the probability of choosing digit $d$ is $\log_{10}{(d+1)}-\log_{10}{d}$. The probability that the digit $2$ is chosen is exactly $\frac{1}{2}$ the probability that the digit chosen is in the set | "{4, 5, 6, 7, 8}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:524"}] | {
"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
} |
[
"3"
] | [
"deepscaler"
] | 5728e8b336e3564c9f90a7a3756cb8476d7199273b403d8ddd4077b45d638048 | [
{
"content": "On an algebra quiz, $10\\%$ of the students scored $70$ points, $35\\%$ scored $80$ points, $30\\%$ scored $90$ points, and the rest scored $100$ points. What is the difference between the mean and median score of the students' scores on this quiz?",
"role": "user"
}
] | On an algebra quiz, $10\%$ of the students scored $70$ points, $35\%$ scored $80$ points, $30\%$ scored $90$ points, and the rest scored $100$ points. What is the difference between the mean and median score of the students' scores on this quiz? | "3" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:525"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:614"}] | {
"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}{4}"
] | [
"deepscaler"
] | fe0a4a02325cb0c76facdf3cba69d0e900f219f58535570257b250f542d8cf66 | [
{
"content": "A point is chosen at random from within a circular region. What is the probability that the point is closer to the center of the region than it is to the boundary of the region?",
"role": "user"
}
] | A point is chosen at random from within a circular region. What is the probability that the point is closer to the center of the region than it is to the boundary of the region? | "\\frac{1}{4}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:526"}] | {
"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
} |
[
"54"
] | [
"deepscaler"
] | be39f3d3b95626c198a879eae9ba3aece3e6fa5a1b6c50134798f59febfdec3a | [
{
"content": "A dress originally priced at $80$ dollars was put on sale for $25\\%$ off. If $10\\%$ tax was added to the sale price, then the total selling price (in dollars) of the dress was",
"role": "user"
}
] | A dress originally priced at $80$ dollars was put on sale for $25\%$ off. If $10\%$ tax was added to the sale price, then the total selling price (in dollars) of the dress was | "54" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:527"}] | {
"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
} |
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