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 |
|---|---|---|---|---|---|---|---|---|
[
"\\sqrt{14}"
] | [
"deepscaler"
] | f592afeb55b65a6a5c7e982a5480510f2f72104e802269c78f3706754889febb | [
{
"content": "The total area of all the faces of a rectangular solid is $22\\text{cm}^2$, and the total length of all its edges is $24\\text{cm}$. Then the length in cm of any one of its interior diagonals is",
"role": "user"
}
] | The total area of all the faces of a rectangular solid is $22\text{cm}^2$, and the total length of all its edges is $24\text{cm}$. Then the length in cm of any one of its interior diagonals is | "\\sqrt{14}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:750"}] | {
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} |
[
"12"
] | [
"deepscaler"
] | 4576eac46f9a64df73200cfc77f21028445d6e0d39ffdf0736d82c92bcea21e7 | [
{
"content": "A dealer bought $n$ radios for $d$ dollars, $d$ a positive integer. He contributed two radios to a community bazaar at half their cost. The rest he sold at a profit of $8 on each radio sold. If the overall profit was $72, then the least possible value of $n$ for the given information is:",
... | A dealer bought $n$ radios for $d$ dollars, $d$ a positive integer. He contributed two radios to a community bazaar at half their cost. The rest he sold at a profit of $8 on each radio sold. If the overall profit was $72, then the least possible value of $n$ for the given information is: | "12" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:751"}] | {
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} |
[
"24"
] | [
"deepscaler"
] | c8d3300ed2697b6586c8d0bf166b80224e096d0ca1f0fe0143e3094a221ae0af | [
{
"content": "A $\\text{palindrome}$, such as $83438$, is a number that remains the same when its digits are reversed. The numbers $x$ and $x+32$ are three-digit and four-digit palindromes, respectively. What is the sum of the digits of $x$?",
"role": "user"
}
] | A $\text{palindrome}$, such as $83438$, is a number that remains the same when its digits are reversed. The numbers $x$ and $x+32$ are three-digit and four-digit palindromes, respectively. What is the sum of the digits of $x$? | "24" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:752"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1197"}] | {
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} |
[
"B"
] | [
"deepscaler"
] | 14a5d74b62699b168597e4e1077b1123adf11e5895ebaa4588f2d5f074d0555e | [
{
"content": "Six squares are colored, front and back, (R = red, B = blue, O = orange, Y = yellow, G = green, and W = white). They are hinged together as shown, then folded to form a cube. The face opposite the white face is",
"role": "user"
}
] | Six squares are colored, front and back, (R = red, B = blue, O = orange, Y = yellow, G = green, and W = white). They are hinged together as shown, then folded to form a cube. The face opposite the white face is | "B" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:753"}] | {
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[
"8"
] | [
"deepscaler"
] | 7aa295af767c4d8866b78ef5ed45457f5e0a1fc1c7506e60b5179fec84cbb9ec | [
{
"content": "A triangular corner with side lengths $DB=EB=1$ is cut from equilateral triangle ABC of side length $3$. The perimeter of the remaining quadrilateral is",
"role": "user"
}
] | A triangular corner with side lengths $DB=EB=1$ is cut from equilateral triangle ABC of side length $3$. The perimeter of the remaining quadrilateral is | "8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:754"}] | {
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} |
[
"\\frac{1}{2}(180-A)"
] | [
"deepscaler"
] | 947b3042611a02861a4033d772ce1705ea95c509ed6d35b84fbb41cf5d6d6be3 | [
{
"content": "Let the bisectors of the exterior angles at $B$ and $C$ of triangle $ABC$ meet at $D$. Then, if all measurements are in degrees, angle $BDC$ equals:",
"role": "user"
}
] | Let the bisectors of the exterior angles at $B$ and $C$ of triangle $ABC$ meet at $D$. Then, if all measurements are in degrees, angle $BDC$ equals: | "\\frac{1}{2}(180-A)" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:755"}] | {
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} |
[
"8"
] | [
"deepscaler"
] | a26b34739f0a4b19a01d75bd9cc712bbe786233a7aeb111e4c87fc4ab402313e | [
{
"content": "All three vertices of $\\triangle ABC$ lie on the parabola defined by $y=x^2$, with $A$ at the origin and $\\overline{BC}$ parallel to the $x$-axis. The area of the triangle is $64$. What is the length of $BC$?",
"role": "user"
}
] | All three vertices of $\triangle ABC$ lie on the parabola defined by $y=x^2$, with $A$ at the origin and $\overline{BC}$ parallel to the $x$-axis. The area of the triangle is $64$. What is the length of $BC$? | "8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:756"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1551"}] | {
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} |
[
"15"
] | [
"deepscaler"
] | 93391db646d28baffef6af3099eee1aeadb3ecd6786df25126cb2fc8b478f581 | [
{
"content": "Each face of a regular tetrahedron is painted either red, white, or blue. Two colorings are considered indistinguishable if two congruent tetrahedra with those colorings can be rotated so that their appearances are identical. How many distinguishable colorings are possible?",
"role": "user"
... | Each face of a regular tetrahedron is painted either red, white, or blue. Two colorings are considered indistinguishable if two congruent tetrahedra with those colorings can be rotated so that their appearances are identical. How many distinguishable colorings are possible? | "15" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:757"}] | {
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} |
[
"132"
] | [
"deepscaler"
] | eec13f435d0b002b499b32e5aed0b58f4369bd9d8d81c2e76f66883d64187f76 | [
{
"content": "Amy, Beth, and Jo listen to four different songs and discuss which ones they like. No song is liked by all three. Furthermore, for each of the three pairs of the girls, there is at least one song liked by those two girls but disliked by the third. In how many different ways is this possible?",
... | Amy, Beth, and Jo listen to four different songs and discuss which ones they like. No song is liked by all three. Furthermore, for each of the three pairs of the girls, there is at least one song liked by those two girls but disliked by the third. In how many different ways is this possible? | "132" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:758"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2824"}] | {
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} |
[
"36"
] | [
"deepscaler"
] | 042f5a2db286b992a3bb191bc12f64ef468ac238fa88ab20ef428a8d9f5df210 | [
{
"content": "Sides $AB, BC, CD$ and $DA$ of convex polygon $ABCD$ have lengths 3, 4, 12, and 13, respectively, and $\\angle CBA$ is a right angle. The area of the quadrilateral is",
"role": "user"
}
] | Sides $AB, BC, CD$ and $DA$ of convex polygon $ABCD$ have lengths 3, 4, 12, and 13, respectively, and $\angle CBA$ is a right angle. The area of the quadrilateral is | "36" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:759"}] | {
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} |
[
"100\\left(\\frac{A-B}{B}\\right)"
] | [
"deepscaler"
] | 3b9bb0848ea12c9cafe49474fd257a52d352a60137d96a5c581e16dc9d38d2db | [
{
"content": "Suppose $A>B>0$ and A is $x$% greater than $B$. What is $x$?",
"role": "user"
}
] | Suppose $A>B>0$ and A is $x$% greater than $B$. What is $x$? | "100\\left(\\frac{A-B}{B}\\right)" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:760"}] | {
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} |
[
"32000"
] | [
"deepscaler"
] | 091e8a2eb2f9f93fd9472b6db72365053c9d6ae052481ecacd9bc17f2cb0f846 | [
{
"content": "The state income tax where Kristin lives is levied at the rate of $p\\%$ of the first $\\$28000$ of annual income plus $(p + 2)\\%$ of any amount above $\\$28000$. Kristin noticed that the state income tax she paid amounted to $(p + 0.25)\\%$ of her annual income. What was her annual income?",
... | The state income tax where Kristin lives is levied at the rate of $p\%$ of the first $\$28000$ of annual income plus $(p + 2)\%$ of any amount above $\$28000$. Kristin noticed that the state income tax she paid amounted to $(p + 0.25)\%$ of her annual income. What was her annual income? | "32000" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:761"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2555"}] | {
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} |
[
"540"
] | [
"deepscaler"
] | 013bb5cfcd91b3937e5a25a6c6adfcda356cce57e2ed41d6f1067938c70f8841 | [
{
"content": "A quadrilateral is inscribed in a circle. If an angle is inscribed into each of the four segments outside the quadrilateral, the sum of these four angles, expressed in degrees, is:",
"role": "user"
}
] | A quadrilateral is inscribed in a circle. If an angle is inscribed into each of the four segments outside the quadrilateral, the sum of these four angles, expressed in degrees, is: | "540" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:762"}] | {
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"plain_numeric_reference": true,
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} |
[
"$x=1$"
] | [
"deepscaler"
] | f6413420cfe0795fb19b22118fb8e9c6fadb39e34917d26c6ff9f5007b147a6c | [
{
"content": "The solution of $\\sqrt{5x-1}+\\sqrt{x-1}=2$ is:",
"role": "user"
}
] | The solution of $\sqrt{5x-1}+\sqrt{x-1}=2$ is: | "$x=1$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:763"}] | {
"all_reference_components_parse": true,
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} |
[
"84"
] | [
"deepscaler"
] | 64f5e884402526416805436ba7890b8f16492ac54790611d95e12c7a10330cf5 | [
{
"content": "A solid cube of side length $1$ is removed from each corner of a solid cube of side length $3$. How many edges does the remaining solid have?",
"role": "user"
}
] | A solid cube of side length $1$ is removed from each corner of a solid cube of side length $3$. How many edges does the remaining solid have? | "84" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:764"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
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} |
[
"7"
] | [
"deepscaler"
] | be908c23bb862676aae28354ea2dbe75c186b02fab53fca9c8445a2f3a46f37c | [
{
"content": "Ralph went to the store and bought 12 pairs of socks for a total of $24. Some of the socks he bought cost $1 a pair, some of the socks he bought cost $3 a pair, and some of the socks he bought cost $4 a pair. If he bought at least one pair of each type, how many pairs of $1 socks did Ralph buy?",
... | Ralph went to the store and bought 12 pairs of socks for a total of $24. Some of the socks he bought cost $1 a pair, some of the socks he bought cost $3 a pair, and some of the socks he bought cost $4 a pair. If he bought at least one pair of each type, how many pairs of $1 socks did Ralph buy? | "7" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:765"}] | {
"all_reference_components_parse": true,
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} |
[
"\\frac{1}{80}"
] | [
"deepscaler"
] | 10a3ba5dd5fbcf383fe255bad3782953b89d0599272ba3ae5b3316b0d0546ffb | [
{
"content": "Al, Bill, and Cal will each randomly be assigned a whole number from $1$ to $10$, inclusive, with no two of them getting the same number. What is the probability that Al's number will be a whole number multiple of Bill's and Bill's number will be a whole number multiple of Cal's?",
"role": "us... | Al, Bill, and Cal will each randomly be assigned a whole number from $1$ to $10$, inclusive, with no two of them getting the same number. What is the probability that Al's number will be a whole number multiple of Bill's and Bill's number will be a whole number multiple of Cal's? | "\\frac{1}{80}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:767"}] | {
"all_reference_components_parse": true,
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} |
[
"\\frac{12}{25}"
] | [
"deepscaler"
] | c1ba029bc308e308f6c24a8804d8b2ab0e09aacbacb0d1c018465ba5f4d83618 | [
{
"content": "The ratio of the length to the width of a rectangle is $4$ : $3$. If the rectangle has diagonal of length $d$, then the area may be expressed as $kd^2$ for some constant $k$. What is $k$?",
"role": "user"
}
] | The ratio of the length to the width of a rectangle is $4$ : $3$. If the rectangle has diagonal of length $d$, then the area may be expressed as $kd^2$ for some constant $k$. What is $k$? | "\\frac{12}{25}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:768"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1015"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"78"
] | [
"deepscaler"
] | 9577b54fad21cc9814efe117a52cb661636fe45254914ea36f209e8ce50d828e | [
{
"content": "The area of a pizza with radius $4$ is $N$ percent larger than the area of a pizza with radius $3$ inches. What is the integer closest to $N$?",
"role": "user"
}
] | The area of a pizza with radius $4$ is $N$ percent larger than the area of a pizza with radius $3$ inches. What is the integer closest to $N$? | "78" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:769"}] | {
"all_reference_components_parse": true,
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} |
[
"\\frac{4y}{y-6}=x"
] | [
"deepscaler"
] | b97101a5d20776216000831b27b635aea6f9666abe0e982e4e5458b3619a845c | [
{
"content": "If $x \\ne 0$ or $4$ and $y \\ne 0$ or $6$, then $\\frac{2}{x} + \\frac{3}{y} = \\frac{1}{2}$ is equivalent to",
"role": "user"
}
] | If $x \ne 0$ or $4$ and $y \ne 0$ or $6$, then $\frac{2}{x} + \frac{3}{y} = \frac{1}{2}$ is equivalent to | "\\frac{4y}{y-6}=x" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:770"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"127"
] | [
"deepscaler"
] | 1e4607d8782f0376e59b1642efcb978694bff394478c37936a5ea5f5a0e95844 | [
{
"content": "The number of solutions in positive integers of $2x+3y=763$ is:",
"role": "user"
}
] | The number of solutions in positive integers of $2x+3y=763$ is: | "127" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:771"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"11"
] | [
"deepscaler"
] | f53d792253595dca13095eb74c9943e9bbff919110e7d68bb3c0e37f94f3d7ff | [
{
"content": "Joey and Chloe and their daughter Zoe all have the same birthday. Joey is 1 year older than Chloe, and Zoe is exactly 1 year old today. Today is the first of the 9 birthdays on which Chloe's age will be an integral multiple of Zoe's age. What will be the sum of the two digits of Joey's age the nex... | Joey and Chloe and their daughter Zoe all have the same birthday. Joey is 1 year older than Chloe, and Zoe is exactly 1 year old today. Today is the first of the 9 birthdays on which Chloe's age will be an integral multiple of Zoe's age. What will be the sum of the two digits of Joey's age the next time his age is a mu... | "11" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:772"}] | {
"all_reference_components_parse": true,
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} |
[
"8"
] | [
"deepscaler"
] | 5f571e836c13fed486a8d677b5209006232e61eca7e58253b938292dfe00d5c3 | [
{
"content": "Mary is $20\\%$ older than Sally, and Sally is $40\\%$ younger than Danielle. The sum of their ages is $23.2$ years. How old will Mary be on her next birthday?",
"role": "user"
}
] | Mary is $20\%$ older than Sally, and Sally is $40\%$ younger than Danielle. The sum of their ages is $23.2$ years. How old will Mary be on her next birthday? | "8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:773"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"42"
] | [
"deepscaler"
] | 000c48eb84a2c1eb257f2e7e0184999e4f6773781241c9b273b3c442bc8b613b | [
{
"content": "Halfway through a 100-shot archery tournament, Chelsea leads by 50 points. For each shot a bullseye scores 10 points, with other possible scores being 8, 4, 2, and 0 points. Chelsea always scores at least 4 points on each shot. If Chelsea's next $n$ shots are bullseyes she will be guaranteed victo... | Halfway through a 100-shot archery tournament, Chelsea leads by 50 points. For each shot a bullseye scores 10 points, with other possible scores being 8, 4, 2, and 0 points. Chelsea always scores at least 4 points on each shot. If Chelsea's next $n$ shots are bullseyes she will be guaranteed victory. What is the minimu... | "42" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:774"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"240"
] | [
"deepscaler"
] | 0f43d6540f33c7d962fd86e2c04a8f51d7fc7964989107d7cc17c814979bc329 | [
{
"content": "Maria buys computer disks at a price of $4$ for $\\$5$ and sells them at a price of $3$ for $\\$5$. How many computer disks must she sell in order to make a profit of $\\$100$?",
"role": "user"
}
] | Maria buys computer disks at a price of $4$ for $\$5$ and sells them at a price of $3$ for $\$5$. How many computer disks must she sell in order to make a profit of $\$100$? | "240" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:775"}] | {
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} |
[
"8\\text{ months}"
] | [
"deepscaler"
] | 4898a479230ac5218535a8ac6d7272fac6dda0ac09366f997fefb4efd7a1430f | [
{
"content": "To control her blood pressure, Jill's grandmother takes one half of a pill every other day. If one supply of medicine contains $60$ pills, then the supply of medicine would last approximately",
"role": "user"
}
] | To control her blood pressure, Jill's grandmother takes one half of a pill every other day. If one supply of medicine contains $60$ pills, then the supply of medicine would last approximately | "8\\text{ months}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:776"}] | {
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"reference_components": 1,
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} |
[
"4"
] | [
"deepscaler"
] | 8fc9826f56a603a24ec68b6fa82679418a4f8cee7c711771c4422dfe155d1db3 | [
{
"content": "If the Highest Common Divisor of $6432$ and $132$ is diminished by $8$, it will equal:",
"role": "user"
}
] | If the Highest Common Divisor of $6432$ and $132$ is diminished by $8$, it will equal: | "4" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:777"}] | {
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"reference_components": 1,
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} |
[
"2"
] | [
"deepscaler"
] | 1db46ff613892bbf74ac067028c1c312e7f5d8e606ff2bd6c639968604f79359 | [
{
"content": "How many real numbers $x$ satisfy the equation $3^{2x+2}-3^{x+3}-3^x+3=0$?",
"role": "user"
}
] | How many real numbers $x$ satisfy the equation $3^{2x+2}-3^{x+3}-3^x+3=0$? | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:778"}] | {
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"reference_components": 1,
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} |
[
"6"
] | [
"deepscaler"
] | ea5bc36785ee1eaa259df43fe59a33ddfca4b27be1185afb85d961da8645646d | [
{
"content": "If $200 \\leq a \\leq 400$ and $600 \\leq b \\leq 1200$, then the largest value of the quotient $\\frac{b}{a}$ is",
"role": "user"
}
] | If $200 \leq a \leq 400$ and $600 \leq b \leq 1200$, then the largest value of the quotient $\frac{b}{a}$ is | "6" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:779"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"10"
] | [
"deepscaler"
] | 5b3250e45e7069880a0205930820dff84c21e528bee2c4b9f3f76b4cd7ce5427 | [
{
"content": "Suppose that $a * b$ means $3a-b.$ What is the value of $x$ if $2 * (5 * x)=1$",
"role": "user"
}
] | Suppose that $a * b$ means $3a-b.$ What is the value of $x$ if $2 * (5 * x)=1$ | "10" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:780"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\pi"
] | [
"deepscaler"
] | 41b6bcd598d9e9777791cbf947c989f6bc60561b5b0de34f11755a7a0a185647 | [
{
"content": "If the radius of a circle is increased by $1$ unit, the ratio of the new circumference to the new diameter is:",
"role": "user"
}
] | If the radius of a circle is increased by $1$ unit, the ratio of the new circumference to the new diameter is: | "\\pi" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:781"}] | {
"all_reference_components_parse": true,
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} |
[
"2501"
] | [
"deepscaler"
] | 825e036babe7b1212fe7d8b4121802fc366edf0bf0ef7a84e4aa0a8cfed51875 | [
{
"content": "What is the smallest positive integer $n$ such that $\\sqrt{n}-\\sqrt{n-1}<.01$?",
"role": "user"
}
] | What is the smallest positive integer $n$ such that $\sqrt{n}-\sqrt{n-1}<.01$? | "2501" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:782"}] | {
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} |
[
"\\frac{21}{13}"
] | [
"deepscaler"
] | d9d1b41b4dc40b367010656cbfc82c1a693c08fc2de0bb88a0ca0ebe516043a6 | [
{
"content": "Triangle $ABC$ is equilateral with $AB=1$. Points $E$ and $G$ are on $\\overline{AC}$ and points $D$ and $F$ are on $\\overline{AB}$ such that both $\\overline{DE}$ and $\\overline{FG}$ are parallel to $\\overline{BC}$. Furthermore, triangle $ADE$ and trapezoids $DFGE$ and $FBCG$ all have the same... | Triangle $ABC$ is equilateral with $AB=1$. Points $E$ and $G$ are on $\overline{AC}$ and points $D$ and $F$ are on $\overline{AB}$ such that both $\overline{DE}$ and $\overline{FG}$ are parallel to $\overline{BC}$. Furthermore, triangle $ADE$ and trapezoids $DFGE$ and $FBCG$ all have the same perimeter. What is $DE+FG$... | "\\frac{21}{13}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:784"}] | {
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} |
[
"3"
] | [
"deepscaler"
] | 113b94d22f1838bdaf687786a91c682830c37962d0e9630f892cf9ddae24e120 | [
{
"content": "Let $P$ be the product of any three consecutive positive odd integers. The largest integer dividing all such $P$ is:",
"role": "user"
}
] | Let $P$ be the product of any three consecutive positive odd integers. The largest integer dividing all such $P$ is: | "3" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:785"}] | {
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} |
[
"74"
] | [
"deepscaler"
] | 093b1798a367899f9f59b80e29b511d966c4dee172f458ada2e7ee1ee9043bd2 | [
{
"content": "Let $M$ be the least common multiple of all the integers $10$ through $30,$ inclusive. Let $N$ be the least common multiple of $M,32,33,34,35,36,37,38,39,$ and $40.$ What is the value of $\\frac{N}{M}$?",
"role": "user"
}
] | Let $M$ be the least common multiple of all the integers $10$ through $30,$ inclusive. Let $N$ be the least common multiple of $M,32,33,34,35,36,37,38,39,$ and $40.$ What is the value of $\frac{N}{M}$? | "74" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:787"}] | {
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} |
[
"\\sqrt[3]{2}"
] | [
"deepscaler"
] | 69ae6dd48eb1be5492213a0889cb780cc61e791cb3b29c791d881bebb510a069 | [
{
"content": "In $\\triangle ABC$, $D$ is on $AC$ and $F$ is on $BC$. Also, $AB \\perp AC$, $AF \\perp BC$, and $BD=DC=FC=1$. Find $AC$.",
"role": "user"
}
] | In $\triangle ABC$, $D$ is on $AC$ and $F$ is on $BC$. Also, $AB \perp AC$, $AF \perp BC$, and $BD=DC=FC=1$. Find $AC$. | "\\sqrt[3]{2}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:788"}] | {
"all_reference_components_parse": true,
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} |
[
"337"
] | [
"deepscaler"
] | 28c98862289f662512ccdc5daa4fee840d95bc8cc1d8e9dcd25372887bce4263 | [
{
"content": "When $n$ standard 6-sided dice are rolled, the probability of obtaining a sum of 1994 is greater than zero and is the same as the probability of obtaining a sum of $S$. The smallest possible value of $S$ is",
"role": "user"
}
] | When $n$ standard 6-sided dice are rolled, the probability of obtaining a sum of 1994 is greater than zero and is the same as the probability of obtaining a sum of $S$. The smallest possible value of $S$ is | "337" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:789"}] | {
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"reference_components": 1,
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} |
[
"7"
] | [
"deepscaler"
] | 3138304be798d9b533413d9c0c137f55bb512970f0c2edf2a1083366189844ee | [
{
"content": "In a mathematics contest with ten problems, a student gains 5 points for a correct answer and loses 2 points for an incorrect answer. If Olivia answered every problem and her score was 29, how many correct answers did she have?",
"role": "user"
}
] | In a mathematics contest with ten problems, a student gains 5 points for a correct answer and loses 2 points for an incorrect answer. If Olivia answered every problem and her score was 29, how many correct answers did she have? | "7" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:790"}] | {
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} |
[
"15"
] | [
"deepscaler"
] | 7613adeb55627e77aba0959a1c3a2b1fd6fa15f834286137621c140355bfc060 | [
{
"content": "A parabolic arch has a height of $16$ inches and a span of $40$ inches. The height, in inches, of the arch at the point $5$ inches from the center $M$ is:",
"role": "user"
}
] | A parabolic arch has a height of $16$ inches and a span of $40$ inches. The height, in inches, of the arch at the point $5$ inches from the center $M$ is: | "15" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:791"}] | {
"all_reference_components_parse": true,
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} |
[
"0"
] | [
"deepscaler"
] | 94e41f60078ec06ba7d600de05bb382d72ea154bd93638cea1c0d43d9852b36c | [
{
"content": "The value of $x$ at the intersection of $y=\\frac{8}{x^2+4}$ and $x+y=2$ is:",
"role": "user"
}
] | The value of $x$ at the intersection of $y=\frac{8}{x^2+4}$ and $x+y=2$ is: | "0" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:792"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"5"
] | [
"deepscaler"
] | 64873f029f31c306eaf28cb1ea27357a209eb92b016291f776bf3039083a43df | [
{
"content": "On a sheet of paper, Isabella draws a circle of radius $2$, a circle of radius $3$, and all possible lines simultaneously tangent to both circles. Isabella notices that she has drawn exactly $k \\ge 0$ lines. How many different values of $k$ are possible?",
"role": "user"
}
] | On a sheet of paper, Isabella draws a circle of radius $2$, a circle of radius $3$, and all possible lines simultaneously tangent to both circles. Isabella notices that she has drawn exactly $k \ge 0$ lines. How many different values of $k$ are possible? | "5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:793"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"0"
] | [
"deepscaler"
] | e759ca3cd67a2d1ef0a296a98b20ba73104d6b1a0d5fe57cad00a3c5dc1665af | [
{
"content": "If two factors of $2x^3-hx+k$ are $x+2$ and $x-1$, the value of $|2h-3k|$ is",
"role": "user"
}
] | If two factors of $2x^3-hx+k$ are $x+2$ and $x-1$, the value of $|2h-3k|$ is | "0" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:794"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
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} |
[
"\\frac{b^2}{f}"
] | [
"deepscaler"
] | f410bb4ad302c94a5271b5ec9c1eb5113566ea42ee2266e6c3364eda1105ec0f | [
{
"content": "If $b$ men take $c$ days to lay $f$ bricks, then the number of days it will take $c$ men working at the same rate to lay $b$ bricks, is",
"role": "user"
}
] | If $b$ men take $c$ days to lay $f$ bricks, then the number of days it will take $c$ men working at the same rate to lay $b$ bricks, is | "\\frac{b^2}{f}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:795"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"54"
] | [
"deepscaler"
] | a8437d177290a81cdc9c11095bb92e0dd798fdd2e1712d7bfc5e0354b8f27a62 | [
{
"content": "Gilda has a bag of marbles. She gives $20\\%$ of them to her friend Pedro. Then Gilda gives $10\\%$ of what is left to another friend, Ebony. Finally, Gilda gives $25\\%$ of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for he... | Gilda has a bag of marbles. She gives $20\%$ of them to her friend Pedro. Then Gilda gives $10\%$ of what is left to another friend, Ebony. Finally, Gilda gives $25\%$ of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself? | "54" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:796"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"60"
] | [
"deepscaler"
] | dddbbbf9847dda609489154614f0fe0a18aa5ba0e302d3953fb68dc3b6dce5e4 | [
{
"content": "Grandma has just finished baking a large rectangular pan of brownies. She is planning to make rectangular pieces of equal size and shape, with straight cuts parallel to the sides of the pan. Each cut must be made entirely across the pan. Grandma wants to make the same number of interior pieces as ... | Grandma has just finished baking a large rectangular pan of brownies. She is planning to make rectangular pieces of equal size and shape, with straight cuts parallel to the sides of the pan. Each cut must be made entirely across the pan. Grandma wants to make the same number of interior pieces as pieces along the perim... | "60" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:797"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"32"
] | [
"deepscaler"
] | f68fcad4811d07fc36d90c90ef036e4aa21b3d0a41c01fa1200a36a11563273d | [
{
"content": "Three congruent circles with centers $P$, $Q$, and $R$ are tangent to the sides of rectangle $ABCD$ as shown. The circle centered at $Q$ has diameter $4$ and passes through points $P$ and $R$. The area of the rectangle is",
"role": "user"
}
] | Three congruent circles with centers $P$, $Q$, and $R$ are tangent to the sides of rectangle $ABCD$ as shown. The circle centered at $Q$ has diameter $4$ and passes through points $P$ and $R$. The area of the rectangle is | "32" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:798"}] | {
"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"
] | a7a139c855028afdccc1f0fdecbea5588f1f48564fd7a0d831a5f214cc26ae7b | [
{
"content": "A group of children riding on bicycles and tricycles rode past Billy Bob's house. Billy Bob counted $7$ children and $19$ wheels. How many tricycles were there?",
"role": "user"
}
] | A group of children riding on bicycles and tricycles rode past Billy Bob's house. Billy Bob counted $7$ children and $19$ wheels. How many tricycles were there? | "5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:799"}] | {
"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"
] | 6f4da96ed8ad18c8e7bca2e034ee90cca95a4e33eeb176e2138f586ad9ab8932 | [
{
"content": "A store prices an item in dollars and cents so that when 4% sales tax is added, no rounding is necessary because the result is exactly $n$ dollars where $n$ is a positive integer. The smallest value of $n$ is",
"role": "user"
}
] | A store prices an item in dollars and cents so that when 4% sales tax is added, no rounding is necessary because the result is exactly $n$ dollars where $n$ is a positive integer. The smallest value of $n$ is | "13" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:800"}] | {
"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"
] | afc75fcb2395a74a1ad3748bb90fbca18cc7362ffbef88bacca6fc96b18a9075 | [
{
"content": "Some boys and girls are having a car wash to raise money for a class trip to China. Initially $40\\%$ of the group are girls. Shortly thereafter two girls leave and two boys arrive, and then $30\\%$ of the group are girls. How many girls were initially in the group?",
"role": "user"
}
] | Some boys and girls are having a car wash to raise money for a class trip to China. Initially $40\%$ of the group are girls. Shortly thereafter two girls leave and two boys arrive, and then $30\%$ of the group are girls. How many girls were initially in the group? | "8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:801"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1496"}] | {
"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{10}{3}"
] | [
"deepscaler"
] | 5fbb55d595a7657c4a09b041853709d5668fcce75db00bae1e199e9ab14dccba | [
{
"content": "Let $a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5$. What is $a + b + c + d$?",
"role": "user"
}
] | Let $a + 1 = b + 2 = c + 3 = d + 4 = a + b + c + d + 5$. What is $a + b + c + d$? | "-\\frac{10}{3}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:802"}] | {
"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{8}{15}"
] | [
"deepscaler"
] | beb6f9bfc559b400e1c70fdf2409de21bea1cd25ca9188c6802226032a8782cb | [
{
"content": "A fair standard six-sided dice is tossed three times. Given that the sum of the first two tosses equal the third, what is the probability that at least one \"2\" is tossed?",
"role": "user"
}
] | A fair standard six-sided dice is tossed three times. Given that the sum of the first two tosses equal the third, what is the probability that at least one "2" is tossed? | "\\frac{8}{15}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:803"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"28.00"
] | [
"deepscaler"
] | 87baf211d1d3aac620783a385946036e8ecfff866ecbcbb829e032de510f1c56 | [
{
"content": "A cell phone plan costs $20$ dollars each month, plus $5$ cents per text message sent, plus $10$ cents for each minute used over $30$ hours. In January Michelle sent $100$ text messages and talked for $30.5$ hours. How much did she have to pay?",
"role": "user"
}
] | A cell phone plan costs $20$ dollars each month, plus $5$ cents per text message sent, plus $10$ cents for each minute used over $30$ hours. In January Michelle sent $100$ text messages and talked for $30.5$ hours. How much did she have to pay? | "28.00" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:804"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2242"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"9"
] | [
"deepscaler"
] | 18c1ec2235ad2a9a0cb4c4929ae5f5dc9ffc04418939d38868f577f73df2ec52 | [
{
"content": "The sides $PQ$ and $PR$ of triangle $PQR$ are respectively of lengths $4$ inches, and $7$ inches. The median $PM$ is $3\\frac{1}{2}$ inches. Then $QR$, in inches, is:",
"role": "user"
}
] | The sides $PQ$ and $PR$ of triangle $PQR$ are respectively of lengths $4$ inches, and $7$ inches. The median $PM$ is $3\frac{1}{2}$ inches. Then $QR$, in inches, is: | "9" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:805"}] | {
"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
} |
[
"30"
] | [
"deepscaler"
] | 4113d68d6913b314183ebd4a2991951dc83eca5e9b7d2e8f91a84ddeca4dc7d1 | [
{
"content": "The mean of three numbers is $10$ more than the least of the numbers and $15$ less than the greatest. The median of the three numbers is $5$. What is their sum?",
"role": "user"
}
] | The mean of three numbers is $10$ more than the least of the numbers and $15$ less than the greatest. The median of the three numbers is $5$. What is their sum? | "30" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:806"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2708"}] | {
"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"
] | 744ca57b364a387b52e6a253eba31a005486588c8c75bf2b59c2599ed3565afd | [
{
"content": "The $y$-intercepts, $P$ and $Q$, of two perpendicular lines intersecting at the point $A(6,8)$ have a sum of zero. What is the area of $\\triangle APQ$?",
"role": "user"
}
] | The $y$-intercepts, $P$ and $Q$, of two perpendicular lines intersecting at the point $A(6,8)$ have a sum of zero. What is the area of $\triangle APQ$? | "60" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:807"}] | {
"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
} |
[
"512"
] | [
"deepscaler"
] | 5ae54308f5ad532d276df456eaed84d94618ef51381db35008b4acb919b0c659 | [
{
"content": "Let ($a_1$, $a_2$, ... $a_{10}$) be a list of the first 10 positive integers such that for each $2 \\le i \\le 10$ either $a_i + 1$ or $a_i - 1$ or both appear somewhere before $a_i$ in the list. How many such lists are there?",
"role": "user"
}
] | Let ($a_1$, $a_2$, ... $a_{10}$) be a list of the first 10 positive integers such that for each $2 \le i \le 10$ either $a_i + 1$ or $a_i - 1$ or both appear somewhere before $a_i$ in the list. How many such lists are there? | "512" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:808"}] | {
"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
} |
[
"18"
] | [
"deepscaler"
] | bd1b01d8afe49739c0ee8b59e6b5ac1d2eec5037dfe91fab775eee3c81a42c56 | [
{
"content": "Side $\\overline{AB}$ of $\\triangle ABC$ has length $10$. The bisector of angle $A$ meets $\\overline{BC}$ at $D$, and $CD = 3$. The set of all possible values of $AC$ is an open interval $(m,n)$. What is $m+n$?",
"role": "user"
}
] | Side $\overline{AB}$ of $\triangle ABC$ has length $10$. The bisector of angle $A$ meets $\overline{BC}$ at $D$, and $CD = 3$. The set of all possible values of $AC$ is an open interval $(m,n)$. What is $m+n$? | "18" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:809"}] | {
"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
} |
[
"41\\%"
] | [
"deepscaler"
] | b95da7ac7fa4bda6223675c111b8f97f52e3ff2685ac5132252648ebddf574c8 | [
{
"content": "Walter has exactly one penny, one nickel, one dime and one quarter in his pocket. What percent of one dollar is in his pocket?",
"role": "user"
}
] | Walter has exactly one penny, one nickel, one dime and one quarter in his pocket. What percent of one dollar is in his pocket? | "41\\%" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:810"}] | {
"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{7}{72}"
] | [
"deepscaler"
] | 45012589d0d9430095f0b237fce10ae03f6587d2013f248430b709b1ef3cba7c | [
{
"content": "Four fair six-sided dice are rolled. What is the probability that at least three of the four dice show the same value?",
"role": "user"
}
] | Four fair six-sided dice are rolled. What is the probability that at least three of the four dice show the same value? | "\\frac{7}{72}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:811"}] | {
"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"
] | f55388538371fb8acd2c1c585805ff21bbb7552d4e9bc065c0c2623df653d48a | [
{
"content": "Joe has a collection of $23$ coins, consisting of $5$-cent coins, $10$-cent coins, and $25$-cent coins. He has $3$ more $10$-cent coins than $5$-cent coins, and the total value of his collection is $320$ cents. How many more $25$-cent coins does Joe have than $5$-cent coins?",
"role": "user"
... | Joe has a collection of $23$ coins, consisting of $5$-cent coins, $10$-cent coins, and $25$-cent coins. He has $3$ more $10$-cent coins than $5$-cent coins, and the total value of his collection is $320$ cents. How many more $25$-cent coins does Joe have than $5$-cent coins? | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:812"}] | {
"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
} |
[
"66"
] | [
"deepscaler"
] | e177548855199e89a3e9ef42aced678bde36273865287649b851677f5ee61760 | [
{
"content": "In the expansion of $(a + b)^n$ there are $n + 1$ dissimilar terms. The number of dissimilar terms in the expansion of $(a + b + c)^{10}$ is:",
"role": "user"
}
] | In the expansion of $(a + b)^n$ there are $n + 1$ dissimilar terms. The number of dissimilar terms in the expansion of $(a + b + c)^{10}$ is: | "66" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:813"}] | {
"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
} |
[
"$3\\sqrt{2}$"
] | [
"deepscaler"
] | 4cba34f24d2c85704c57dfadfa949324d53f1716c18f21105138ee18e110379f | [
{
"content": "The circular base of a hemisphere of radius $2$ rests on the base of a square pyramid of height $6$. The hemisphere is tangent to the other four faces of the pyramid. What is the edge-length of the base of the pyramid?",
"role": "user"
}
] | The circular base of a hemisphere of radius $2$ rests on the base of a square pyramid of height $6$. The hemisphere is tangent to the other four faces of the pyramid. What is the edge-length of the base of the pyramid? | "$3\\sqrt{2}$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:814"}] | {
"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
} |
[
"30^\\circ"
] | [
"deepscaler"
] | 2b23b0f8561ff4f2861058e514d08bd93fcfbe50a4a14a9f27f90c0c87be3ed8 | [
{
"content": "In $\\triangle ABC$, $\\angle A = 100^\\circ$, $\\angle B = 50^\\circ$, $\\angle C = 30^\\circ$, $\\overline{AH}$ is an altitude, and $\\overline{BM}$ is a median. Then $\\angle MHC=$",
"role": "user"
}
] | In $\triangle ABC$, $\angle A = 100^\circ$, $\angle B = 50^\circ$, $\angle C = 30^\circ$, $\overline{AH}$ is an altitude, and $\overline{BM}$ is a median. Then $\angle MHC=$ | "30^\\circ" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:815"}] | {
"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"
] | 3597122caace914e922dad417bcfe0fa904ae3df32473c4f144374ad9b69edfe | [
{
"content": "Set $u_0 = \\frac{1}{4}$, and for $k \\ge 0$ let $u_{k+1}$ be determined by the recurrence\n\\[u_{k+1} = 2u_k - 2u_k^2.\\]This sequence tends to a limit; call it $L$. What is the least value of $k$ such that\n\\[|u_k-L| \\le \\frac{1}{2^{1000}}?\\]",
"role": "user"
}
] | Set $u_0 = \frac{1}{4}$, and for $k \ge 0$ let $u_{k+1}$ be determined by the recurrence
\[u_{k+1} = 2u_k - 2u_k^2.\]This sequence tends to a limit; call it $L$. What is the least value of $k$ such that
\[|u_k-L| \le \frac{1}{2^{1000}}?\] | "10" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:816"}] | {
"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
} |
[
"18"
] | [
"deepscaler"
] | 5b914083e21f1f40987b65d3c3d558cd8c9fc68a36e8650e97f710947484153b | [
{
"content": "Let $a_1, a_2, \\dots, a_k$ be a finite arithmetic sequence with $a_4 + a_7 + a_{10} = 17$ and $a_4 + a_5 + \\dots + a_{13} + a_{14} = 77$. If $a_k = 13$, then $k = $",
"role": "user"
}
] | Let $a_1, a_2, \dots, a_k$ be a finite arithmetic sequence with $a_4 + a_7 + a_{10} = 17$ and $a_4 + a_5 + \dots + a_{13} + a_{14} = 77$. If $a_k = 13$, then $k = $ | "18" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:817"}] | {
"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
} |
[
"970"
] | [
"deepscaler"
] | 0c6c1bb6d36d7d118fc2ab6a443a6d7a88de96e678c3b57c171e6b11458acfd8 | [
{
"content": "What is the smallest integer larger than $(\\sqrt{3}+\\sqrt{2})^6$?",
"role": "user"
}
] | What is the smallest integer larger than $(\sqrt{3}+\sqrt{2})^6$? | "970" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:818"}] | {
"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
} |
[
"$(3+\\sqrt{10})\\pi$"
] | [
"deepscaler"
] | abc0a8f7c5ad96e89d825b62a606e23b991f36f2096724257dd38fa3a0d0918f | [
{
"content": "Rectangle $PQRS$ lies in a plane with $PQ=RS=2$ and $QR=SP=6$. The rectangle is rotated $90^\\circ$ clockwise about $R$, then rotated $90^\\circ$ clockwise about the point $S$ moved to after the first rotation. What is the length of the path traveled by point $P$?",
"role": "user"
}
] | Rectangle $PQRS$ lies in a plane with $PQ=RS=2$ and $QR=SP=6$. The rectangle is rotated $90^\circ$ clockwise about $R$, then rotated $90^\circ$ clockwise about the point $S$ moved to after the first rotation. What is the length of the path traveled by point $P$? | "$(3+\\sqrt{10})\\pi$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:819"}] | {
"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
} |
[
"\\text{4:10 P.M.}"
] | [
"deepscaler"
] | 2b84f76494edc9df803326fede2dc022b13f4c38205a0ba717473cac43062481 | [
{
"content": "Each day Maria must work $8$ hours. This does not include the $45$ minutes she takes for lunch. If she begins working at $\\text{7:25 A.M.}$ and takes her lunch break at noon, then her working day will end at",
"role": "user"
}
] | Each day Maria must work $8$ hours. This does not include the $45$ minutes she takes for lunch. If she begins working at $\text{7:25 A.M.}$ and takes her lunch break at noon, then her working day will end at | "\\text{4:10 P.M.}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:820"}] | {
"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"
] | a807857daeb0573f1c9d9ae6f1bc10ece62d4eff9cd4c0d67e5526b1aaa1bf8c | [
{
"content": "Bag A has three chips labeled 1, 3, and 5. Bag B has three chips labeled 2, 4, and 6. If one chip is drawn from each bag, how many different values are possible for the sum of the two numbers on the chips?",
"role": "user"
}
] | Bag A has three chips labeled 1, 3, and 5. Bag B has three chips labeled 2, 4, and 6. If one chip is drawn from each bag, how many different values are possible for the sum of the two numbers on the chips? | "5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:821"}] | {
"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"
] | db4146949cebc30f7df33899c8236614895c4233b6090977c8c037fdbe321b3c | [
{
"content": "When $x^9-x$ is factored as completely as possible into polynomials and monomials with integral coefficients, the number of factors is:",
"role": "user"
}
] | When $x^9-x$ is factored as completely as possible into polynomials and monomials with integral coefficients, the number of factors is: | "5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:822"}] | {
"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}{20}"
] | [
"deepscaler"
] | 48d09b4c333835597c08e3f4229184c302a19fc1062e692c6edb93a64a6ca0b4 | [
{
"content": "A number $m$ is randomly selected from the set $\\{11,13,15,17,19\\}$, and a number $n$ is randomly selected from $\\{1999,2000,2001,\\ldots,2018\\}$. What is the probability that $m^n$ has a units digit of $1$?",
"role": "user"
}
] | A number $m$ is randomly selected from the set $\{11,13,15,17,19\}$, and a number $n$ is randomly selected from $\{1999,2000,2001,\ldots,2018\}$. What is the probability that $m^n$ has a units digit of $1$? | "\\frac{7}{20}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:823"}] | {
"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{7}{18}"
] | [
"deepscaler"
] | 9815e6812e188e748f8fbf5c3ab285601b5a312a2ce5370ba26b7ee4d6c3bff9 | [
{
"content": "Suppose [$a$ $b$] denotes the average of $a$ and $b$, and {$a$ $b$ $c$} denotes the average of $a$, $b$, and $c$. What is {{1 1 0} {0 1} 0}?",
"role": "user"
}
] | Suppose [$a$ $b$] denotes the average of $a$ and $b$, and {$a$ $b$ $c$} denotes the average of $a$, $b$, and $c$. What is {{1 1 0} {0 1} 0}? | "\\frac{7}{18}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:824"}] | {
"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
} |
[
"14"
] | [
"deepscaler"
] | 5ec692f4d49b5ff674e797cefc45e5fa7becfe4b7d9f23590373021ab772de40 | [
{
"content": "For some particular value of $N$, when $(a+b+c+d+1)^N$ is expanded and like terms are combined, the resulting expression contains exactly $1001$ terms that include all four variables $a, b,c,$ and $d$, each to some positive power. What is $N$?",
"role": "user"
}
] | For some particular value of $N$, when $(a+b+c+d+1)^N$ is expanded and like terms are combined, the resulting expression contains exactly $1001$ terms that include all four variables $a, b,c,$ and $d$, each to some positive power. What is $N$? | "14" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:827"}] | {
"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"
] | 58f81fba133687fa938e120f51b5e3570be000eb5ac1e4fdb2aa843ed7ca853c | [
{
"content": "The data set $[6, 19, 33, 33, 39, 41, 41, 43, 51, 57]$ has median $Q_2 = 40$, first quartile $Q_1 = 33$, and third quartile $Q_3 = 43$. An outlier in a data set is a value that is more than $1.5$ times the interquartile range below the first quartle ($Q_1$) or more than $1.5$ times the interquarti... | The data set $[6, 19, 33, 33, 39, 41, 41, 43, 51, 57]$ has median $Q_2 = 40$, first quartile $Q_1 = 33$, and third quartile $Q_3 = 43$. An outlier in a data set is a value that is more than $1.5$ times the interquartile range below the first quartle ($Q_1$) or more than $1.5$ times the interquartile range above the thi... | "1" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:828"}] | {
"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"
] | c1e9e2e6bccf00209e0300b9d0226512dab21226f31dc9400cabf148bec32331 | [
{
"content": "For the positive integer $n$, let $\\langle n\\rangle$ denote the sum of all the positive divisors of $n$ with the exception of $n$ itself. For example, $\\langle 4\\rangle=1+2=3$ and $\\langle 12 \\rangle =1+2+3+4+6=16$. What is $\\langle\\langle\\langle 6\\rangle\\rangle\\rangle$?",
"role": ... | For the positive integer $n$, let $\langle n\rangle$ denote the sum of all the positive divisors of $n$ with the exception of $n$ itself. For example, $\langle 4\rangle=1+2=3$ and $\langle 12 \rangle =1+2+3+4+6=16$. What is $\langle\langle\langle 6\rangle\rangle\rangle$? | "6" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:829"}] | {
"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"
] | [
"deepscaler"
] | 03abbbeddeb4bcdeec25e5a75adce4a430fe5702ba4a9af7fe4f5c5f28cd6ddf | [
{
"content": "The limit of $\\frac {x^2-1}{x-1}$ as $x$ approaches $1$ as a limit is:",
"role": "user"
}
] | The limit of $\frac {x^2-1}{x-1}$ as $x$ approaches $1$ as a limit is: | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:830"}] | {
"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"
] | d8c0c69c5824b3a9377f538c251ba4c3e3ab719566d0bc85dc34ac5e454a9709 | [
{
"content": "How many different four-digit numbers can be formed by rearranging the four digits in $2004$?",
"role": "user"
}
] | How many different four-digit numbers can be formed by rearranging the four digits in $2004$? | "6" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:831"}] | {
"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{2}{3}"
] | [
"deepscaler"
] | edca8436015bb2d9cc41992bb0eb0d899fbd969542e1980f7d2d85aae1312e72 | [
{
"content": "Larry and Julius are playing a game, taking turns throwing a ball at a bottle sitting on a ledge. Larry throws first. The winner is the first person to knock the bottle off the ledge. At each turn the probability that a player knocks the bottle off the ledge is $\\tfrac{1}{2}$, independently of wh... | Larry and Julius are playing a game, taking turns throwing a ball at a bottle sitting on a ledge. Larry throws first. The winner is the first person to knock the bottle off the ledge. At each turn the probability that a player knocks the bottle off the ledge is $\tfrac{1}{2}$, independently of what has happened before.... | "\\frac{2}{3}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:832"}] | {
"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
} |
[
"13"
] | [
"deepscaler"
] | e4c0a50c5d1f41b33658c70173392ff995846720ea1f5a240949fcde1b384df9 | [
{
"content": "On the AMC 8 contest Billy answers 13 questions correctly, answers 7 questions incorrectly and doesn't answer the last 5. What is his score?",
"role": "user"
}
] | On the AMC 8 contest Billy answers 13 questions correctly, answers 7 questions incorrectly and doesn't answer the last 5. What is his score? | "13" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:833"}] | {
"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
} |
[
"12"
] | [
"deepscaler"
] | 79aa2ba4b49b82d8b52bf0accc83cbda770239b7ade14c72d3ebc14240ba6a28 | [
{
"content": "One of the sides of a triangle is divided into segments of $6$ and $8$ units by the point of tangency of the inscribed circle. If the radius of the circle is $4$, then the length of the shortest side is",
"role": "user"
}
] | One of the sides of a triangle is divided into segments of $6$ and $8$ units by the point of tangency of the inscribed circle. If the radius of the circle is $4$, then the length of the shortest side is | "12" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:834"}] | {
"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
} |
[
"2075"
] | [
"deepscaler"
] | 0881fe3caafe6f1ed388f8478e01b991ce3e9be3c5a52c5b541158730b925db3 | [
{
"content": "Estimate the year in which the population of Nisos will be approximately 6,000.",
"role": "user"
}
] | Estimate the year in which the population of Nisos will be approximately 6,000. | "2075" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:835"}] | {
"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"
] | [
"deepscaler"
] | 838ca9d0edf9a16f35f1f1ba12b5e8e84f7d85b7f87b1cc441e37468982409aa | [
{
"content": "Let n be the number of real values of $p$ for which the roots of \n$x^2-px+p=0$\nare equal. Then n equals:",
"role": "user"
}
] | Let n be the number of real values of $p$ for which the roots of
$x^2-px+p=0$
are equal. Then n equals: | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:836"}] | {
"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:\\pi"
] | [
"deepscaler"
] | c78bcd9b0d80fc43d5488b5b431db46692783b771ee872a65d70a987c415f5f3 | [
{
"content": "A decorative window is made up of a rectangle with semicircles at either end. The ratio of $AD$ to $AB$ is $3:2$. And $AB$ is 30 inches. What is the ratio of the area of the rectangle to the combined area of the semicircles?",
"role": "user"
}
] | A decorative window is made up of a rectangle with semicircles at either end. The ratio of $AD$ to $AB$ is $3:2$. And $AB$ is 30 inches. What is the ratio of the area of the rectangle to the combined area of the semicircles? | "6:\\pi" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:837"}] | {
"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{281}{13}"
] | [
"deepscaler"
] | 6df7450179dbbf9475a23f8e5d9e457eff188591fabf093ea4e910d8d80af55c | [
{
"content": "The line $12x+5y=60$ forms a triangle with the coordinate axes. What is the sum of the lengths of the altitudes of this triangle?",
"role": "user"
}
] | The line $12x+5y=60$ forms a triangle with the coordinate axes. What is the sum of the lengths of the altitudes of this triangle? | "\\frac{281}{13}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:838"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1253"}] | {
"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"
] | 940a3da7bd342e2cb63be6dcf009e65701d3fa3aebebf8cdcf7743cce9d4c980 | [
{
"content": "$5y$ varies inversely as the square of $x$. When $y=16$, $x=1$. When $x=8$, $y$ equals:",
"role": "user"
}
] | $5y$ varies inversely as the square of $x$. When $y=16$, $x=1$. When $x=8$, $y$ equals: | "\\frac{1}{4}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:840"}] | {
"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, 8, and 49"
] | [
"deepscaler"
] | 5e216c247725a31a9df9875a213f80c9ec54eadc0af21e5c5c24ddde0101c1c6 | [
{
"content": "If the sum $1 + 2 + 3 + \\cdots + K$ is a perfect square $N^2$ and if $N$ is less than $100$, then the possible values for $K$ are:",
"role": "user"
}
] | If the sum $1 + 2 + 3 + \cdots + K$ is a perfect square $N^2$ and if $N$ is less than $100$, then the possible values for $K$ are: | "1, 8, and 49" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:842"}] | {
"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
} |
[
"$f(1)=0$"
] | [
"deepscaler"
] | 40d7e9e4e8487ae532733c2ae1473683b42a3137ad3b442bf80cfa0ec62cd1d1 | [
{
"content": "If $y=f(x)=\\frac{x+2}{x-1}$, then it is incorrect to say:",
"role": "user"
}
] | If $y=f(x)=\frac{x+2}{x-1}$, then it is incorrect to say: | "$f(1)=0$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:843"}] | {
"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
} |
[
"25"
] | [
"deepscaler"
] | 244ee54aeb20b364056feea1639be673d8b8fca14902bf458d44c7a554dc0847 | [
{
"content": "Sides $AB$, $BC$, and $CD$ of (simple*) quadrilateral $ABCD$ have lengths $4$, $5$, and $20$, respectively. \nIf vertex angles $B$ and $C$ are obtuse and $\\sin C = - \\cos B = \\frac{3}{5}$, then side $AD$ has length\nA polygon is called “simple” if it is not self intersecting.",
"role": "use... | Sides $AB$, $BC$, and $CD$ of (simple*) quadrilateral $ABCD$ have lengths $4$, $5$, and $20$, respectively.
If vertex angles $B$ and $C$ are obtuse and $\sin C = - \cos B = \frac{3}{5}$, then side $AD$ has length
A polygon is called “simple” if it is not self intersecting. | "25" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:844"}] | {
"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 : 14"
] | [
"deepscaler"
] | 4a9b8532aaf9bce468ea0919e5c1935bef7f269dc8e62baefbf10dc64ed0cde0 | [
{
"content": "Let $N = 34 \\cdot 34 \\cdot 63 \\cdot 270$. What is the ratio of the sum of the odd divisors of $N$ to the sum of the even divisors of $N$?",
"role": "user"
}
] | Let $N = 34 \cdot 34 \cdot 63 \cdot 270$. What is the ratio of the sum of the odd divisors of $N$ to the sum of the even divisors of $N$? | "1 : 14" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:845"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1901"}] | {
"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"
] | 3df6024cd4bb5f0c5dab7d0508b4d350d0d65f7edb19b6733705a50b982604dd | [
{
"content": "In the expansion of $\\left(a - \\dfrac{1}{\\sqrt{a}}\\right)^7$ the coefficient of $a^{-\\frac{1}{2}}$ is:",
"role": "user"
}
] | In the expansion of $\left(a - \dfrac{1}{\sqrt{a}}\right)^7$ the coefficient of $a^{-\frac{1}{2}}$ is: | "-21" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:846"}] | {
"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}{5}"
] | [
"deepscaler"
] | 4eccb38ba31c9777aa412ff6892faae3238327c00904b9ec290d4405b916aa47 | [
{
"content": "If $x$ varies as the cube of $y$, and $y$ varies as the fifth root of $z$, then $x$ varies as the nth power of $z$, where n is:",
"role": "user"
}
] | If $x$ varies as the cube of $y$, and $y$ varies as the fifth root of $z$, then $x$ varies as the nth power of $z$, where n is: | "\\frac{3}{5}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:847"}] | {
"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
} |
[
"35"
] | [
"deepscaler"
] | ca057b6dbb5a4fb666ea1e514cadeceb013e7763307403c6e9cd148b85b9fb0c | [
{
"content": "If the value of $20$ quarters and $10$ dimes equals the value of $10$ quarters and $n$ dimes, then $n=$",
"role": "user"
}
] | If the value of $20$ quarters and $10$ dimes equals the value of $10$ quarters and $n$ dimes, then $n=$ | "35" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:849"}] | {
"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"
] | 2adc6f5f949da6f178bb06aa3b85333565b5e9580ba7db5080f213c33c7ebfec | [
{
"content": "How many different integers can be expressed as the sum of three distinct members of the set $\\{1,4,7,10,13,16,19\\}$?",
"role": "user"
}
] | How many different integers can be expressed as the sum of three distinct members of the set $\{1,4,7,10,13,16,19\}$? | "13" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:850"}] | {
"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
} |
[
"11"
] | [
"deepscaler"
] | 0463dd0b6cafb7b5c9856800d96d840ac8741d1756e2d724a2f6626f3d493b82 | [
{
"content": "Given the progression $10^{\\frac{1}{11}}, 10^{\\frac{2}{11}}, 10^{\\frac{3}{11}}, 10^{\\frac{4}{11}},\\dots , 10^{\\frac{n}{11}}$. The least positive integer $n$ such that the product of the first $n$ terms of the progression exceeds $100,000$ is",
"role": "user"
}
] | Given the progression $10^{\frac{1}{11}}, 10^{\frac{2}{11}}, 10^{\frac{3}{11}}, 10^{\frac{4}{11}},\dots , 10^{\frac{n}{11}}$. The least positive integer $n$ such that the product of the first $n$ terms of the progression exceeds $100,000$ is | "11" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:851"}] | {
"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
} |
[
"150"
] | [
"deepscaler"
] | 30025b8dd1448a132af48c46315a5721b15e80aea4ca53061f19acf64a474701 | [
{
"content": "Yesterday Han drove 1 hour longer than Ian at an average speed 5 miles per hour faster than Ian. Jan drove 2 hours longer than Ian at an average speed 10 miles per hour faster than Ian. Han drove 70 miles more than Ian. How many more miles did Jan drive than Ian?",
"role": "user"
}
] | Yesterday Han drove 1 hour longer than Ian at an average speed 5 miles per hour faster than Ian. Jan drove 2 hours longer than Ian at an average speed 10 miles per hour faster than Ian. Han drove 70 miles more than Ian. How many more miles did Jan drive than Ian? | "150" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:852"}] | {
"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"
] | [
"deepscaler"
] | 70c4ca62ad3fd9fea0b80a81a52ca1831d28fb18f5d97e70594e0d7e247e4661 | [
{
"content": "The number of real values of $x$ satisfying the equation $2^{2x^2 - 7x + 5} = 1$ is:",
"role": "user"
}
] | The number of real values of $x$ satisfying the equation $2^{2x^2 - 7x + 5} = 1$ is: | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:853"}] | {
"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
} |
[
"1341"
] | [
"deepscaler"
] | aa46e07a076479ab938b24c980e54336a5e620d5a21e1280fad6a296969135f1 | [
{
"content": "Let $\\{a_k\\}_{k=1}^{2011}$ be the sequence of real numbers defined by $a_1=0.201,$ $a_2=(0.2011)^{a_1},$ $a_3=(0.20101)^{a_2},$ $a_4=(0.201011)^{a_3}$, and in general,\n\\[a_k=\\begin{cases}(0.\\underbrace{20101\\cdots 0101}_{k+2\\text{ digits}})^{a_{k-1}}\\qquad\\text{if }k\\text{ is odd,}\\\\(... | Let $\{a_k\}_{k=1}^{2011}$ be the sequence of real numbers defined by $a_1=0.201,$ $a_2=(0.2011)^{a_1},$ $a_3=(0.20101)^{a_2},$ $a_4=(0.201011)^{a_3}$, and in general,
\[a_k=\begin{cases}(0.\underbrace{20101\cdots 0101}_{k+2\text{ digits}})^{a_{k-1}}\qquad\text{if }k\text{ is odd,}\\(0.\underbrace{20101\cdots 01011}_{k... | "1341" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:854"}] | {
"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
} |
[
"12"
] | [
"deepscaler"
] | c25a6a4c997d5b6fb136f983a287edc806c7a369a6288ed795ba11fd39fd5912 | [
{
"content": "Let $n$ be the largest integer that is the product of exactly 3 distinct prime numbers $d$, $e$, and $10d+e$, where $d$ and $e$ are single digits. What is the sum of the digits of $n$?",
"role": "user"
}
] | Let $n$ be the largest integer that is the product of exactly 3 distinct prime numbers $d$, $e$, and $10d+e$, where $d$ and $e$ are single digits. What is the sum of the digits of $n$? | "12" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:855"}] | {
"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"
] | [
"deepscaler"
] | 53dee4f9918557a2d980adaefa0820659fbaf1512af220341b3bd6966d90e399 | [
{
"content": "The number of triples $(a, b, c)$ of positive integers which satisfy the simultaneous equations\n$ab+bc=44$\n$ac+bc=23$\nis",
"role": "user"
}
] | The number of triples $(a, b, c)$ of positive integers which satisfy the simultaneous equations
$ab+bc=44$
$ac+bc=23$
is | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:856"}] | {
"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"
] | [
"deepscaler"
] | ea6d133794a4a1a536d617bcc8ad71933b8591f023f3df491d09d07186b3db85 | [
{
"content": "Each morning of her five-day workweek, Jane bought either a $50$-cent muffin or a $75$-cent bagel. Her total cost for the week was a whole number of dollars. How many bagels did she buy?",
"role": "user"
}
] | Each morning of her five-day workweek, Jane bought either a $50$-cent muffin or a $75$-cent bagel. Her total cost for the week was a whole number of dollars. How many bagels did she buy? | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:857"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2410"}] | {
"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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