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 |
|---|---|---|---|---|---|---|---|---|
[
"8"
] | [
"deepscaler"
] | a3f013e005e2f5f1bebe57c1260b3952b3ff819e7ed6966753cb5c60177ee9e3 | [
{
"content": "Elmer the emu takes $44$ equal strides to walk between consecutive telephone poles on a rural road. Oscar the ostrich can cover the same distance in $12$ equal leaps. The telephone poles are evenly spaced, and the $41$st pole along this road is exactly one mile ($5280$ feet) from the first pole. H... | Elmer the emu takes $44$ equal strides to walk between consecutive telephone poles on a rural road. Oscar the ostrich can cover the same distance in $12$ equal leaps. The telephone poles are evenly spaced, and the $41$st pole along this road is exactly one mile ($5280$ feet) from the first pole. How much longer, in fee... | "8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:528"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1833"}] | {
"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
} |
[
"32"
] | [
"deepscaler"
] | bd1d776d4ef12e6b00e1327661f80c14fb0d65c58e9dc67365109d03ad3b8ce8 | [
{
"content": "Last summer $100$ students attended basketball camp. Of those attending, $52$ were boys and $48$ were girls. Also, $40$ students were from Jonas Middle School and $60$ were from Clay Middle School. Twenty of the girls were from Jonas Middle School. How many of the boys were from Clay Middle Sc... | Last summer $100$ students attended basketball camp. Of those attending, $52$ were boys and $48$ were girls. Also, $40$ students were from Jonas Middle School and $60$ were from Clay Middle School. Twenty of the girls were from Jonas Middle School. How many of the boys were from Clay Middle School? | "32" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:529"}] | {
"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"
] | 693651712db15af8b5412ac7aa17a01e5231bb10263691c66f74d68e97639143 | [
{
"content": "Points $R$, $S$ and $T$ are vertices of an equilateral triangle, and points $X$, $Y$ and $Z$ are midpoints of its sides. How many noncongruent triangles can be drawn using any three of these six points as vertices?",
"role": "user"
}
] | Points $R$, $S$ and $T$ are vertices of an equilateral triangle, and points $X$, $Y$ and $Z$ are midpoints of its sides. How many noncongruent triangles can be drawn using any three of these six points as vertices? | "4" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:530"}] | {
"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
} |
[
"180001"
] | [
"deepscaler"
] | 1683d479e5af0913630934c3162aad33aec71455762355116f28d0e548717adb | [
{
"content": "Find the sum of digits of all the numbers in the sequence $1,2,3,4,\\cdots ,10000$.",
"role": "user"
}
] | Find the sum of digits of all the numbers in the sequence $1,2,3,4,\cdots ,10000$. | "180001" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:531"}] | {
"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{35}{72}"
] | [
"deepscaler"
] | 661529336c908e0f1597a758b0a95cc83f2a3410d80bb9fe3fa9aa4871af0c20 | [
{
"content": "On the dart board shown in the figure below, the outer circle has radius $6$ and the inner circle has radius $3$. Three radii divide each circle into three congruent regions, with point values shown. The probability that a dart will hit a given region is proportional to the area of the region. Whe... | On the dart board shown in the figure below, the outer circle has radius $6$ and the inner circle has radius $3$. Three radii divide each circle into three congruent regions, with point values shown. The probability that a dart will hit a given region is proportional to the area of the region. When two darts hit this b... | "\\frac{35}{72}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:532"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"22"
] | [
"deepscaler"
] | 14e05bea2a332f403e6330d391ec5498b4a52c183683deb64be59b0861b99cce | [
{
"content": "A big $L$ is formed as shown. What is its area?",
"role": "user"
}
] | A big $L$ is formed as shown. What is its area? | "22" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:533"}] | {
"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"
] | 3d368761728e930955ad6f7c258b9374a189dcb5f33d2428edd159352ac0c62b | [
{
"content": "Right triangle $ABC$ has leg lengths $AB=20$ and $BC=21$. Including $\\overline{AB}$ and $\\overline{BC}$, how many line segments with integer length can be drawn from vertex $B$ to a point on hypotenuse $\\overline{AC}$?",
"role": "user"
}
] | Right triangle $ABC$ has leg lengths $AB=20$ and $BC=21$. Including $\overline{AB}$ and $\overline{BC}$, how many line segments with integer length can be drawn from vertex $B$ to a point on hypotenuse $\overline{AC}$? | "12" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:534"}] | {
"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
} |
[
"603"
] | [
"deepscaler"
] | fbfd3738305faf60b2f36063bbd34b829476f900d78cc414c780fa62fcac84c1 | [
{
"content": "Jerry cuts a wedge from a 6-cm cylinder of bologna as shown by the dashed curve. Which answer choice is closest to the volume of his wedge in cubic centimeters?",
"role": "user"
}
] | Jerry cuts a wedge from a 6-cm cylinder of bologna as shown by the dashed curve. Which answer choice is closest to the volume of his wedge in cubic centimeters? | "603" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:535"}] | {
"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"
] | 0fd202c7a305796aed7fd1a43400bc0985d56e2ac520721de0d8084f82212d62 | [
{
"content": "An equilateral triangle and a regular hexagon have equal perimeters. If the triangle's area is 4, what is the area of the hexagon?",
"role": "user"
}
] | An equilateral triangle and a regular hexagon have equal perimeters. If the triangle's area is 4, what is the area of the hexagon? | "6" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:537"}] | {
"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
} |
[
"$\\frac{24}5$"
] | [
"deepscaler"
] | a9c39d33b17339b7ac64322ee1c8787c7383912cf8307f2209639174a9c1f6a1 | [
{
"content": "Tetrahedron $ABCD$ has $AB=5$, $AC=3$, $BC=4$, $BD=4$, $AD=3$, and $CD=\\frac{12}5\\sqrt2$. What is the volume of the tetrahedron?",
"role": "user"
}
] | Tetrahedron $ABCD$ has $AB=5$, $AC=3$, $BC=4$, $BD=4$, $AD=3$, and $CD=\frac{12}5\sqrt2$. What is the volume of the tetrahedron? | "$\\frac{24}5$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:538"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:636"}] | {
"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
} |
[
"100"
] | [
"deepscaler"
] | 41d2dbc1b2114f7f4b4ea7c8efb37729347c4c4a7c4daacd54e6e012009a4ceb | [
{
"content": "In racing over a distance $d$ at uniform speed, $A$ can beat $B$ by $20$ yards, $B$ can beat $C$ by $10$ yards, and $A$ can beat $C$ by $28$ yards. Then $d$, in yards, equals:",
"role": "user"
}
] | In racing over a distance $d$ at uniform speed, $A$ can beat $B$ by $20$ yards, $B$ can beat $C$ by $10$ yards, and $A$ can beat $C$ by $28$ yards. Then $d$, in yards, equals: | "100" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:539"}] | {
"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{31}{300}"
] | [
"deepscaler"
] | 692d44119c1cbfdf8b9f7db6e69b43d507bc76da9015d0834a32a1f9bb90a2a5 | [
{
"content": "Two distinct numbers $a$ and $b$ are chosen randomly from the set $\\{2, 2^2, 2^3, ..., 2^{25}\\}$. What is the probability that $\\log_a b$ is an integer?",
"role": "user"
}
] | Two distinct numbers $a$ and $b$ are chosen randomly from the set $\{2, 2^2, 2^3, ..., 2^{25}\}$. What is the probability that $\log_a b$ is an integer? | "\\frac{31}{300}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:540"}] | {
"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
} |
[
"68"
] | [
"deepscaler"
] | 36855ec050ef1b16f84d377ec2f077d4f8511d217b0e2d218b6b7b07a7c6a10c | [
{
"content": "Regular polygons with $5, 6, 7,$ and $8$ sides are inscribed in the same circle. No two of the polygons share a vertex, and no three of their sides intersect at a common point. At how many points inside the circle do two of their sides intersect?",
"role": "user"
}
] | Regular polygons with $5, 6, 7,$ and $8$ sides are inscribed in the same circle. No two of the polygons share a vertex, and no three of their sides intersect at a common point. At how many points inside the circle do two of their sides intersect? | "68" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:541"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2327"}] | {
"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
} |
[
"125"
] | [
"deepscaler"
] | 5ea8081f9dd50231f76ebd4972dd9123639e8dc732d50a3eeb5bc8f5ba7bfe22 | [
{
"content": "If $\\log_{k}{x} \\cdot \\log_{5}{k} = 3$, then $x$ equals:",
"role": "user"
}
] | If $\log_{k}{x} \cdot \log_{5}{k} = 3$, then $x$ equals: | "125" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:542"}] | {
"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
} |
[
"61"
] | [
"deepscaler"
] | 226bf86ef8993e07f62a46c1ea0ec3721cc49c1ef221fe9728d649f9215f33a4 | [
{
"content": "In $\\triangle ABC$, $AB = 86$, and $AC = 97$. A circle with center $A$ and radius $AB$ intersects $\\overline{BC}$ at points $B$ and $X$. Moreover $\\overline{BX}$ and $\\overline{CX}$ have integer lengths. What is $BC$?",
"role": "user"
}
] | In $\triangle ABC$, $AB = 86$, and $AC = 97$. A circle with center $A$ and radius $AB$ intersects $\overline{BC}$ at points $B$ and $X$. Moreover $\overline{BX}$ and $\overline{CX}$ have integer lengths. What is $BC$? | "61" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:543"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:826"}] | {
"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"
] | 665420aab98bc099876b76c4015ee5338911a2b4d8c8a506afa3672425266d4f | [
{
"content": "In Theresa's first $8$ basketball games, she scored $7, 4, 3, 6, 8, 3, 1$ and $5$ points. In her ninth game, she scored fewer than $10$ points and her points-per-game average for the nine games was an integer. Similarly in her tenth game, she scored fewer than $10$ points and her points-per-game a... | In Theresa's first $8$ basketball games, she scored $7, 4, 3, 6, 8, 3, 1$ and $5$ points. In her ninth game, she scored fewer than $10$ points and her points-per-game average for the nine games was an integer. Similarly in her tenth game, she scored fewer than $10$ points and her points-per-game average for the $10$ ga... | "40" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:544"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{1}{2}(n+2-ni)"
] | [
"deepscaler"
] | 9c4db1fee7204cb4533b87a06df65ccebd74c0831537794cdbcf0d081dd6e922 | [
{
"content": "If $n$ is a multiple of $4$, the sum $s=1+2i+3i^2+\\cdots+(n+1)i^n$, where $i=\\sqrt{-1}$, equals:",
"role": "user"
}
] | If $n$ is a multiple of $4$, the sum $s=1+2i+3i^2+\cdots+(n+1)i^n$, where $i=\sqrt{-1}$, equals: | "\\frac{1}{2}(n+2-ni)" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:545"}] | {
"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
} |
[
"16089"
] | [
"deepscaler"
] | 03aee682e576b9cda847e4b48ffdd98236a3086a4675d392e9ddd59d46bee83b | [
{
"content": "Let $f(x) = 10^{10x}$, $g(x) = \\log_{10}\\left(\\frac{x}{10}\\right)$, $h_1(x) = g(f(x))$, and $h_n(x) = h_1(h_{n-1}(x))$ for integers $n \\geq 2$. What is the sum of the digits of $h_{2011}(1)$?",
"role": "user"
}
] | Let $f(x) = 10^{10x}$, $g(x) = \log_{10}\left(\frac{x}{10}\right)$, $h_1(x) = g(f(x))$, and $h_n(x) = h_1(h_{n-1}(x))$ for integers $n \geq 2$. What is the sum of the digits of $h_{2011}(1)$? | "16089" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:546"}] | {
"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
} |
[
"20"
] | [
"deepscaler"
] | fbcc0a3df6ec58841d66f01b793c6da2e0c972385d451f582075a7fba3666563 | [
{
"content": "Set $A$ has $20$ elements, and set $B$ has $15$ elements. What is the smallest possible number of elements in $A \\cup B$?",
"role": "user"
}
] | Set $A$ has $20$ elements, and set $B$ has $15$ elements. What is the smallest possible number of elements in $A \cup B$? | "20" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:547"}] | {
"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
} |
[
"48"
] | [
"deepscaler"
] | 95deddf10f7863f2b31bd72d1000e553f3b9c0ce31e40034bb16d66f3a7ac605 | [
{
"content": "Paula the painter and her two helpers each paint at constant, but different, rates. They always start at 8:00 AM, and all three always take the same amount of time to eat lunch. On Monday the three of them painted 50% of a house, quitting at 4:00 PM. On Tuesday, when Paula wasn't there, the two he... | Paula the painter and her two helpers each paint at constant, but different, rates. They always start at 8:00 AM, and all three always take the same amount of time to eat lunch. On Monday the three of them painted 50% of a house, quitting at 4:00 PM. On Tuesday, when Paula wasn't there, the two helpers painted only 24%... | "48" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:548"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2485"}] | {
"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"
] | 0db1c185eb9bd3f2b0e2857b4f14ad5223d208e40804a96c0ac6c61353fa280d | [
{
"content": "Pauline Bunyan can shovel snow at the rate of $20$ cubic yards for the first hour, $19$ cubic yards for the second, $18$ for the third, etc., always shoveling one cubic yard less per hour than the previous hour. If her driveway is $4$ yards wide, $10$ yards long, and covered with snow $3$ yards d... | Pauline Bunyan can shovel snow at the rate of $20$ cubic yards for the first hour, $19$ cubic yards for the second, $18$ for the third, etc., always shoveling one cubic yard less per hour than the previous hour. If her driveway is $4$ yards wide, $10$ yards long, and covered with snow $3$ yards deep, then the number o... | "7" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:549"}] | {
"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"
] | 07c0e23041cffc16f2bbf8cfe4563e7f1d1691811d5dd736cbf3f860616b916a | [
{
"content": "Miki has a dozen oranges of the same size and a dozen pears of the same size. Miki uses her juicer to extract 8 ounces of pear juice from 3 pears and 8 ounces of orange juice from 2 oranges. She makes a pear-orange juice blend from an equal number of pears and oranges. What percent of the blend is... | Miki has a dozen oranges of the same size and a dozen pears of the same size. Miki uses her juicer to extract 8 ounces of pear juice from 3 pears and 8 ounces of orange juice from 2 oranges. She makes a pear-orange juice blend from an equal number of pears and oranges. What percent of the blend is pear juice? | "40" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:550"}] | {
"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"
] | 8458e6adb1628d8f077ac341e26b8e9815c596cbb285026eb57d7fcdd9b4444d | [
{
"content": "It takes $5$ seconds for a clock to strike $6$ o'clock beginning at $6:00$ o'clock precisely. If the strikings are uniformly spaced, how long, in seconds, does it take to strike $12$ o'clock?",
"role": "user"
}
] | It takes $5$ seconds for a clock to strike $6$ o'clock beginning at $6:00$ o'clock precisely. If the strikings are uniformly spaced, how long, in seconds, does it take to strike $12$ o'clock? | "11" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:551"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"3"
] | [
"deepscaler"
] | 6b6e42cb75b831c82e1215f9df6e088ee8034bb603b2a4daa3e049bdeb29aa05 | [
{
"content": "There are 3 numbers A, B, and C, such that $1001C - 2002A = 4004$, and $1001B + 3003A = 5005$. What is the average of A, B, and C?",
"role": "user"
}
] | There are 3 numbers A, B, and C, such that $1001C - 2002A = 4004$, and $1001B + 3003A = 5005$. What is the average of A, B, and C? | "3" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:552"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"7"
] | [
"deepscaler"
] | 8edb34bdf28328791d8358964a25a0c51a98f0965872ce5784ce6fc2b61f4fc9 | [
{
"content": "Each of the letters $W$, $X$, $Y$, and $Z$ represents a different integer in the set $\\{ 1,2,3,4\\}$, but not necessarily in that order. If $\\frac{W}{X} - \\frac{Y}{Z}=1$, then the sum of $W$ and $Y$ is",
"role": "user"
}
] | Each of the letters $W$, $X$, $Y$, and $Z$ represents a different integer in the set $\{ 1,2,3,4\}$, but not necessarily in that order. If $\frac{W}{X} - \frac{Y}{Z}=1$, then the sum of $W$ and $Y$ is | "7" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:553"}] | {
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} |
[
"5"
] | [
"deepscaler"
] | c39b1e2867d311a1c7b5d28211ecf73638c68e8d6e47b2de4cc9b4a059787999 | [
{
"content": "How many positive three-digit integers have a remainder of 2 when divided by 6, a remainder of 5 when divided by 9, and a remainder of 7 when divided by 11?",
"role": "user"
}
] | How many positive three-digit integers have a remainder of 2 when divided by 6, a remainder of 5 when divided by 9, and a remainder of 7 when divided by 11? | "5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:554"}] | {
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"plain_numeric_reference": true,
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} |
[
"5\\sqrt{2} - 7"
] | [
"deepscaler"
] | 34738f5696f91cf8a33b34daf65c79aa1f584cfcefc8e9cef08eac0876bf69d7 | [
{
"content": "A pyramid has a square base with side of length 1 and has lateral faces that are equilateral triangles. A cube is placed within the pyramid so that one face is on the base of the pyramid and its opposite face has all its edges on the lateral faces of the pyramid. What is the volume of this cube?",... | A pyramid has a square base with side of length 1 and has lateral faces that are equilateral triangles. A cube is placed within the pyramid so that one face is on the base of the pyramid and its opposite face has all its edges on the lateral faces of the pyramid. What is the volume of this cube? | "5\\sqrt{2} - 7" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:556"}] | {
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} |
[
"$782"
] | [
"deepscaler"
] | 6ce31a5bbd189bbb5d183bdc7044035ebd937ab3ec77a866ca0b7678f93fd44d | [
{
"content": "A charity sells $140$ benefit tickets for a total of $2001$ dollars. Some tickets sell for full price (a whole dollar amount), and the rest sells for half price. How much money is raised by the full-price tickets?",
"role": "user"
}
] | A charity sells $140$ benefit tickets for a total of $2001$ dollars. Some tickets sell for full price (a whole dollar amount), and the rest sells for half price. How much money is raised by the full-price tickets? | "$782" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:557"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"11"
] | [
"deepscaler"
] | f49daf5646a6e4fdfae0212a4062ba2c1be3a8fbf75723997ac1d9d10316c473 | [
{
"content": "A one-cubic-foot cube is cut into four pieces by three cuts parallel to the top face of the cube. The first cut is $\\frac{1}{2}$ foot from the top face. The second cut is $\\frac{1}{3}$ foot below the first cut, and the third cut is $\\frac{1}{17}$ foot below the second cut. From the top to the b... | A one-cubic-foot cube is cut into four pieces by three cuts parallel to the top face of the cube. The first cut is $\frac{1}{2}$ foot from the top face. The second cut is $\frac{1}{3}$ foot below the first cut, and the third cut is $\frac{1}{17}$ foot below the second cut. From the top to the bottom the pieces are labe... | "11" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:558"}] | {
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} |
[
"-\\sqrt{3} + i"
] | [
"deepscaler"
] | b0fcf64ef34c41d85ebde7b2dcc6dbc600338119e36c5f6ebd142ccd709df2c0 | [
{
"content": "Of the following complex numbers $z$, which one has the property that $z^5$ has the greatest real part?",
"role": "user"
}
] | Of the following complex numbers $z$, which one has the property that $z^5$ has the greatest real part? | "-\\sqrt{3} + i" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:559"}] | {
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} |
[
"11"
] | [
"deepscaler"
] | f5df3ce427c4b7e6f05db758c44a46aeaac61dc3162bd96940074c51da817c2e | [
{
"content": "A majority of the $30$ students in Ms. Demeanor's class bought pencils at the school bookstore. Each of these students bought the same number of pencils, and this number was greater than $1$. The cost of a pencil in cents was greater than the number of pencils each student bought, and the total co... | A majority of the $30$ students in Ms. Demeanor's class bought pencils at the school bookstore. Each of these students bought the same number of pencils, and this number was greater than $1$. The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils ... | "11" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:560"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:841"}] | {
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} |
[
"\\frac{55}{3}"
] | [
"deepscaler"
] | a3fe49d0a944c9c278481fde4475b90f8a5ed89ec7089d293c9d5db1521df796 | [
{
"content": "For any positive integer $n$, let \n$f(n) =\\begin{cases}\\log_{8}{n}, &\\text{if }\\log_{8}{n}\\text{ is rational,}\\\\ 0, &\\text{otherwise.}\\end{cases}$\nWhat is $\\sum_{n = 1}^{1997}{f(n)}$?",
"role": "user"
}
] | For any positive integer $n$, let
$f(n) =\begin{cases}\log_{8}{n}, &\text{if }\log_{8}{n}\text{ is rational,}\\ 0, &\text{otherwise.}\end{cases}$
What is $\sum_{n = 1}^{1997}{f(n)}$? | "\\frac{55}{3}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:561"}] | {
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} |
[
"(1997,0)"
] | [
"deepscaler"
] | 3fddd8a819b0aca178ff29f88bc07bce37ef8d8fd32d4edf8b59e766172333a2 | [
{
"content": "If $m$ and $b$ are real numbers and $mb>0$, then the line whose equation is $y=mx+b$ cannot contain the point",
"role": "user"
}
] | If $m$ and $b$ are real numbers and $mb>0$, then the line whose equation is $y=mx+b$ cannot contain the point | "(1997,0)" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:562"}] | {
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"plain_numeric_reference": false,
"reference_components": 1,
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} |
[
"9 \\%"
] | [
"deepscaler"
] | bc7a708d6a5a0e99a389abe04d20dfdfec70c8042f9634443d8c79d5c3ee186f | [
{
"content": "A housewife saved $2.50 in buying a dress on sale. If she spent $25 for the dress, she saved about:",
"role": "user"
}
] | A housewife saved $2.50 in buying a dress on sale. If she spent $25 for the dress, she saved about: | "9 \\%" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:563"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"876"
] | [
"deepscaler"
] | a4b02b21d59762386d29ef9df3e5a15d8ffae51ce4c658887ae9ce876ab844c8 | [
{
"content": "Isabella's house has $3$ bedrooms. Each bedroom is $12$ feet long, $10$ feet wide, and $8$ feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy $60$ square feet in each bedroom. How many square feet of walls must be painted?",
"r... | Isabella's house has $3$ bedrooms. Each bedroom is $12$ feet long, $10$ feet wide, and $8$ feet high. Isabella must paint the walls of all the bedrooms. Doorways and windows, which will not be painted, occupy $60$ square feet in each bedroom. How many square feet of walls must be painted? | "876" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:564"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:658"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"25\\%"
] | [
"deepscaler"
] | 7dc6239b17e36ce5d99dc1dc11c3702f5bea8848c82a05814b0af3582fb8ee66 | [
{
"content": "When one ounce of water is added to a mixture of acid and water, the new mixture is $20\\%$ acid. When one ounce of acid is added to the new mixture, the result is $33\\frac13\\%$ acid. The percentage of acid in the original mixture is",
"role": "user"
}
] | When one ounce of water is added to a mixture of acid and water, the new mixture is $20\%$ acid. When one ounce of acid is added to the new mixture, the result is $33\frac13\%$ acid. The percentage of acid in the original mixture is | "25\\%" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:565"}] | {
"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
} |
[
"\\pi + 2"
] | [
"deepscaler"
] | cef24921978aa29df2993462b41fc1151cc26343fa34645d0c0fb7051a7fd62c | [
{
"content": "What is the area of the region enclosed by the graph of the equation $x^2+y^2=|x|+|y|?$",
"role": "user"
}
] | What is the area of the region enclosed by the graph of the equation $x^2+y^2=|x|+|y|?$ | "\\pi + 2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:566"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1272"}] | {
"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
} |
[
"40"
] | [
"deepscaler"
] | e72922359e6c4ae1c529ccd701762b571a5b717da4e411765869b624661c41e6 | [
{
"content": "A mixture of $30$ liters of paint is $25\\%$ red tint, $30\\%$ yellow tint and $45\\%$ water. Five liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture?",
"role": "user"
}
] | A mixture of $30$ liters of paint is $25\%$ red tint, $30\%$ yellow tint and $45\%$ water. Five liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture? | "40" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:567"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"27"
] | [
"deepscaler"
] | a38fb9d5ef5a015c3fa9f3830e1a807fc5909eb3465b3b87f3d1080a2a88ecad | [
{
"content": "What is the area of the polygon whose vertices are the points of intersection of the curves $x^2 + y^2 = 25$ and $(x-4)^2 + 9y^2 = 81?$",
"role": "user"
}
] | What is the area of the polygon whose vertices are the points of intersection of the curves $x^2 + y^2 = 25$ and $(x-4)^2 + 9y^2 = 81?$ | "27" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:568"}] | {
"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"
] | 98e39604ce445781db55eba4707b106ea2847303045728c4a25b3c74b7d2d1d7 | [
{
"content": "Kate rode her bicycle for 30 minutes at a speed of 16 mph, then walked for 90 minutes at a speed of 4 mph. What was her overall average speed in miles per hour?",
"role": "user"
}
] | Kate rode her bicycle for 30 minutes at a speed of 16 mph, then walked for 90 minutes at a speed of 4 mph. What was her overall average speed in miles per hour? | "7" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:570"}] | {
"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, -1"
] | [
"deepscaler"
] | 4b7cb0b8db234c8351de1bb486104a443e7ed47c719a702a86674d1a39624b65 | [
{
"content": "The fraction $\\frac {5x - 11}{2x^2 + x - 6}$ was obtained by adding the two fractions $\\frac {A}{x + 2}$ and $\\frac {B}{2x - 3}$. The values of $A$ and $B$ must be, respectively:",
"role": "user"
}
] | The fraction $\frac {5x - 11}{2x^2 + x - 6}$ was obtained by adding the two fractions $\frac {A}{x + 2}$ and $\frac {B}{2x - 3}$. The values of $A$ and $B$ must be, respectively: | "3, -1" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:571"}] | {
"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
} |
[
"24"
] | [
"deepscaler"
] | d12cc7a13fefbc57f7ef24f0b1039217c0da10cd437e14d12d0421f07b663912 | [
{
"content": "A college student drove his compact car $120$ miles home for the weekend and averaged $30$ miles per gallon. On the return trip the student drove his parents' SUV and averaged only $20$ miles per gallon. What was the average gas mileage, in miles per gallon, for the round trip?",
"role": "user... | A college student drove his compact car $120$ miles home for the weekend and averaged $30$ miles per gallon. On the return trip the student drove his parents' SUV and averaged only $20$ miles per gallon. What was the average gas mileage, in miles per gallon, for the round trip? | "24" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:572"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1201"}] | {
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"$(3-2\\sqrt{2})p^2$"
] | [
"deepscaler"
] | 562fb9371129c499bd032ecae33d30a6d64285ae8311593d0e37738e0eb59063 | [
{
"content": "The perimeter of an isosceles right triangle is $2p$. Its area is:",
"role": "user"
}
] | The perimeter of an isosceles right triangle is $2p$. Its area is: | "$(3-2\\sqrt{2})p^2$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:573"}] | {
"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"
] | 24d69b0496a11c46ba883542a62c73cf04694cc06541180bc58ac7505d42db2f | [
{
"content": "At his usual rate a man rows 15 miles downstream in five hours less time than it takes him to return. If he doubles his usual rate, the time downstream is only one hour less than the time upstream. In miles per hour, the rate of the stream's current is:",
"role": "user"
}
] | At his usual rate a man rows 15 miles downstream in five hours less time than it takes him to return. If he doubles his usual rate, the time downstream is only one hour less than the time upstream. In miles per hour, the rate of the stream's current is: | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:574"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"16''"
] | [
"deepscaler"
] | b90ab9c078887cacd27a0541d85fe4e4633beec09e00e6b6aa005d2ac8f55b3f | [
{
"content": "If two poles $20''$ and $80''$ high are $100''$ apart, then the height of the intersection of the lines joining the top of each pole to the foot of the opposite pole is:",
"role": "user"
}
] | If two poles $20''$ and $80''$ high are $100''$ apart, then the height of the intersection of the lines joining the top of each pole to the foot of the opposite pole is: | "16''" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:575"}] | {
"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"
] | ce3170cbb3bae6ad13cdefb281b9f3365784be7a581a1c55179687e048935e91 | [
{
"content": "Let $x$ be the least real number greater than $1$ such that $\\sin(x) = \\sin(x^2)$, where the arguments are in degrees. What is $x$ rounded up to the closest integer?",
"role": "user"
}
] | Let $x$ be the least real number greater than $1$ such that $\sin(x) = \sin(x^2)$, where the arguments are in degrees. What is $x$ rounded up to the closest integer? | "13" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:576"}] | {
"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^{\\circ}"
] | [
"deepscaler"
] | 308c8a01f7427dd44d89f42b3b3cb06cc21f29c8cd8d0a203a040b0aa01b6de8 | [
{
"content": "Triangle $ABC$ has $AB=2 \\cdot AC$. Let $D$ and $E$ be on $\\overline{AB}$ and $\\overline{BC}$, respectively, such that $\\angle BAE = \\angle ACD$. Let $F$ be the intersection of segments $AE$ and $CD$, and suppose that $\\triangle CFE$ is equilateral. What is $\\angle ACB$?",
"role": "user... | Triangle $ABC$ has $AB=2 \cdot AC$. Let $D$ and $E$ be on $\overline{AB}$ and $\overline{BC}$, respectively, such that $\angle BAE = \angle ACD$. Let $F$ be the intersection of segments $AE$ and $CD$, and suppose that $\triangle CFE$ is equilateral. What is $\angle ACB$? | "90^{\\circ}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:577"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:953"}] | {
"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"
] | edfb502609fd13a9275673973e00c3f208779c8b5b1946d12d7891babcf7183a | [
{
"content": "How many positive integers less than $50$ have an odd number of positive integer divisors?",
"role": "user"
}
] | How many positive integers less than $50$ have an odd number of positive integer divisors? | "7" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:578"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
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} |
[
"11"
] | [
"deepscaler"
] | 28e9379716f6c6f9e7038ae5a4a1583c58b544c3664f0da12e34858f832be22f | [
{
"content": "Define binary operations $\\diamondsuit$ and $\\heartsuit$ by $a \\diamondsuit b = a^{\\log_{7}(b)}$ and $a \\heartsuit b = a^{\\frac{1}{\\log_{7}(b)}}$ for all real numbers $a$ and $b$ for which these expressions are defined. The sequence $(a_n)$ is defined recursively by $a_3 = 3 \\heartsuit 2$ ... | Define binary operations $\diamondsuit$ and $\heartsuit$ by $a \diamondsuit b = a^{\log_{7}(b)}$ and $a \heartsuit b = a^{\frac{1}{\log_{7}(b)}}$ for all real numbers $a$ and $b$ for which these expressions are defined. The sequence $(a_n)$ is defined recursively by $a_3 = 3 \heartsuit 2$ and $a_n = (n \heartsuit (n-1)... | "11" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:579"}] | {
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} |
[
"8"
] | [
"deepscaler"
] | ab6aa03bf04af08ead766604704210d9406f1d3c27a420be599f7446a271c16b | [
{
"content": "For every $3^\\circ$ rise in temperature, the volume of a certain gas expands by $4$ cubic centimeters. If the volume of the gas is $24$ cubic centimeters when the temperature is $32^\\circ$, what was the volume of the gas in cubic centimeters when the temperature was $20^\\circ$?",
"role": "... | For every $3^\circ$ rise in temperature, the volume of a certain gas expands by $4$ cubic centimeters. If the volume of the gas is $24$ cubic centimeters when the temperature is $32^\circ$, what was the volume of the gas in cubic centimeters when the temperature was $20^\circ$? | "8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:580"}] | {
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} |
[
"7 minutes and 5 seconds"
] | [
"deepscaler"
] | 584a921577de1cb49e32b2907c77c0c4ab1ca90de24bb2c58b3d4829f6224ef2 | [
{
"content": "Sofia ran $5$ laps around the $400$-meter track at her school. For each lap, she ran the first $100$ meters at an average speed of $4$ meters per second and the remaining $300$ meters at an average speed of $5$ meters per second. How much time did Sofia take running the $5$ laps?",
"role": "us... | Sofia ran $5$ laps around the $400$-meter track at her school. For each lap, she ran the first $100$ meters at an average speed of $4$ meters per second and the remaining $300$ meters at an average speed of $5$ meters per second. How much time did Sofia take running the $5$ laps? | "7 minutes and 5 seconds" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:581"}] | {
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} |
[
"5"
] | [
"deepscaler"
] | e373459dece230f36a7f38b0d997865e9574b30eedb24dba6a2c4e92af547e4d | [
{
"content": "Each half of this figure is composed of 3 red triangles, 5 blue triangles and 8 white triangles. When the upper half is folded down over the centerline, 2 pairs of red triangles coincide, as do 3 pairs of blue triangles. There are 2 red-white pairs. How many white pairs coincide?",
"role": "us... | Each half of this figure is composed of 3 red triangles, 5 blue triangles and 8 white triangles. When the upper half is folded down over the centerline, 2 pairs of red triangles coincide, as do 3 pairs of blue triangles. There are 2 red-white pairs. How many white pairs coincide? | "5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:582"}] | {
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} |
[
"8"
] | [
"deepscaler"
] | 259ab1dcdfd0590b510f8c5e2139ec4bebaef9d44113c93641d588ef83ab464b | [
{
"content": "What is the sum of the exponents of the prime factors of the square root of the largest perfect square that divides $12!$?",
"role": "user"
}
] | What is the sum of the exponents of the prime factors of the square root of the largest perfect square that divides $12!$? | "8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:583"}] | {
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} |
[
"13"
] | [
"deepscaler"
] | 38889d069e155e4f590d14a12de73cc7fd4739669d621df82f509d898a547ac8 | [
{
"content": "The players on a basketball team made some three-point shots, some two-point shots, and some one-point free throws. They scored as many points with two-point shots as with three-point shots. Their number of successful free throws was one more than their number of successful two-point shots. The te... | The players on a basketball team made some three-point shots, some two-point shots, and some one-point free throws. They scored as many points with two-point shots as with three-point shots. Their number of successful free throws was one more than their number of successful two-point shots. The team's total score was $... | "13" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:584"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1596"}] | {
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"reference_components": 1,
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} |
[
"48"
] | [
"deepscaler"
] | 62189fe5a4843f2c851c50788866ecef7db591cd1e68f6ad0134f2642a4b3038 | [
{
"content": "How many positive integers $n$ are there such that $n$ is a multiple of $5$, and the least common multiple of $5!$ and $n$ equals $5$ times the greatest common divisor of $10!$ and $n?$",
"role": "user"
}
] | How many positive integers $n$ are there such that $n$ is a multiple of $5$, and the least common multiple of $5!$ and $n$ equals $5$ times the greatest common divisor of $10!$ and $n?$ | "48" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:585"}] | {
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"reference_components": 1,
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} |
[
"2S + 12"
] | [
"deepscaler"
] | f343e35725ca2efe6c6b58544f64ee7d2225bfcb5097b4843804ce09d24d0366 | [
{
"content": "The sum of two numbers is $S$. Suppose $3$ is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two numbers?",
"role": "user"
}
] | The sum of two numbers is $S$. Suppose $3$ is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two numbers? | "2S + 12" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:586"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1038"}] | {
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} |
[
"-1"
] | [
"deepscaler"
] | a7b012e09306ee8fe05fb0e1a4c353b7fc5dbf5bd9365ae2fecc03a3b9c662cb | [
{
"content": "When simplified, $\\log{8} \\div \\log{\\frac{1}{8}}$ becomes:",
"role": "user"
}
] | When simplified, $\log{8} \div \log{\frac{1}{8}}$ becomes: | "-1" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:587"}] | {
"all_reference_components_parse": true,
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} |
[
"-\\frac{1}{2}"
] | [
"deepscaler"
] | e2c0b21ba15706f8a6a2d14db2da0ad315cccc4f99dc84c133f45a714813b999 | [
{
"content": "In the equation $\\frac {x(x - 1) - (m + 1)}{(x - 1)(m - 1)} = \\frac {x}{m}$ the roots are equal when",
"role": "user"
}
] | In the equation $\frac {x(x - 1) - (m + 1)}{(x - 1)(m - 1)} = \frac {x}{m}$ the roots are equal when | "-\\frac{1}{2}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:588"}] | {
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} |
[
"$3 \\pi \\sqrt{7}$"
] | [
"deepscaler"
] | 1c836ae31428a33d32867b960ce06d13f8942d50b454a94cdf1ed5aa2f849a1d | [
{
"content": "A three-quarter sector of a circle of radius $4$ inches together with its interior can be rolled up to form the lateral surface area of a right circular cone by taping together along the two radii shown. What is the volume of the cone in cubic inches?",
"role": "user"
}
] | A three-quarter sector of a circle of radius $4$ inches together with its interior can be rolled up to form the lateral surface area of a right circular cone by taping together along the two radii shown. What is the volume of the cone in cubic inches? | "$3 \\pi \\sqrt{7}$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:589"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2830"}] | {
"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
} |
[
"200"
] | [
"deepscaler"
] | 867176a7513a19551f817df386f03f0779d49aa5be7ab0f913657f0ff957d15f | [
{
"content": "A circle of radius 5 is inscribed in a rectangle as shown. The ratio of the length of the rectangle to its width is 2:1. What is the area of the rectangle?",
"role": "user"
}
] | A circle of radius 5 is inscribed in a rectangle as shown. The ratio of the length of the rectangle to its width is 2:1. What is the area of the rectangle? | "200" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:591"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1082"}] | {
"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
} |
[
"93"
] | [
"deepscaler"
] | 5e8a14a4d12dee1d938ba37a17bd6b2fed9a2223d0db8adcdbda09028df3ab08 | [
{
"content": "A teacher gave a test to a class in which $10\\%$ of the students are juniors and $90\\%$ are seniors. The average score on the test was $84.$ The juniors all received the same score, and the average score of the seniors was $83.$ What score did each of the juniors receive on the test?",
"role... | A teacher gave a test to a class in which $10\%$ of the students are juniors and $90\%$ are seniors. The average score on the test was $84.$ The juniors all received the same score, and the average score of the seniors was $83.$ What score did each of the juniors receive on the test? | "93" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:592"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2879"}] | {
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"31"
] | [
"deepscaler"
] | 62d5e14b47241ccd38ea3282310b51262b605f1a671b9cc2a2c8df2d612f7ffa | [
{
"content": "Let $x$ and $y$ be positive integers such that $7x^5 = 11y^{13}.$ The minimum possible value of $x$ has a prime factorization $a^cb^d.$ What is $a + b + c + d?$",
"role": "user"
}
] | Let $x$ and $y$ be positive integers such that $7x^5 = 11y^{13}.$ The minimum possible value of $x$ has a prime factorization $a^cb^d.$ What is $a + b + c + d?$ | "31" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:593"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"54"
] | [
"deepscaler"
] | a36f37b4d7170f837048f59bfbee5f22e897b5044a4b3a156a8c718a30a7b08a | [
{
"content": "Daphne is visited periodically by her three best friends: Alice, Beatrix, and Claire. Alice visits every third day, Beatrix visits every fourth day, and Claire visits every fifth day. All three friends visited Daphne yesterday. How many days of the next $365$-day period will exactly two friends... | Daphne is visited periodically by her three best friends: Alice, Beatrix, and Claire. Alice visits every third day, Beatrix visits every fourth day, and Claire visits every fifth day. All three friends visited Daphne yesterday. How many days of the next $365$-day period will exactly two friends visit her? | "54" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:594"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{2}{3}"
] | [
"deepscaler"
] | 9ad2fc479f6d0c044cf0b9859a1c17bf557c064ef2c0633db1cf1ac545c5d5d3 | [
{
"content": "Three machines $\\text{P, Q, and R,}$ working together, can do a job in $x$ hours. When working alone, $\\text{P}$ needs an additional $6$ hours to do the job; $\\text{Q}$, one additional hour; and $\\text{R}$, $x$ additional hours. The value of $x$ is:",
"role": "user"
}
] | Three machines $\text{P, Q, and R,}$ working together, can do a job in $x$ hours. When working alone, $\text{P}$ needs an additional $6$ hours to do the job; $\text{Q}$, one additional hour; and $\text{R}$, $x$ additional hours. The value of $x$ is: | "\\frac{2}{3}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:595"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"750"
] | [
"deepscaler"
] | 0d32612c08ea0060aea009947c3d3bdecfd173794df72e8c8dfd9d71d1c68249 | [
{
"content": "Heather compares the price of a new computer at two different stores. Store $A$ offers $15\\%$ off the sticker price followed by a $\\$90$ rebate, and store $B$ offers $25\\%$ off the same sticker price with no rebate. Heather saves $\\$15$ by buying the computer at store $A$ instead of store $B$.... | Heather compares the price of a new computer at two different stores. Store $A$ offers $15\%$ off the sticker price followed by a $\$90$ rebate, and store $B$ offers $25\%$ off the same sticker price with no rebate. Heather saves $\$15$ by buying the computer at store $A$ instead of store $B$. What is the sticker price... | "750" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:596"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:2836"}] | {
"all_reference_components_parse": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"15"
] | [
"deepscaler"
] | 5ebd3d09d21aee0ff784df490cfc9431cf744df1427580e38739085a6a261216 | [
{
"content": "Pat wants to buy four donuts from an ample supply of three types of donuts: glazed, chocolate, and powdered. How many different selections are possible?",
"role": "user"
}
] | Pat wants to buy four donuts from an ample supply of three types of donuts: glazed, chocolate, and powdered. How many different selections are possible? | "15" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:597"}] | {
"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"
] | 3584c6e125ec0d9861e00e23cb123f95722d9cd9ceea5015c075f6d83465b378 | [
{
"content": "Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of $\\triangle ABC$?",
"role": "user"
}
] | Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of $\triangle ABC$? | "\\frac{1}{5}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:598"}] | {
"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
} |
[
"90"
] | [
"deepscaler"
] | 9cfa393a605b49b0a5458703e8fa381e54a1b413532d78403fa2a5e9d8758f7f | [
{
"content": "Values for $A, B, C,$ and $D$ are to be selected from $\\{1, 2, 3, 4, 5, 6\\}$ without replacement (i.e. no two letters have the same value). How many ways are there to make such choices so that the two curves $y=Ax^2+B$ and $y=Cx^2+D$ intersect? (The order in which the curves are listed does not ... | Values for $A, B, C,$ and $D$ are to be selected from $\{1, 2, 3, 4, 5, 6\}$ without replacement (i.e. no two letters have the same value). How many ways are there to make such choices so that the two curves $y=Ax^2+B$ and $y=Cx^2+D$ intersect? (The order in which the curves are listed does not matter; for example, the... | "90" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:599"}] | {
"all_reference_components_parse": true,
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"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"37500"
] | [
"deepscaler"
] | f7decb8646dc1f9df3669cb88d3c2ce8e1e8ce3d00d16782b24fe45e724d3e9f | [
{
"content": "Last year Mr. Jon Q. Public received an inheritance. He paid $20\\%$ in federal taxes on the inheritance, and paid $10\\%$ of what he had left in state taxes. He paid a total of $\\textdollar10500$ for both taxes. How many dollars was his inheritance?",
"role": "user"
}
] | Last year Mr. Jon Q. Public received an inheritance. He paid $20\%$ in federal taxes on the inheritance, and paid $10\%$ of what he had left in state taxes. He paid a total of $\textdollar10500$ for both taxes. How many dollars was his inheritance? | "37500" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:600"}] | {
"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
} |
[
"22"
] | [
"deepscaler"
] | f86e965e4c91b9e83ee9c1ed07994fd025b02e503b2f7f0a1de8d3b785da047d | [
{
"content": "For how many positive integers $n \\le 1000$ is$\\left\\lfloor \\dfrac{998}{n} \\right\\rfloor+\\left\\lfloor \\dfrac{999}{n} \\right\\rfloor+\\left\\lfloor \\dfrac{1000}{n}\\right \\rfloor$not divisible by $3$?",
"role": "user"
}
] | For how many positive integers $n \le 1000$ is$\left\lfloor \dfrac{998}{n} \right\rfloor+\left\lfloor \dfrac{999}{n} \right\rfloor+\left\lfloor \dfrac{1000}{n}\right \rfloor$not divisible by $3$? | "22" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:601"}] | {
"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"
] | e747ffca8aa5a432f0796e136df52b2a1879cbb62ac24419eb331a51923b24b9 | [
{
"content": "For how many positive integers $x$ is $\\log_{10}(x-40) + \\log_{10}(60-x) < 2$?",
"role": "user"
}
] | For how many positive integers $x$ is $\log_{10}(x-40) + \log_{10}(60-x) < 2$? | "18" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:602"}] | {
"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 and 4"
] | [
"deepscaler"
] | 93d0af04d7ea52aa630ebe6adffd7599dd195532efc175b3d777f8de7931edbd | [
{
"content": "Let $F=\\frac{6x^2+16x+3m}{6}$ be the square of an expression which is linear in $x$. Then $m$ has a particular value between:",
"role": "user"
}
] | Let $F=\frac{6x^2+16x+3m}{6}$ be the square of an expression which is linear in $x$. Then $m$ has a particular value between: | "3 and 4" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:603"}] | {
"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{(b-a)^2}{8a}"
] | [
"deepscaler"
] | 3a1cd028e51163125c778b1762b54c1c4cc68fbff9332f9ff5dc18158e1517e6 | [
{
"content": "Given two positive numbers $a$, $b$ such that $a<b$. Let $A.M.$ be their arithmetic mean and let $G.M.$ be their positive geometric mean. Then $A.M.$ minus $G.M.$ is always less than:",
"role": "user"
}
] | Given two positive numbers $a$, $b$ such that $a<b$. Let $A.M.$ be their arithmetic mean and let $G.M.$ be their positive geometric mean. Then $A.M.$ minus $G.M.$ is always less than: | "\\frac{(b-a)^2}{8a}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:604"}] | {
"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
} |
[
"225"
] | [
"deepscaler"
] | 7ad765ef9968aa7b569e96556accb24823b2e10c806054adce760f73c1323a3e | [
{
"content": "A list of $2018$ positive integers has a unique mode, which occurs exactly $10$ times. What is the least number of distinct values that can occur in the list?",
"role": "user"
}
] | A list of $2018$ positive integers has a unique mode, which occurs exactly $10$ times. What is the least number of distinct values that can occur in the list? | "225" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:605"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1392"}] | {
"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"
] | 84ef98b91219376f47a2661ed611a5c109549b5c43cf29cf4a4c8a4b5c8cda3e | [
{
"content": "A nickel is placed on a table. The number of nickels which can be placed around it, each tangent to it and to two others is:",
"role": "user"
}
] | A nickel is placed on a table. The number of nickels which can be placed around it, each tangent to it and to two others is: | "6" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:606"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"28"
] | [
"deepscaler"
] | 856dcd2c7a336c69ad4951739979691d2786cf99809d06b458282cef3fc395bc | [
{
"content": "What is the largest difference that can be formed by subtracting two numbers chosen from the set $\\{ -16,-4,0,2,4,12 \\}$?",
"role": "user"
}
] | What is the largest difference that can be formed by subtracting two numbers chosen from the set $\{ -16,-4,0,2,4,12 \}$? | "28" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:607"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"12"
] | [
"deepscaler"
] | 4fdbf27e9dc344ebccb3c8040fdb9f265f8a6b04a72f59324465332a489a0841 | [
{
"content": "What is the largest quotient that can be formed using two numbers chosen from the set $\\{ -24, -3, -2, 1, 2, 8 \\}$?",
"role": "user"
}
] | What is the largest quotient that can be formed using two numbers chosen from the set $\{ -24, -3, -2, 1, 2, 8 \}$? | "12" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:608"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
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"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\frac{hd}{2h+d}"
] | [
"deepscaler"
] | 4a92493433cffef7d1f01c1b0c0812149c4683b1668a3ee5cb11f3f9598cdfcc | [
{
"content": "In the right triangle shown the sum of the distances $BM$ and $MA$ is equal to the sum of the distances $BC$ and $CA$. \nIf $MB = x, CB = h$, and $CA = d$, then $x$ equals:",
"role": "user"
}
] | In the right triangle shown the sum of the distances $BM$ and $MA$ is equal to the sum of the distances $BC$ and $CA$.
If $MB = x, CB = h$, and $CA = d$, then $x$ equals: | "\\frac{hd}{2h+d}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:609"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
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"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"$4(\\pi - \\sqrt{3})$"
] | [
"deepscaler"
] | 911a86de53bd84a4c3684b2e818b480cddb800c370a3744eb78daf907c141be6 | [
{
"content": "A circle of radius 2 is centered at $A$. An equilateral triangle with side 4 has a vertex at $A$. What is the difference between the area of the region that lies inside the circle but outside the triangle and the area of the region that lies inside the triangle but outside the circle?",
"role"... | A circle of radius 2 is centered at $A$. An equilateral triangle with side 4 has a vertex at $A$. What is the difference between the area of the region that lies inside the circle but outside the triangle and the area of the region that lies inside the triangle but outside the circle? | "$4(\\pi - \\sqrt{3})$" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:610"}] | {
"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
} |
[
"130"
] | [
"deepscaler"
] | 7f484510fdfefa34aef7450d35397f86edeeac3efdc97b9e3e590d82caae6e3f | [
{
"content": "The third exit on a highway is located at milepost 40 and the tenth exit is at milepost 160. There is a service center on the highway located three-fourths of the way from the third exit to the tenth exit. At what milepost would you expect to find this service center?",
"role": "user"
}
] | The third exit on a highway is located at milepost 40 and the tenth exit is at milepost 160. There is a service center on the highway located three-fourths of the way from the third exit to the tenth exit. At what milepost would you expect to find this service center? | "130" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:611"}] | {
"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
} |
[
"440"
] | [
"deepscaler"
] | 3f537b3b885ee19f1b146638fa2823cba14bb7a8a78a49ecfc0ee22b2cd3e7c6 | [
{
"content": "Real numbers $x$ and $y$ satisfy $x + y = 4$ and $x \\cdot y = -2$. What is the value of \n\\[x + \\frac{x^3}{y^2} + \\frac{y^3}{x^2} + y?\\]",
"role": "user"
}
] | Real numbers $x$ and $y$ satisfy $x + y = 4$ and $x \cdot y = -2$. What is the value of
\[x + \frac{x^3}{y^2} + \frac{y^3}{x^2} + y?\] | "440" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:612"}] | {
"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"
] | 87f76641231d1d20a1a638e6b8cfd76f21a7b21de735841debe35fc623e20a20 | [
{
"content": "If $3^p + 3^4 = 90$, $2^r + 44 = 76$, and $5^3 + 6^s = 1421$, what is the product of $p$, $r$, and $s$?",
"role": "user"
}
] | If $3^p + 3^4 = 90$, $2^r + 44 = 76$, and $5^3 + 6^s = 1421$, what is the product of $p$, $r$, and $s$? | "40" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:613"}] | {
"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
} |
[
"20"
] | [
"deepscaler"
] | eba93221249fed1ac48a819406126f6cdd1f9096212e9e6b2a1126f6c3de2067 | [
{
"content": "Samuel's birthday cake is in the form of a $4 \\times 4 \\times 4$ inch cube. The cake has icing on the top and the four side faces, and no icing on the bottom. Suppose the cake is cut into $64$ smaller cubes, each measuring $1 \\times 1 \\times 1$ inch, as shown below. How many of the small piece... | Samuel's birthday cake is in the form of a $4 \times 4 \times 4$ inch cube. The cake has icing on the top and the four side faces, and no icing on the bottom. Suppose the cake is cut into $64$ smaller cubes, each measuring $1 \times 1 \times 1$ inch, as shown below. How many of the small pieces will have icing on exact... | "20" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:615"}] | {
"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"
] | f52e99967b32f9b332fad2ed4cdb1e2037024dbe6abed568e6ba7f377c0377c4 | [
{
"content": "If for any three distinct numbers $a$, $b$, and $c$ we define $f(a,b,c)=\\frac{c+a}{c-b}$, then $f(1,-2,-3)$ is",
"role": "user"
}
] | If for any three distinct numbers $a$, $b$, and $c$ we define $f(a,b,c)=\frac{c+a}{c-b}$, then $f(1,-2,-3)$ is | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:616"}] | {
"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
} |
[
"20"
] | [
"deepscaler"
] | d93da31c097604b8b431bf5f724bb1e10f70444b1076b18445587584b95bf25c | [
{
"content": "When the mean, median, and mode of the list\n\\[10,2,5,2,4,2,x\\]\nare arranged in increasing order, they form a non-constant arithmetic progression. What is the sum of all possible real values of $x$?",
"role": "user"
}
] | When the mean, median, and mode of the list
\[10,2,5,2,4,2,x\]
are arranged in increasing order, they form a non-constant arithmetic progression. What is the sum of all possible real values of $x$? | "20" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:617"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:947"}] | {
"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"
] | b95ad90cc836d465a590add70bc15b9f660d847d7ec0b93024064512cc951401 | [
{
"content": "Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise.\nIn a turn of the game, Alice moves 5 points clockwise and Bob moves 9 ... | Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise.
In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points counterclockwise... | "6" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:618"}] | {
"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}{4}"
] | [
"deepscaler"
] | 092051352b47ab8570e139a701f7f675d77fbf7d74a78c39479f2e2c4520afaf | [
{
"content": "The bar graph shows the grades in a mathematics class for the last grading period. If A, B, C, and D are satisfactory grades, what fraction of the grades shown in the graph are satisfactory?",
"role": "user"
}
] | The bar graph shows the grades in a mathematics class for the last grading period. If A, B, C, and D are satisfactory grades, what fraction of the grades shown in the graph are satisfactory? | "\\frac{3}{4}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:619"}] | {
"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"
] | cd58d8267c0a9bd097b261fe055fc43f2d98cf979b8c99d424b211af2bb02972 | [
{
"content": "How many subsets of two elements can be removed from the set $\\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\\}$ so that the mean (average) of the remaining numbers is 6?",
"role": "user"
}
] | How many subsets of two elements can be removed from the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}$ so that the mean (average) of the remaining numbers is 6? | "5" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:620"}] | {
"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"
] | a2ddc55f58c828cdf15e7846a83e7c7f446b4f2ff6460ec9cae20da313b73c3f | [
{
"content": "If the side of one square is the diagonal of a second square, what is the ratio of the area of the first square to the area of the second?",
"role": "user"
}
] | If the side of one square is the diagonal of a second square, what is the ratio of the area of the first square to the area of the second? | "2" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:621"}] | {
"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
} |
[
"P"
] | [
"deepscaler"
] | a4e3ba3c4006976b0a028464f10f709c6d0a1d6ccbb392d06da574675c42291c | [
{
"content": "On this monthly calendar, the date behind one of the letters is added to the date behind $\\text{C}$. If this sum equals the sum of the dates behind $\\text{A}$ and $\\text{B}$, then the letter is",
"role": "user"
}
] | On this monthly calendar, the date behind one of the letters is added to the date behind $\text{C}$. If this sum equals the sum of the dates behind $\text{A}$ and $\text{B}$, then the letter is | "P" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:622"}] | {
"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"
] | a6a9297f38f0981b06c2a7284cee033f8ae413698054e4a336896d5ffec05b92 | [
{
"content": "The sum of seven integers is $-1$. What is the maximum number of the seven integers that can be larger than $13$?",
"role": "user"
}
] | The sum of seven integers is $-1$. What is the maximum number of the seven integers that can be larger than $13$? | "6" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:624"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"36"
] | [
"deepscaler"
] | 16919c9af7a584802744dda0fe63ffe0105a0afee67966eba9e4511d3e3e4fff | [
{
"content": "Part of an \\(n\\)-pointed regular star is shown. It is a simple closed polygon in which all \\(2n\\) edges are congruent, angles \\(A_1,A_2,\\cdots,A_n\\) are congruent, and angles \\(B_1,B_2,\\cdots,B_n\\) are congruent. If the acute angle at \\(A_1\\) is \\(10^\\circ\\) less than the acute angl... | Part of an \(n\)-pointed regular star is shown. It is a simple closed polygon in which all \(2n\) edges are congruent, angles \(A_1,A_2,\cdots,A_n\) are congruent, and angles \(B_1,B_2,\cdots,B_n\) are congruent. If the acute angle at \(A_1\) is \(10^\circ\) less than the acute angle at \(B_1\), then \(n=\) | "36" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:626"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"15"
] | [
"deepscaler"
] | 8b7394afd9f8c7720a0b0353fa81b6ed64cc26fce074da808d48af0eddcbbc1e | [
{
"content": "Connie multiplies a number by 2 and gets 60 as her answer. However, she should have divided the number by 2 to get the correct answer. What is the correct answer?",
"role": "user"
}
] | Connie multiplies a number by 2 and gets 60 as her answer. However, she should have divided the number by 2 to get the correct answer. What is the correct answer? | "15" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:628"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": true,
"reference_components": 1,
"reference_present": true
} |
[
"\\sqrt{3}"
] | [
"deepscaler"
] | 5e07fa83ff31e6235ff7b8e3e37ecec813d0afaab5367dc69e061a44a274050e | [
{
"content": "Four of the eight vertices of a cube are the vertices of a regular tetrahedron. Find the ratio of the surface area of the cube to the surface area of the tetrahedron.",
"role": "user"
}
] | Four of the eight vertices of a cube are the vertices of a regular tetrahedron. Find the ratio of the surface area of the cube to the surface area of the tetrahedron. | "\\sqrt{3}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:629"}] | {
"all_reference_components_parse": true,
"any_reference_component_parses": true,
"label_correctness_independently_verified": false,
"plain_numeric_reference": false,
"reference_components": 1,
"reference_present": true
} |
[
"18"
] | [
"deepscaler"
] | d664f487cb33e82b0964474a26c72fcc8326b54a14b0d3ace01d7b5646957554 | [
{
"content": "The two digits in Jack's age are the same as the digits in Bill's age, but in reverse order. In five years Jack will be twice as old as Bill will be then. What is the difference in their current ages?",
"role": "user"
}
] | The two digits in Jack's age are the same as the digits in Bill's age, but in reverse order. In five years Jack will be twice as old as Bill will be then. What is the difference in their current ages? | "18" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:630"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:993"}] | {
"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
} |
[
"3030"
] | [
"deepscaler"
] | 4aed7a2dc68c0daa1545b57e4e53c8a0b34328511969447d04716c6871a9ffa7 | [
{
"content": "Find the sum of the arithmetic series\n\\[20+20\\frac{1}{5}+20\\frac{2}{5}+\\cdots+40\\]",
"role": "user"
}
] | Find the sum of the arithmetic series
\[20+20\frac{1}{5}+20\frac{2}{5}+\cdots+40\] | "3030" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:632"}] | {
"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
} |
[
"175"
] | [
"deepscaler"
] | f0b751e2e01e1364dd493abc906c109a49d0e25ef2530ac42421e3e32fbc7f75 | [
{
"content": "Squares $ABCD$ and $EFGH$ are congruent, $AB=10$, and $G$ is the center of square $ABCD$. The area of the region in the plane covered by these squares is",
"role": "user"
}
] | Squares $ABCD$ and $EFGH$ are congruent, $AB=10$, and $G$ is the center of square $ABCD$. The area of the region in the plane covered by these squares is | "175" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:633"}] | {
"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{17}{8}"
] | [
"deepscaler"
] | 52d6e1050013ba297a021a6ee26010ad7970a9384b98fbb05950cf09b11499cb | [
{
"content": "An iterative average of the numbers 1, 2, 3, 4, and 5 is computed the following way. Arrange the five numbers in some order. Find the mean of the first two numbers, then find the mean of that with the third number, then the mean of that with the fourth number, and finally the mean of that with the... | An iterative average of the numbers 1, 2, 3, 4, and 5 is computed the following way. Arrange the five numbers in some order. Find the mean of the first two numbers, then find the mean of that with the third number, then the mean of that with the fourth number, and finally the mean of that with the fifth number. What is... | "\\frac{17}{8}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:634"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:839"}] | {
"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{15}{19}"
] | [
"deepscaler"
] | 583dd55cbf7e3793c97e788ceaabe59e889e92fb3571fc13abf45d6f242ad656 | [
{
"content": "Two counterfeit coins of equal weight are mixed with $8$ identical genuine coins. The weight of each of the counterfeit coins is different from the weight of each of the genuine coins. A pair of coins is selected at random without replacement from the $10$ coins. A second pair is selected at rando... | Two counterfeit coins of equal weight are mixed with $8$ identical genuine coins. The weight of each of the counterfeit coins is different from the weight of each of the genuine coins. A pair of coins is selected at random without replacement from the $10$ coins. A second pair is selected at random without replacement ... | "\\frac{15}{19}" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:635"}] | {
"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"
] | 08f6a5ed04911533daef435ba35c411552b6e73a17af9da5f55510269dee4c37 | [
{
"content": "Isaac has written down one integer two times and another integer three times. The sum of the five numbers is 100, and one of the numbers is 28. What is the other number?",
"role": "user"
}
] | Isaac has written down one integer two times and another integer three times. The sum of the five numbers is 100, and one of the numbers is 28. What is the other number? | "8" | deepscaler | [{"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:637"}, {"dataset": "deepscaler", "extra_info": null, "file": "deepscaler.json", "row_id": "deepscaler:deepscaler.json:1193"}] | {
"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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